From 1d647aa8b79b4034f6cfd5e6b8cb834caf20b4c5 Mon Sep 17 00:00:00 2001 From: Duane Nykamp Date: Wed, 29 Mar 2023 17:16:54 -0500 Subject: [PATCH 1/2] evaluate_to_constant returns NaN for non-numeric, by default --- build/math-expressions.js | 4 ++-- build/math-expressions_umd.js | 4 ++-- lib/assumptions/element_of_sets.js | 10 +++++----- lib/expression/evaluation.js | 17 ++++++++++------- lib/expression/simplify.js | 8 ++++---- lib/polynomial/polynomial.js | 12 ++++++------ package-lock.json | 4 ++-- package.json | 2 +- spec/slow_simplify.spec.js | 16 ++++++++-------- 9 files changed, 40 insertions(+), 37 deletions(-) diff --git a/build/math-expressions.js b/build/math-expressions.js index a2e20d4..194f93c 100644 --- a/build/math-expressions.js +++ b/build/math-expressions.js @@ -1,4 +1,4 @@ -const get_tree=function(e){if(null!=e)return void 0!==e.tree?e.tree:e};function*subsets(e,t){var r=e.length;if(void 0===t&&(t=r),0!==t){for(let 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e?format$3(e,t):isBigNumber(e)?format$2(e,t):looksLikeFraction(e)?t&&"decimal"===t.fraction?e.toString():e.s*e.n+"/"+e.d:Array.isArray(e)?formatArray(e,t):isString$1(e)?'"'+e+'"':"function"==typeof e?e.syntax?String(e.syntax):"function":e&&"object"==typeof e?"function"==typeof e.format?e.format(t):e&&e.toString(t)!=={}.toString()?e.toString(t):"{"+Object.keys(e).map((r=>'"'+r+'": '+format$1(e[r],t))).join(", ")+"}":String(e)}function stringify(e){for(var t=String(e),r="",n=0;n/g,">")}function formatArray(e,t){if(Array.isArray(e)){for(var r="[",n=e.length,i=0;it?1:-1}function DimensionError(e,t,r){if(!(this instanceof DimensionError))throw new SyntaxError("Constructor must be called with the new operator");this.actual=e,this.expected=t,this.relation=r,this.message="Dimension mismatch ("+(Array.isArray(e)?"["+e.join(", ")+"]":e)+" "+(this.relation||"!=")+" "+(Array.isArray(t)?"["+t.join(", ")+"]":t)+")",this.stack=(new Error).stack}function IndexError(e,t,r){if(!(this instanceof IndexError))throw new SyntaxError("Constructor must be called with the new operator");this.index=e,arguments.length<3?(this.min=0,this.max=t):(this.min=t,this.max=r),void 0!==this.min&&this.index=this.max?this.message="Index out of range ("+this.index+" > "+(this.max-1)+")":this.message="Index out of range ("+this.index+")",this.stack=(new Error).stack}function arraySize(e){for(var t=[];Array.isArray(e);)t.push(e.length),e=e[0];return t}function _validate(e,t,r){var n,i=e.length;if(i!==t[r])throw new DimensionError(i,t[r]);if(r")}function validate(e,t){if(0===t.length){if(Array.isArray(e))throw new DimensionError(e.length,0)}else _validate(e,t,0)}function validateIndex(e,t){if(!isNumber$1(e)||!isInteger$1(e))throw new TypeError("Index must be an integer (value: "+e+")");if(e<0||"number"==typeof t&&e>=t)throw new IndexError(e,t)}function resize$1(e,t,r){if(!Array.isArray(e)||!Array.isArray(t))throw new TypeError("Array expected");if(0===t.length)throw new Error("Resizing to scalar is not supported");return t.forEach((function(e){if(!isNumber$1(e)||!isInteger$1(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(t)+")")})),_resize(e,t,0,void 0!==r?r:0),e}function _resize(e,t,r,n){var i,a,o=e.length,s=t[r],u=Math.min(o,s);if(e.length=s,r=0){if(!(t%r==0))throw new Error("Could not replace wildcard, since "+t+" is no multiple of "+-r);n[i]=-t/r}return n}function product$1(e){return e.reduce(((e,t)=>e*t),1)}function _reshape(e,t){for(var r,n=e,i=t.length-1;i>0;i--){var a=t[i];r=[];for(var o=n.length/a,s=0;st.test(e)))}function join(e,t){return Array.prototype.join.call(e,t)}function identify(e){if(!Array.isArray(e))throw new TypeError("Array input expected");if(0===e.length)return e;var t=[],r=0;t[0]={value:e[0],identifier:0};for(var n=1;n!isOptionalDependency(e))).every((e=>void 0!==r[e]))){var n=t.filter((e=>void 0===r[e]));throw new Error('Cannot create function "'.concat(e,'", ')+"some dependencies are missing: ".concat(n.map((e=>'"'.concat(e,'"'))).join(", "),"."))}}function isOptionalDependency(e){return e&&"?"===e[0]}function stripOptionalNotation(e){return e&&"?"===e[0]?e.slice(1):e}function getSafeProperty(e,t){if(isPlainObject(e)&&isSafeProperty(e,t))return e[t];if("function"==typeof e[t]&&isSafeMethod(e,t))throw new Error('Cannot access method "'+t+'" as a property');throw new Error('No access to property "'+t+'"')}function setSafeProperty(e,t,r){if(isPlainObject(e)&&isSafeProperty(e,t))return e[t]=r,r;throw new Error('No access to property "'+t+'"')}function hasSafeProperty(e,t){return t in e}function isSafeProperty(e,t){return!(!e||"object"!=typeof e)&&(!!hasOwnProperty$2(safeNativeProperties,t)||!(t in Object.prototype)&&!(t in Function.prototype))}function validateSafeMethod(e,t){if(!isSafeMethod(e,t))throw new Error('No access to method "'+t+'"')}function isSafeMethod(e,t){return null!=e&&"function"==typeof e[t]&&(!(hasOwnProperty$2(e,t)&&Object.getPrototypeOf&&t in Object.getPrototypeOf(e))&&(!!hasOwnProperty$2(safeNativeMethods,t)||!(t in Object.prototype)&&!(t in Function.prototype)))}function isPlainObject(e){return"object"==typeof e&&e&&e.constructor===Object}DimensionError.prototype=new RangeError,DimensionError.prototype.constructor=RangeError,DimensionError.prototype.name="DimensionError",DimensionError.prototype.isDimensionError=!0,IndexError.prototype=new RangeError,IndexError.prototype.constructor=RangeError,IndexError.prototype.name="IndexError",IndexError.prototype.isIndexError=!0;var safeNativeProperties={length:!0,name:!0},safeNativeMethods={toString:!0,valueOf:!0,toLocaleString:!0};class ObjectWrappingMap{constructor(e){this.wrappedObject=e}keys(){return Object.keys(this.wrappedObject)}get(e){return getSafeProperty(this.wrappedObject,e)}set(e,t){return setSafeProperty(this.wrappedObject,e,t),this}has(e){return hasSafeProperty(this.wrappedObject,e)}}function createEmptyMap(){return new Map}function createMap$1(e){if(!e)return createEmptyMap();if(isMap$1(e))return e;if(isObject$1(e))return new ObjectWrappingMap(e);throw new Error("createMap can create maps from objects or Maps")}function toObject(e){if(e instanceof ObjectWrappingMap)return e.wrappedObject;var t={};for(var r of e.keys()){setSafeProperty(t,r,e.get(r))}return t}function isMap$1(e){return!!e&&(e instanceof Map||e instanceof ObjectWrappingMap||"function"==typeof e.set&&"function"==typeof e.get&&"function"==typeof e.keys&&"function"==typeof e.has)}function assign(e){for(var t=arguments.length,r=new Array(t>1?t-1:0),n=1;n15)throw new TypeError("Cannot implicitly convert a number with >15 significant digits to BigNumber (value: "+e+"). Use function bignumber(x) to convert to BigNumber.");return new t(e)}},{from:"number",to:"Complex",convert:function(e){return r||throwNoComplex(e),new r(e,0)}},{from:"number",to:"string",convert:function(e){return e+""}},{from:"BigNumber",to:"Complex",convert:function(e){return r||throwNoComplex(e),new r(e.toNumber(),0)}},{from:"Fraction",to:"BigNumber",convert:function(e){throw new TypeError("Cannot implicitly convert a Fraction to BigNumber or vice versa. Use function bignumber(x) to convert to BigNumber or fraction(x) to convert to Fraction.")}},{from:"Fraction",to:"Complex",convert:function(e){return r||throwNoComplex(e),new r(e.valueOf(),0)}},{from:"number",to:"Fraction",convert:function(e){i||throwNoFraction(e);var t=new i(e);if(t.valueOf()!==e)throw new TypeError("Cannot implicitly convert a number to a Fraction when there will be a loss of precision (value: "+e+"). Use function fraction(x) to convert to Fraction.");return t}},{from:"string",to:"number",convert:function(e){var t=Number(e);if(isNaN(t))throw new Error('Cannot convert "'+e+'" to a number');return t}},{from:"string",to:"BigNumber",convert:function(e){t||throwNoBignumber(e);try{return new t(e)}catch(t){throw new Error('Cannot convert "'+e+'" to BigNumber')}}},{from:"string",to:"Fraction",convert:function(e){i||throwNoFraction(e);try{return new i(e)}catch(t){throw new Error('Cannot convert "'+e+'" to Fraction')}}},{from:"string",to:"Complex",convert:function(e){r||throwNoComplex(e);try{return new r(e)}catch(t){throw new Error('Cannot convert "'+e+'" to Complex')}}},{from:"boolean",to:"number",convert:function(e){return+e}},{from:"boolean",to:"BigNumber",convert:function(e){return t||throwNoBignumber(e),new t(+e)}},{from:"boolean",to:"Fraction",convert:function(e){return i||throwNoFraction(e),new i(+e)}},{from:"boolean",to:"string",convert:function(e){return String(e)}},{from:"Array",to:"Matrix",convert:function(e){return n||throwNoMatrix(),new n(e)}},{from:"Matrix",to:"Array",convert:function(e){return e.valueOf()}}],a}));function throwNoBignumber(e){throw new Error("Cannot convert value ".concat(e," into a BigNumber: no class 'BigNumber' provided"))}function throwNoComplex(e){throw new Error("Cannot convert value ".concat(e," into a Complex number: no class 'Complex' provided"))}function throwNoMatrix(){throw new Error("Cannot convert array into a Matrix: no class 'DenseMatrix' provided")}function throwNoFraction(e){throw new Error("Cannot convert value ".concat(e," into a Fraction, no class 'Fraction' provided."))}var name$4C="ResultSet",dependencies$4C=[],createResultSet=factory(name$4C,dependencies$4C,(()=>{function e(t){if(!(this instanceof e))throw new SyntaxError("Constructor must be called with the new operator");this.entries=t||[]}return e.prototype.type="ResultSet",e.prototype.isResultSet=!0,e.prototype.valueOf=function(){return 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i,a,o,s;for(a=e[0];a>=10;a/=10)--t;return--t<0?(t+=LOG_BASE,i=0):(i=Math.ceil((t+1)/LOG_BASE),t%=LOG_BASE),a=mathpow(10,LOG_BASE-t),s=e[i]%a|0,null==n?t<3?(0==t?s=s/100|0:1==t&&(s=s/10|0),o=r<4&&99999==s||r>3&&49999==s||5e4==s||0==s):o=(r<4&&s+1==a||r>3&&s+1==a/2)&&(e[i+1]/a/100|0)==mathpow(10,t-2)-1||(s==a/2||0==s)&&0==(e[i+1]/a/100|0):t<4?(0==t?s=s/1e3|0:1==t?s=s/100|0:2==t&&(s=s/10|0),o=(n||r<4)&&9999==s||!n&&r>3&&4999==s):o=((n||r<4)&&s+1==a||!n&&r>3&&s+1==a/2)&&(e[i+1]/a/1e3|0)==mathpow(10,t-3)-1,o}function convertBase(e,t,r){for(var n,i,a=[0],o=0,s=e.length;or-1&&(void 0===a[n+1]&&(a[n+1]=0),a[n+1]+=a[n]/r|0,a[n]%=r)}return a.reverse()}function cosine(e,t){var r,n,i;if(t.isZero())return t;(n=t.d.length)<32?i=(1/tinyPow(4,r=Math.ceil(n/3))).toString():(r=16,i="2.3283064365386962890625e-10"),e.precision+=r,t=taylorSeries(e,1,t.times(i),new e(1));for(var a=r;a--;){var o=t.times(t);t=o.times(o).minus(o).times(8).plus(1)}return e.precision-=r,t}P$1.absoluteValue=P$1.abs=function(){var e=new this.constructor(this);return e.s<0&&(e.s=1),finalise(e)},P$1.ceil=function(){return finalise(new this.constructor(this),this.e+1,2)},P$1.clampedTo=P$1.clamp=function(e,t){var r=this,n=r.constructor;if(e=new n(e),t=new n(t),!e.s||!t.s)return new n(NaN);if(e.gt(t))throw Error(invalidArgument+t);return r.cmp(e)<0?e:r.cmp(t)>0?t:new n(r)},P$1.comparedTo=P$1.cmp=function(e){var t,r,n,i,a=this,o=a.d,s=(e=new a.constructor(e)).d,u=a.s,c=e.s;if(!o||!s)return u&&c?u!==c?u:o===s?0:!o^u<0?1:-1:NaN;if(!o[0]||!s[0])return o[0]?u:s[0]?-c:0;if(u!==c)return u;if(a.e!==e.e)return a.e>e.e^u<0?1:-1;for(t=0,r=(n=o.length)<(i=s.length)?n:i;ts[t]^u<0?1:-1;return n===i?0:n>i^u<0?1:-1},P$1.cosine=P$1.cos=function(){var e,t,r=this,n=r.constructor;return r.d?r.d[0]?(e=n.precision,t=n.rounding,n.precision=e+Math.max(r.e,r.sd())+LOG_BASE,n.rounding=1,r=cosine(n,toLessThanHalfPi(n,r)),n.precision=e,n.rounding=t,finalise(2==quadrant||3==quadrant?r.neg():r,e,t,!0)):new n(1):new 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r,n,i,a,o,s,u,c,l,f,p,m=1,d=e,h=d.d,y=d.constructor,g=y.rounding,v=y.precision;if(d.s<0||!h||!h[0]||!d.e&&1==h[0]&&1==h.length)return new y(h&&!h[0]?-1/0:1!=d.s?NaN:h?0:d);if(null==t?(external=!1,l=v):l=t,y.precision=l+=10,n=(r=digitsToString(h)).charAt(0),!(Math.abs(a=d.e)<15e14))return c=getLn10(y,l+2,v).times(a+""),d=naturalLogarithm(new y(n+"."+r.slice(1)),l-10).plus(c),y.precision=v,null==t?finalise(d,v,g,external=!0):d;for(;n<7&&1!=n||1==n&&r.charAt(1)>3;)n=(r=digitsToString((d=d.times(e)).d)).charAt(0),m++;for(a=d.e,n>1?(d=new y("0."+r),a++):d=new y(n+"."+r.slice(1)),f=d,u=o=d=divide$2(d.minus(1),d.plus(1),l,1),p=finalise(d.times(d),l,1),i=3;;){if(o=finalise(o.times(p),l,1),digitsToString((c=u.plus(divide$2(o,new y(i),l,1))).d).slice(0,l)===digitsToString(u.d).slice(0,l)){if(u=u.times(2),0!==a&&(u=u.plus(getLn10(y,l+2,v).times(a+""))),u=divide$2(u,new y(m),l,1),null!=t)return y.precision=v,u;if(!checkRoundingDigits(u.d,l-10,g,s))return 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e.s&&t.s?e.d||t.d?!t.d||e.isZero()?(r=t.s<0?getPi(this,n,i):new this(0)).s=e.s:!e.d||t.isZero()?(r=getPi(this,a,1).times(.5)).s=e.s:t.s<0?(this.precision=a,this.rounding=1,r=this.atan(divide$2(e,t,a,1)),t=getPi(this,a,1),this.precision=n,this.rounding=i,r=e.s<0?r.minus(t):r.plus(t)):r=this.atan(divide$2(e,t,a,1)):(r=getPi(this,a,1).times(t.s>0?.25:.75)).s=e.s:r=new this(NaN),r}function cbrt$1(e){return new this(e).cbrt()}function ceil$1(e){return finalise(e=new this(e),e.e+1,2)}function clamp(e,t,r){return new this(e).clamp(t,r)}function config$1(e){if(!e||"object"!=typeof e)throw Error(decimalError+"Object expected");var t,r,n,i=!0===e.defaults,a=["precision",1,MAX_DIGITS,"rounding",0,8,"toExpNeg",-EXP_LIMIT,0,"toExpPos",0,EXP_LIMIT,"maxE",0,EXP_LIMIT,"minE",-EXP_LIMIT,0,"modulo",0,9];for(t=0;t=a[t+1]&&n<=a[t+2]))throw Error(invalidArgument+r+": "+n);this[r]=n}if(r="crypto",i&&(this[r]=DEFAULTS[r]),void 0!==(n=e[r])){if(!0!==n&&!1!==n&&0!==n&&1!==n)throw Error(invalidArgument+r+": 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n.prototype=Object.create(n.prototype),n.prototype.type="BigNumber",n.prototype.isBigNumber=!0,n.prototype.toJSON=function(){return{mathjs:"BigNumber",value:this.toString()}},n.fromJSON=function(e){return new n(e.value)},t&&t("config",(function(e,t){e.precision!==t.precision&&n.config({precision:e.precision})})),n}),{isClass:!0}),complex$1={exports:{}},module; +const get_tree=function(e){if(null!=e)return void 0!==e.tree?e.tree:e};function*subsets(e,t){var r=e.length;if(void 0===t&&(t=r),0!==t){for(let t=0;t2?i=i.concat(n[a].slice(1)):i.push(n[a]);n=i}return[r].concat(n)}const unflattenRight=function(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if((n=n.map((function(e,t){return unflattenRight(e)}))).length>2&&is_associative$1[r]){for(var i=[r,n[0],void 0],a=i,o=1;o2&&is_associative$1[r]){for(var i=[r,void 0,n[n.length-1]],a=i,o=n.length-2;o>0;o--)a[1]=[r,void 0,n[o]],a=a[1];return a[1]=n[0],i}return[r].concat(n)},allChildren=function(e){if(!Array.isArray(e))return[];var t=e[0],r=e.slice(1);return is_associative$1[t]?r.reduce((function(e,r){return Array.isArray(r)&&r[0]===t?e.concat(allChildren(r)):e.concat([r])}),[]):r};function get_all_units(){return{"%":{scale:e=>["/",e,100],only_scales:!0},$:{prefix:!0,scale:e=>e},deg:{scale:e=>["/",["*",e,"pi"],180],only_scales:!0}}}let all_units$1=get_all_units();function get_unit_of_tree(e){if("unit"===e[0])for(let t in all_units$1)if(all_units$1[t].prefix){if(e[1]===t)return t}else if(e[2]===t)return t;return null}function get_unit_value_of_tree(e){if("unit"===e[0])for(let t in all_units$1)if(all_units$1[t].prefix){if(e[1]===t)return[t,e[2]]}else if(e[2]===t)return[t,e[1]];return null}function remove_duplicate_negatives(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);return"-"===t&&Array.isArray(r[0])&&"-"===r[0][0]?remove_duplicate_negatives(r[0][1]):(r=r.map(remove_duplicate_negatives),[t].concat(r))}function normalize_negatives_in_factors(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if(r=r.map(normalize_negatives_in_factors),"*"!==t&&"/"!==t)return[t].concat(r);for(var n=1,i=[],a=0;asort_key(e,t)))):s=[sort_key(a,t)],i.push([o,s]),i}if("unit"===r){let[r,n]=get_unit_value_of_tree(e);if(r){let e=sort_key(n,t);return e[1]+="_"+r,e}}var u=n.length,c=n.map(sort_key,t);return"*"===r?[4,"product",u,c]:"/"===r?[4,"quotient",u,c]:"+"===r?[5,"sum",u,c]:"-"===r?t.ignore_negatives?c[0]:[6,"minus",u,c]:[7,r,u,c]}function arrayCompare(e,t){if(Array.isArray(e)){if(Array.isArray(t)){let r=Math.min(e.length,t.length);for(let n=0;nt.length?1:0}return 1}return Array.isArray(t)||et?1:0}function compare_function(e,t,r={}){return arrayCompare(sort_key(e,r),sort_key(t,r))}function coeff_factors_from_term(e,t){if("string"==typeof e){let r=t.indexOf(e);-1===r&&(t.push(e),r=t.length-1);let n=[];return n[r]=1,{factor_contains:n,coeff:1}}if(Array.isArray(e)){let r=e[0],n=e.slice(1);if("*"===r){let 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e>0?this.step>0?this.start:this.start+(e-1)*this.step:void 0},e.prototype.max=function(){var e=this.size()[0];return e>0?this.step>0?this.start+(e-1)*this.step:this.start:void 0},e.prototype.forEach=function(e){var t=this.start,r=this.step,n=this.end,i=0;if(r>0)for(;tn;)e(t,[i],this),t+=r,i++},e.prototype.map=function(e){var t=[];return this.forEach((function(r,n,i){t[n[0]]=e(r,n,i)})),t},e.prototype.toArray=function(){var e=[];return this.forEach((function(t,r){e[r[0]]=t})),e},e.prototype.valueOf=function(){return this.toArray()},e.prototype.format=function(e){var t=format$3(this.start,e);return 1!==this.step&&(t+=":"+format$3(this.step,e)),t+=":"+format$3(this.end,e)},e.prototype.toString=function(){return this.format()},e.prototype.toJSON=function(){return{mathjs:"Range",start:this.start,end:this.end,step:this.step}},e.fromJSON=function(t){return new e(t.start,t.end,t.step)},e}),{isClass:!0}),name$4x="Matrix",dependencies$4x=[],createMatrixClass=factory(name$4x,dependencies$4x,(()=>{function e(){if(!(this instanceof e))throw new SyntaxError("Constructor must be called with the new operator")}return e.prototype.type="Matrix",e.prototype.isMatrix=!0,e.prototype.storage=function(){throw new Error("Cannot invoke storage on a Matrix interface")},e.prototype.datatype=function(){throw new Error("Cannot invoke datatype on a Matrix interface")},e.prototype.create=function(e,t){throw new Error("Cannot invoke create on a Matrix interface")},e.prototype.subset=function(e,t,r){throw new Error("Cannot invoke subset on a Matrix interface")},e.prototype.get=function(e){throw new Error("Cannot invoke get on a Matrix interface")},e.prototype.set=function(e,t,r){throw new Error("Cannot invoke set on a Matrix interface")},e.prototype.resize=function(e,t){throw new Error("Cannot invoke resize on a Matrix interface")},e.prototype.reshape=function(e,t){throw new Error("Cannot invoke reshape on a Matrix interface")},e.prototype.clone=function(){throw new Error("Cannot invoke clone on a Matrix interface")},e.prototype.size=function(){throw new Error("Cannot invoke size on a Matrix interface")},e.prototype.map=function(e,t){throw new Error("Cannot invoke map on a Matrix interface")},e.prototype.forEach=function(e){throw new Error("Cannot invoke forEach on a Matrix interface")},e.prototype[Symbol.iterator]=function(){throw new Error("Cannot iterate a Matrix interface")},e.prototype.toArray=function(){throw new Error("Cannot invoke toArray on a Matrix interface")},e.prototype.valueOf=function(){throw new Error("Cannot invoke valueOf on a Matrix interface")},e.prototype.format=function(e){throw new Error("Cannot invoke format on a Matrix interface")},e.prototype.toString=function(){throw new Error("Cannot invoke toString on a Matrix interface")},e}),{isClass:!0}),name$4w="DenseMatrix",dependencies$4w=["Matrix"],createDenseMatrixClass=factory(name$4w,dependencies$4w,(e=>{var{Matrix:t}=e;function r(e,t){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");if(t&&!isString$1(t))throw new Error("Invalid datatype: "+t);if(isMatrix(e))"DenseMatrix"===e.type?(this._data=clone$3(e._data),this._size=clone$3(e._size),this._datatype=t||e._datatype):(this._data=e.toArray(),this._size=e.size(),this._datatype=t||e._datatype);else if(e&&isArray$1(e.data)&&isArray$1(e.size))this._data=e.data,this._size=e.size,validate(this._data,this._size),this._datatype=t||e.datatype;else if(isArray$1(e))this._data=s(e),this._size=arraySize(this._data),validate(this._data,this._size),this._datatype=t;else{if(e)throw new TypeError("Unsupported type of data ("+typeOf$1(e)+")");this._data=[],this._size=[0],this._datatype=t}}function n(e,t,r,i){var a=i===r-1,o=t.dimension(i);return a?o.map((function(t){return validateIndex(t,e.length),e[t]})).valueOf():o.map((function(a){return validateIndex(a,e.length),n(e[a],t,r,i+1)})).valueOf()}function i(e,t,r,n,a){var o=a===n-1,s=t.dimension(a);o?s.forEach((function(t,n){validateIndex(t),e[t]=r[n[0]]})):s.forEach((function(o,s){validateIndex(o),i(e[o],t,r[s[0]],n,a+1)}))}function a(e,t,r){if(0===t.length){for(var n=e._data;isArray$1(n);)n=n[0];return n}return e._size=t.slice(0),e._data=resize$1(e._data,e._size,r),e}function o(e,t,r){for(var n=e._size.slice(0),i=!1;n.lengthn[o]&&(n[o]=t[o],i=!0);i&&a(e,n,r)}function s(e){for(var t=0,r=e.length;t");var f=t.max().map((function(e){return e+1}));o(e,f,n);var p=s.length,m=0;i(e._data,t,r,p,m)}return e}(this,e,t,a);default:throw new SyntaxError("Wrong number of arguments")}},r.prototype.get=function(e){if(!isArray$1(e))throw new TypeError("Array expected");if(e.length!==this._size.length)throw new DimensionError(e.length,this._size.length);for(var t=0;tArray.isArray(e)&&1===e.length?e[0]:e));return a(r?this.clone():this,n,t)},r.prototype.reshape=function(e,t){var r=t?this.clone():this;r._data=reshape$1(r._data,e);var n=r._size.reduce(((e,t)=>e*t));return r._size=processSizesWildcard(e,n),r},r.prototype.clone=function(){return new r({data:clone$3(this._data),size:clone$3(this._size),datatype:this._datatype})},r.prototype.size=function(){return this._size.slice(0)},r.prototype.map=function(e){var t=this,n=function r(n,i){return isArray$1(n)?n.map((function(e,t){return r(e,i.concat(t))})):e(n,i,t)}(this._data,[]);return new r(n,void 0!==this._datatype?getArrayDataType(n,typeOf$1):void 0)},r.prototype.forEach=function(e){var t=this;!function r(n,i){isArray$1(n)?n.forEach((function(e,t){r(e,i.concat(t))})):e(n,i,t)}(this._data,[])},r.prototype[Symbol.iterator]=function*(){yield*function*e(t,r){if(isArray$1(t))for(var n=0;n[e[n]]));t.push(new 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dArray.isArray(e)&&1===e.length?e[0]:e));if(2!==n.length)throw new Error("Only two dimensions matrix are supported");return n.forEach((function(e){if(!isNumber$1(e)||!isInteger$1(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(n)+")")})),u(r?this.clone():this,n[0],n[1],t)},i.prototype.reshape=function(e,t){if(!isArray$1(e))throw new TypeError("Array expected");if(2!==e.length)throw new Error("Sparse matrices can only be reshaped in two dimensions");e.forEach((function(t){if(!isNumber$1(t)||!isInteger$1(t)||t<=-2||0===t)throw new TypeError("Invalid size, must contain positive integers or -1 (size: "+format$1(e)+")")}));var r=this._size[0]*this._size[1];if(r!==(e=processSizesWildcard(e,r))[0]*e[1])throw new Error("Reshaping sparse matrix will result in the wrong number of elements");var n=t?this.clone():this;if(this._size[0]===e[0]&&this._size[1]===e[1])return n;for(var i=[],a=0;a=n&&b<=a&&h(e._values[x],b-n,y-o)}else{for(var _={},w=g;w 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0;i.splice(f,0,t),n&&n.splice(f,0,m),i.splice(f<=l?l+1:l,1),n&&n.splice(f<=l?l+1:l,1)}else if(f=c||i[l]!==e)){var d=n?n[f]:void 0;i.splice(l,0,e),n&&n.splice(l,0,d),i.splice(l<=f?f+1:f,1),n&&n.splice(l<=f?f+1:f,1)}}},i}),{isClass:!0}),name$4k="number",dependencies$4k=["typed"];function getNonDecimalNumberParts(e){var t=e.match(/(0[box])([0-9a-fA-F]*)\.([0-9a-fA-F]*)/);return t?{input:e,radix:{"0b":2,"0o":8,"0x":16}[t[1]],integerPart:t[2],fractionalPart:t[3]}:null}function makeNumberFromNonDecimalParts(e){for(var t=parseInt(e.integerPart,e.radix),r=0,n=0;n{var{typed:t}=e,r=t("number",{"":function(){return 0},number:function(e){return e},string:function(e){if("NaN"===e)return NaN;var t=getNonDecimalNumberParts(e);if(t)return makeNumberFromNonDecimalParts(t);var r=0,n=e.match(/(0[box][0-9a-fA-F]*)i([0-9]*)/);n&&(r=Number(n[2]),e=n[1]);var i=Number(e);if(isNaN(i))throw new SyntaxError('String "'+e+'" is no valid number');if(n){if(i>2**r-1)throw new SyntaxError('String "'.concat(e,'" is out 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new TypeError("Unknown matrix type "+JSON.stringify(t)+".")}})),name$4d="matrixFromFunction",dependencies$4d=["typed","matrix","isZero"],createMatrixFromFunction=factory(name$4d,dependencies$4d,(e=>{var{typed:t,matrix:r,isZero:n}=e;return t(name$4d,{"Array | Matrix, function, string, string":function(e,t,r,n){return i(e,t,r,n)},"Array | Matrix, function, string":function(e,t,r){return i(e,t,r)},"Matrix, function":function(e,t){return i(e,t,"dense")},"Array, function":function(e,t){return i(e,t,"dense").toArray()},"Array | Matrix, string, function":function(e,t,r){return i(e,r,t)},"Array | Matrix, string, string, function":function(e,t,r,n){return i(e,n,t,r)}});function i(e,t,i,a){var o;return(o=void 0!==a?r(i,a):r(i)).resize(e),o.forEach((function(e,r){var i=t(r);n(i)||o.set(r,i)})),o}})),name$4c="matrixFromRows",dependencies$4c=["typed","matrix","flatten","size"],createMatrixFromRows=factory(name$4c,dependencies$4c,(e=>{var{typed:t,matrix:r,flatten:n,size:i}=e;return 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n(+e):+e}})})),name$47="abs",dependencies$47=["typed"],createAbs=factory(name$47,dependencies$47,(e=>{var{typed:t}=e;return t(name$47,{number:absNumber,Complex:function(e){return e.abs()},BigNumber:function(e){return e.abs()},Fraction:function(e){return e.abs()},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.abs()}})})),name$46="apply",dependencies$46=["typed","isInteger"],createApply=factory(name$46,dependencies$46,(e=>{var{typed:t,isInteger:r}=e;return t(name$46,{"Array | Matrix, number | BigNumber, function":function(e,t,n){if(!r(t))throw new TypeError("Integer number expected for dimension");var i=Array.isArray(e)?arraySize(e):e.size();if(t<0||t>=i.length)throw new IndexError(t,i.length);return isMatrix(e)?e.create(_apply(e.valueOf(),t,n)):_apply(e,t,n)}})}));function _apply(e,t,r){var n,i,a;if(t<=0){if(Array.isArray(e[0])){for(a=_switch(e),i=[],n=0;n{var{typed:t}=e;return t(name$45,{"number, number":addNumber,"Complex, Complex":function(e,t){return e.add(t)},"BigNumber, BigNumber":function(e,t){return e.plus(t)},"Fraction, Fraction":function(e,t){return e.add(t)},"Unit, Unit":function(e,t){if(null===e.value||void 0===e.value)throw new Error("Parameter x contains a unit with undefined value");if(null===t.value||void 0===t.value)throw new Error("Parameter y contains a unit with undefined value");if(!e.equalBase(t))throw new Error("Units do not match");var r=e.clone();return r.value=this(r.value,t.value),r.fixPrefix=!1,r}})})),name$44="cbrt",dependencies$44=["config","typed","isNegative","unaryMinus","matrix","Complex","BigNumber","Fraction"],createCbrt=factory(name$44,dependencies$44,(e=>{var{config:t,typed:r,isNegative:n,unaryMinus:i,matrix:a,Complex:o,BigNumber:s,Fraction:u}=e;return r(name$44,{number:cbrtNumber,Complex:c,"Complex, boolean":c,BigNumber:function(e){return e.cbrt()},Unit:function(e){if(e.value&&isComplex(e.value)){var t=e.clone();return t.value=1,(t=t.pow(1/3)).value=c(e.value),t}var r,a=n(e.value);a&&(e.value=i(e.value)),r=isBigNumber(e.value)?new s(1).div(3):isFraction(e.value)?new u(1,3):1/3;var o=e.pow(r);return a&&(o.value=i(o.value)),o},"Array | Matrix":function(e){return deepMap(e,this)}});function c(e,r){var n=e.arg()/3,i=e.abs(),s=new o(cbrtNumber(i),0).mul(new o(0,n).exp());if(r){var u=[s,new o(cbrtNumber(i),0).mul(new o(0,n+2*Math.PI/3).exp()),new o(cbrtNumber(i),0).mul(new o(0,n-2*Math.PI/3).exp())];return"Array"===t.matrix?u:a(u)}return s}})),name$43="algorithm11",dependencies$43=["typed","equalScalar"],createAlgorithm11=factory(name$43,dependencies$43,(e=>{var{typed:t,equalScalar:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=r,h=0,y=i;"string"==typeof l&&(f=l,d=t.find(r,[f,f]),h=t.convert(0,f),n=t.convert(n,f),y=t.find(i,[f,f]));for(var g=[],v=[],x=[],b=0;b{var{typed:t,DenseMatrix:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=i;"string"==typeof l&&(f=l,n=t.convert(n,f),d=t.find(i,[f,f]));for(var h=[],y=[],g=[],v=0;v{var{typed:t}=e;return function(e,n,i,a){var o,s=e._data,u=e._size,c=e._datatype,l=i;"string"==typeof c&&(o=c,n=t.convert(n,o),l=t.find(i,[o,o]));var f=u.length>0?r(l,0,u,u[0],s,n,a):[];return e.createDenseMatrix({data:f,size:clone$3(u),datatype:o})};function r(e,t,n,i,a,o,s){var u=[];if(t===n.length-1)for(var c=0;c{var{typed:t,config:r,round:n}=e;return t(name$40,{number:function(e){return nearlyEqual$1(e,n(e),r.epsilon)?n(e):Math.ceil(e)},"number, number":function(e,t){if(nearlyEqual$1(e,n(e,t),r.epsilon))return n(e,t);var[i,a]="".concat(e,"e").split("e"),o=Math.ceil(Number("".concat(i,"e").concat(Number(a)+t)));return[i,a]="".concat(o,"e").split("e"),Number("".concat(i,"e").concat(Number(a)-t))}})})),createCeil=factory(name$40,dependencies$40,(e=>{var{typed:t,config:r,round:n,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}=e,u=createAlgorithm11({typed:t,equalScalar:a}),c=createAlgorithm12({typed:t,DenseMatrix:s}),l=createAlgorithm14({typed:t}),f=createCeilNumber({typed:t,config:r,round:n});return t("ceil",{number:f.signatures.number,"number,number":f.signatures["number,number"],Complex:function(e){return e.ceil()},"Complex, number":function(e,t){return e.ceil(t)},"Complex, BigNumber":function(e,t){return e.ceil(t.toNumber())},BigNumber:function(e){return nearlyEqual(e,n(e),r.epsilon)?n(e):e.ceil()},"BigNumber, BigNumber":function(e,t){return nearlyEqual(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),Decimal.ROUND_CEIL)},Fraction:function(e){return e.ceil()},"Fraction, number":function(e,t){return e.ceil(t)},"Fraction, BigNumber":function(e,t){return e.ceil(t.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},"Array, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(i(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return a(e,0)?o(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3$="cube",dependencies$3$=["typed"],createCube=factory(name$3$,dependencies$3$,(e=>{var{typed:t}=e;return t(name$3$,{number:cubeNumber,Complex:function(e){return e.mul(e).mul(e)},BigNumber:function(e){return e.times(e).times(e)},Fraction:function(e){return e.pow(3)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(3)}})})),name$3_="exp",dependencies$3_=["typed"],createExp=factory(name$3_,dependencies$3_,(e=>{var{typed:t}=e;return t(name$3_,{number:expNumber,Complex:function(e){return e.exp()},BigNumber:function(e){return e.exp()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3Z="expm1",dependencies$3Z=["typed","Complex"],createExpm1=factory(name$3Z,dependencies$3Z,(e=>{var{typed:t,Complex:r}=e;return t(name$3Z,{number:expm1Number,Complex:function(e){var t=Math.exp(e.re);return new r(t*Math.cos(e.im)-1,t*Math.sin(e.im))},BigNumber:function(e){return e.exp().minus(1)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3Y="fix",dependencies$3Y=["typed","Complex","matrix","ceil","floor","equalScalar","zeros","DenseMatrix"],createFixNumber=factory(name$3Y,["typed","ceil","floor"],(e=>{var{typed:t,ceil:r,floor:n}=e;return t(name$3Y,{number:function(e){return e>0?n(e):r(e)},"number, number":function(e,t){return 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Matrix":function(e){return deepMap(e,this)},"Array | Matrix, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(n(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return o(e,0)?s(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3X="floor",dependencies$3X=["typed","config","round","matrix","equalScalar","zeros","DenseMatrix"],createFloorNumber=factory(name$3X,["typed","config","round"],(e=>{var{typed:t,config:r,round:n}=e;return t(name$3X,{number:function(e){return nearlyEqual$1(e,n(e),r.epsilon)?n(e):Math.floor(e)},"number, number":function(e,t){if(nearlyEqual$1(e,n(e,t),r.epsilon))return n(e,t);var[i,a]="".concat(e,"e").split("e"),o=Math.floor(Number("".concat(i,"e").concat(Number(a)+t)));return[i,a]="".concat(o,"e").split("e"),Number("".concat(i,"e").concat(Number(a)-t))}})})),createFloor=factory(name$3X,dependencies$3X,(e=>{var{typed:t,config:r,round:n,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}=e,u=createAlgorithm11({typed:t,equalScalar:a}),c=createAlgorithm12({typed:t,DenseMatrix:s}),l=createAlgorithm14({typed:t}),f=createFloorNumber({typed:t,config:r,round:n});return t("floor",{number:f.signatures.number,"number,number":f.signatures["number,number"],Complex:function(e){return e.floor()},"Complex, number":function(e,t){return e.floor(t)},"Complex, BigNumber":function(e,t){return e.floor(t.toNumber())},BigNumber:function(e){return nearlyEqual(e,n(e),r.epsilon)?n(e):e.floor()},"BigNumber, BigNumber":function(e,t){return nearlyEqual(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),Decimal.ROUND_FLOOR)},Fraction:function(e){return e.floor()},"Fraction, number":function(e,t){return e.floor(t)},"Fraction, BigNumber":function(e,t){return e.floor(t.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},"Array, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(i(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return a(e,0)?o(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3W="algorithm01",dependencies$3W=["typed"],createAlgorithm01=factory(name$3W,dependencies$3W,(e=>{var{typed:t}=e;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,l=r._ptr,f=r._size,p=r._datatype;if(o.length!==f.length)throw new DimensionError(o.length,f.length);if(o[0]!==f[0]||o[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+f+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,d,h=o[0],y=o[1],g="string"==typeof s&&s===p?s:void 0,v=g?t.find(n,[g,g]):n,x=[];for(m=0;m{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A,M=a&&l?[]:void 0,S=[],E=[],T=a&&l?[]:void 0,O=a&&l?[]:void 0,C=[],k=[];for(w=0;w{var{typed:t,DenseMatrix:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=i;"string"==typeof l&&(f=l,n=t.convert(n,f),d=t.find(i,[f,f]));for(var h=[],y=[],g=[],v=0;v{var{typed:t}=e;return function(e,n,i){var a,o=e._data,s=e._size,u=e._datatype,c=n._data,l=n._size,f=n._datatype,p=[];if(s.length!==l.length)throw new DimensionError(s.length,l.length);for(var m=0;m0?r(d,0,p,p[0],o,c):[];return e.createDenseMatrix({data:h,size:p,datatype:a})};function r(e,t,n,i,a,o){var s=[];if(t===n.length-1)for(var u=0;u{var{typed:t,matrix:r,equalScalar:n,BigNumber:i,DenseMatrix:a}=e,o=createAlgorithm01({typed:t}),s=createAlgorithm04({typed:t,equalScalar:n}),u=createAlgorithm10({typed:t,DenseMatrix:a}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t});return t(name$3S,{"number, number":gcdNumber,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function gcd must be integer numbers");var r=new i(0);for(;!t.isZero();){var n=e.mod(t);e=t,t=n}return e.lt(r)?e.neg():e},"Fraction, Fraction":function(e,t){return e.gcd(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return u(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return l(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return l(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i{var{typed:t,equalScalar:r}=e;return function(e,n,i,a){var o=e._data,s=e._size,u=e._datatype,c=n._values,l=n._index,f=n._ptr,p=n._size,m=n._datatype;if(s.length!==p.length)throw new DimensionError(s.length,p.length);if(s[0]!==p[0]||s[1]!==p[1])throw new RangeError("Dimension mismatch. Matrix A ("+s+") must match Matrix B ("+p+")");if(!c)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var d,h=s[0],y=s[1],g=r,v=0,x=i;"string"==typeof u&&u===m&&(d=u,g=t.find(r,[d,d]),v=t.convert(0,d),x=t.find(i,[d,d]));for(var b=[],_=[],w=[],N=0;N{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._size,s=e._datatype,u=n._values,c=n._size,l=n._datatype;if(o.length!==c.length)throw new DimensionError(o.length,c.length);if(o[0]!==c[0]||o[1]!==c[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+c+")");var f,p=o[0],m=o[1],d=r,h=0,y=i;"string"==typeof s&&s===l&&(f=s,d=t.find(r,[f,f]),h=t.convert(0,f),y=t.find(i,[f,f]));for(var g=a&&u?[]:void 0,v=[],x=[],b=g?[]:void 0,_=[],w=[],N=0;N{var{typed:t,matrix:r,equalScalar:n}=e,i=createAlgorithm02({typed:t,equalScalar:n}),a=createAlgorithm06({typed:t,equalScalar:n}),o=createAlgorithm11({typed:t,equalScalar:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3P,{"number, number":lcmNumber,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function lcm must be integer numbers");if(e.isZero())return e;if(t.isZero())return t;var r=e.times(t);for(;!t.isZero();){var n=t;t=e.mod(n),e=n}return r.div(e).abs()},"Fraction, Fraction":function(e,t){return e.lcm(t)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return o(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return o(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return u(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return u(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i{var{typed:t,config:r,Complex:n}=e;return t(name$3O,{number:function(e){return e>=0||r.predictable?log10Number(e):new n(e,0).log().div(Math.LN10)},Complex:function(e){return new n(e).log().div(Math.LN10)},BigNumber:function(e){return!e.isNegative()||r.predictable?e.log():new n(e.toNumber(),0).log().div(Math.LN10)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3N="log2",dependencies$3N=["typed","config","Complex"],createLog2=factory(name$3N,dependencies$3N,(e=>{var{typed:t,config:r,Complex:n}=e;return t(name$3N,{number:function(e){return e>=0||r.predictable?log2Number(e):i(new n(e,0))},Complex:i,BigNumber:function(e){return!e.isNegative()||r.predictable?e.log(2):i(new n(e.toNumber(),0))},"Array | Matrix":function(e){return deepMap(e,this)}});function i(e){var t=Math.sqrt(e.re*e.re+e.im*e.im);return new n(Math.log2?Math.log2(t):Math.log(t)/Math.LN2,Math.atan2(e.im,e.re)/Math.LN2)}})),name$3M="algorithm03",dependencies$3M=["typed"],createAlgorithm03=factory(name$3M,dependencies$3M,(e=>{var{typed:t}=e;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,l=r._ptr,f=r._size,p=r._datatype;if(o.length!==f.length)throw new DimensionError(o.length,f.length);if(o[0]!==f[0]||o[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+f+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,d=o[0],h=o[1],y=0,g=n;"string"==typeof s&&s===p&&(m=s,y=t.convert(0,m),g=t.find(n,[m,m]));for(var v=[],x=0;x{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A=a&&l?[]:void 0,M=[],S=[],E=A?[]:void 0,T=A?[]:void 0,O=[],C=[];for(w=0;w{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm02({typed:t,equalScalar:n}),o=createAlgorithm03({typed:t}),s=createAlgorithm05({typed:t,equalScalar:n}),u=createAlgorithm11({typed:t,equalScalar:n}),c=createAlgorithm12({typed:t,DenseMatrix:i}),l=createAlgorithm13({typed:t}),f=createAlgorithm14({typed:t});return t(name$3K,{"number, number":modNumber,"BigNumber, BigNumber":function(e,t){if(t.isNeg())throw new Error("Cannot calculate mod for a negative divisor");return t.isZero()?e:e.mod(t)},"Fraction, Fraction":function(e,t){if(t.compare(0)<0)throw new Error("Cannot calculate mod for a negative divisor");return e.compare(0)>=0?e.mod(t):e.mod(t).add(t).mod(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return l(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return u(e,t,this,!1)},"DenseMatrix, any":function(e,t){return f(e,t,this,!1)},"any, SparseMatrix":function(e,t){return c(t,e,this,!0)},"any, DenseMatrix":function(e,t){return f(t,e,this,!0)},"Array, any":function(e,t){return f(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return f(r(t),e,this,!0).valueOf()}})})),name$3J="multiplyScalar",dependencies$3J=["typed"],createMultiplyScalar=factory(name$3J,dependencies$3J,(e=>{var{typed:t}=e;return t("multiplyScalar",{"number, number":multiplyNumber,"Complex, Complex":function(e,t){return e.mul(t)},"BigNumber, BigNumber":function(e,t){return e.times(t)},"Fraction, Fraction":function(e,t){return e.mul(t)},"number | Fraction | BigNumber | Complex, Unit":function(e,t){var r=t.clone();return r.value=null===r.value?r._normalize(e):this(r.value,e),r},"Unit, number | Fraction | BigNumber | Complex":function(e,t){var r=e.clone();return r.value=null===r.value?r._normalize(t):this(r.value,t),r},"Unit, Unit":function(e,t){return e.multiply(t)}})})),name$3I="multiply",dependencies$3I=["typed","matrix","addScalar","multiplyScalar","equalScalar","dot"],createMultiply=factory(name$3I,dependencies$3I,(e=>{var{typed:t,matrix:r,addScalar:n,multiplyScalar:i,equalScalar:a,dot:o}=e,s=createAlgorithm11({typed:t,equalScalar:a}),u=createAlgorithm14({typed:t});function c(e,t){switch(e.length){case 1:switch(t.length){case 1:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vectors must have the same length");break;case 2:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vector length ("+e[0]+") must match Matrix rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;case 2:switch(t.length){case 1:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix columns ("+e[1]+") must match Vector length ("+t[0]+")");break;case 2:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix A columns ("+e[1]+") must match Matrix B rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix A has "+e.length+" dimensions)")}}function l(e,r){if("dense"!==r.storage())throw new Error("Support for SparseMatrix not implemented");return function(e,r){var a,o=e._data,s=e._size,u=e._datatype,c=r._data,l=r._size,f=r._datatype,p=s[0],m=l[1],d=n,h=i;u&&f&&u===f&&"string"==typeof u&&(a=u,d=t.find(n,[a,a]),h=t.find(i,[a,a]));for(var y=[],g=0;gM)for(var E=0,T=0;T{var{typed:t,matrix:r,equalScalar:n,BigNumber:i}=e,a=createAlgorithm01({typed:t}),o=createAlgorithm02({typed:t,equalScalar:n}),s=createAlgorithm06({typed:t,equalScalar:n}),u=createAlgorithm11({typed:t,equalScalar:n}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t}),f="Complex number not supported in function nthRoot. Use nthRoots instead.";return t(name$3H,{number:nthRootNumber,"number, number":nthRootNumber,BigNumber:function(e){return p(e,new i(2))},Complex:function(e){throw new Error(f)},"Complex, number":function(e,t){throw new Error(f)},"BigNumber, BigNumber":p,"Array | Matrix":function(e){return this(e,2)},"SparseMatrix, SparseMatrix":function(e,t){if(1===t.density())return s(e,t,this);throw new Error("Root must be non-zero")},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){if(1===t.density())return a(e,t,this,!1);throw new Error("Root must be non-zero")},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){if(1===t.density())return u(t,e,this,!0);throw new Error("Root must be non-zero")},"number | BigNumber, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return this(r(e),t).valueOf()},"number | BigNumber, Array":function(e,t){return this(e,r(t)).valueOf()}});function p(e,t){var r=i.precision,n=i.clone({precision:r+2}),a=new i(0),o=new n(1),s=t.isNegative();if(s&&(t=t.neg()),t.isZero())throw new Error("Root must be non-zero");if(e.isNegative()&&!t.abs().mod(2).equals(1))throw new Error("Root must be odd when a is negative.");if(e.isZero())return s?new n(1/0):0;if(!e.isFinite())return s?a:e;var u=e.abs().pow(o.div(t));return u=e.isNeg()?u.neg():u,new i((s?o.div(u):u).toPrecision(r))}})),name$3G="sign",dependencies$3G=["typed","BigNumber","Fraction","complex"],createSign=factory(name$3G,dependencies$3G,(e=>{var{typed:t,BigNumber:r,complex:n,Fraction:i}=e;return t(name$3G,{number:signNumber,Complex:function(e){return 0===e.im?n(signNumber(e.re)):e.sign()},BigNumber:function(e){return new r(e.cmp(0))},Fraction:function(e){return new i(e.s,1)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){if(!e._isDerived()&&0!==e.units[0].unit.offset)throw new TypeError("sign is ambiguous for units with offset");return this(e.value)}})})),name$3F="sqrt",dependencies$3F=["config","typed","Complex"],createSqrt=factory(name$3F,dependencies$3F,(e=>{var{config:t,typed:r,Complex:n}=e;return r("sqrt",{number:i,Complex:function(e){return e.sqrt()},BigNumber:function(e){return!e.isNegative()||t.predictable?e.sqrt():i(e.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(.5)}});function i(e){return isNaN(e)?NaN:e>=0||t.predictable?Math.sqrt(e):new n(e,0).sqrt()}})),name$3E="square",dependencies$3E=["typed"],createSquare=factory(name$3E,dependencies$3E,(e=>{var{typed:t}=e;return t(name$3E,{number:squareNumber,Complex:function(e){return e.mul(e)},BigNumber:function(e){return e.times(e)},Fraction:function(e){return e.mul(e)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(2)}})})),name$3D="subtract",dependencies$3D=["typed","matrix","equalScalar","addScalar","unaryMinus","DenseMatrix"],createSubtract=factory(name$3D,dependencies$3D,(e=>{var{typed:t,matrix:r,equalScalar:n,addScalar:i,unaryMinus:a,DenseMatrix:o}=e,s=createAlgorithm01({typed:t}),u=createAlgorithm03({typed:t}),c=createAlgorithm05({typed:t,equalScalar:n}),l=createAlgorithm10({typed:t,DenseMatrix:o}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$3D,{"number, number":function(e,t){return e-t},"Complex, Complex":function(e,t){return e.sub(t)},"BigNumber, BigNumber":function(e,t){return e.minus(t)},"Fraction, Fraction":function(e,t){return e.sub(t)},"Unit, Unit":function(e,t){if(null===e.value)throw new Error("Parameter x contains a unit with undefined value");if(null===t.value)throw new Error("Parameter y contains a unit with undefined value");if(!e.equalBase(t))throw new Error("Units do not match");var r=e.clone();return r.value=this(r.value,t.value),r.fixPrefix=!1,r},"SparseMatrix, SparseMatrix":function(e,t){return checkEqualDimensions(e,t),c(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return checkEqualDimensions(e,t),u(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return checkEqualDimensions(e,t),s(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return checkEqualDimensions(e,t),f(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return l(e,a(t),i)},"DenseMatrix, any":function(e,t){return p(e,t,this)},"any, SparseMatrix":function(e,t){return l(t,e,this,!0)},"any, DenseMatrix":function(e,t){return p(t,e,this,!0)},"Array, any":function(e,t){return p(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return p(r(t),e,this,!0).valueOf()}})}));function checkEqualDimensions(e,t){var r=e.size(),n=t.size();if(r.length!==n.length)throw new DimensionError(r.length,n.length)}var name$3C="xgcd",dependencies$3C=["typed","config","matrix","BigNumber"],createXgcd=factory(name$3C,dependencies$3C,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t(name$3C,{"number, number":function(e,t){var i=xgcdNumber(e,t);return"Array"===r.matrix?i:n(i)},"BigNumber, BigNumber":function(e,t){var a,o,s,u,c=new i(0),l=new i(1),f=c,p=l,m=l,d=c;if(!e.isInt()||!t.isInt())throw new Error("Parameters in function xgcd must be integer numbers");for(;!t.isZero();)o=e.div(t).floor(),s=e.mod(t),a=f,f=p.minus(o.times(f)),p=a,a=m,m=d.minus(o.times(m)),d=a,e=t,t=s;u=e.lt(c)?[e.neg(),p.neg(),d.neg()]:[e,e.isZero()?0:p,d];return"Array"===r.matrix?u:n(u)}})})),name$3B="invmod",dependencies$3B=["typed","config","BigNumber","xgcd","equal","smaller","mod","add","isInteger"],createInvmod=factory(name$3B,dependencies$3B,(e=>{var{typed:t,config:r,BigNumber:n,xgcd:i,equal:a,smaller:o,mod:s,add:u,isInteger:c}=e;return t(name$3B,{"number, number":l,"BigNumber, BigNumber":l});function l(e,t){if(!c(e)||!c(t))throw new Error("Parameters in function invmod must be integer numbers");if(e=s(e,t),a(t,0))throw new Error("Divisor must be non zero");var r=i(e,t);r=r.valueOf();var[l,f]=r;return a(l,n(1))?(f=s(f,t),o(f,n(0))&&(f=u(f,t)),f):NaN}})),name$3A="algorithm09",dependencies$3A=["typed","equalScalar"],createAlgorithm09=factory(name$3A,dependencies$3A,(e=>{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A,M=a&&l?[]:void 0,S=[],E=[],T=M?[]:void 0,O=[];for(w=0;w{var{typed:t,matrix:r,equalScalar:n,multiplyScalar:i}=e,a=createAlgorithm02({typed:t,equalScalar:n}),o=createAlgorithm09({typed:t,equalScalar:n}),s=createAlgorithm11({typed:t,equalScalar:n}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3z,{"any, any":i,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,i,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,i,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,i,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,i)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,i,!1)},"DenseMatrix, any":function(e,t){return c(e,t,i,!1)},"any, SparseMatrix":function(e,t){return s(t,e,i,!0)},"any, DenseMatrix":function(e,t){return c(t,e,i,!0)},"Array, any":function(e,t){return c(r(e),t,i,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,i,!0).valueOf()}})}));function bitAndBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitAnd");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero()||t.eq(-1)||e.eq(t))return e;if(t.isZero()||e.eq(-1))return t;if(!e.isFinite()||!t.isFinite()){if(!e.isFinite()&&!t.isFinite())return e.isNegative()===t.isNegative()?e:new r(0);if(!e.isFinite())return t.isNegative()?e:e.isNegative()?new r(0):t;if(!t.isFinite())return e.isNegative()?t:t.isNegative()?new r(0):e}return bitwise(e,t,(function(e,t){return e&t}))}function bitNotBigNumber(e){if(e.isFinite()&&!e.isInteger())throw new Error("Integer expected in function bitNot");var t=e.constructor,r=t.precision;t.config({precision:1e9});var n=e.plus(new t(1));return n.s=-n.s||null,t.config({precision:r}),n}function bitOrBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitOr");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);var n=new r(-1);return e.isZero()||t.eq(n)||e.eq(t)?t:t.isZero()||e.eq(n)?e:e.isFinite()&&t.isFinite()?bitwise(e,t,(function(e,t){return e|t})):!e.isFinite()&&!e.isNegative()&&t.isNegative()||e.isNegative()&&!t.isNegative()&&!t.isFinite()?n:e.isNegative()&&t.isNegative()?e.isFinite()?e:t:e.isFinite()?t:e}function bitwise(e,t,r){var n,i,a,o,s,u=e.constructor,c=+(e.s<0),l=+(t.s<0);if(c){n=decCoefficientToBinaryString(bitNotBigNumber(e));for(var f=0;f0;)r(a[--m],o[--d])===h&&(y=y.plus(g)),g=g.times(v);for(;d>0;)r(s,o[--d])===h&&(y=y.plus(g)),g=g.times(v);return u.config({precision:x}),0===h&&(y.s=-y.s),y}function decCoefficientToBinaryString(e){for(var t=e.d,r=t[0]+"",n=1;n0)if(++s>c)for(s-=c;s--;)u+="0";else s1&&(null!==l[m+1]&&void 0!==l[m+1]||(l[m+1]=0),l[m+1]+=l[m]>>1,l[m]&=1)}return l.reverse()}function bitXor$1(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitXor");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero())return t;if(t.isZero())return e;if(e.eq(t))return new r(0);var n=new r(-1);return e.eq(n)?bitNotBigNumber(t):t.eq(n)?bitNotBigNumber(e):e.isFinite()&&t.isFinite()?bitwise(e,t,(function(e,t){return e^t})):e.isFinite()||t.isFinite()?new r(e.isNegative()===t.isNegative()?1/0:-1/0):n}function leftShiftBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function leftShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:e.isFinite()||t.isFinite()?t.lt(55)?e.times(Math.pow(2,t.toNumber())+""):e.times(new r(2).pow(t)):new r(NaN)}function rightArithShiftBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function rightArithShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:t.isFinite()?t.lt(55)?e.div(Math.pow(2,t.toNumber())+"").floor():e.div(new r(2).pow(t)).floor():e.isNegative()?new r(-1):e.isFinite()?new r(0):new r(NaN)}var name$3y="bitAnd",dependencies$3y=["typed","matrix","equalScalar"],createBitAnd=factory(name$3y,dependencies$3y,(e=>{var{typed:t,matrix:r,equalScalar:n}=e,i=createAlgorithm02({typed:t,equalScalar:n}),a=createAlgorithm06({typed:t,equalScalar:n}),o=createAlgorithm11({typed:t,equalScalar:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3y,{"number, number":bitAndNumber,"BigNumber, BigNumber":bitAndBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3x="bitNot",dependencies$3x=["typed"],createBitNot=factory(name$3x,dependencies$3x,(e=>{var{typed:t}=e;return t(name$3x,{number:bitNotNumber,BigNumber:bitNotBigNumber,"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3w="bitOr",dependencies$3w=["typed","matrix","equalScalar","DenseMatrix"],createBitOr=factory(name$3w,dependencies$3w,(e=>{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm01({typed:t}),o=createAlgorithm04({typed:t,equalScalar:n}),s=createAlgorithm10({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3w,{"number, number":bitOrNumber,"BigNumber, BigNumber":bitOrBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$3v="algorithm07",dependencies$3v=["typed","DenseMatrix"],createAlgorithm07=factory(name$3v,dependencies$3v,(e=>{var{typed:t,DenseMatrix:r}=e;return function(e,i,a){var o=e._size,s=e._datatype,u=i._size,c=i._datatype;if(o.length!==u.length)throw new DimensionError(o.length,u.length);if(o[0]!==u[0]||o[1]!==u[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+u+")");var l,f,p,m=o[0],d=o[1],h=0,y=a;"string"==typeof s&&s===c&&(l=s,h=t.convert(0,l),y=t.find(a,[l,l]));var g=[];for(f=0;f{var{typed:t,matrix:r,DenseMatrix:n}=e,i=createAlgorithm03({typed:t}),a=createAlgorithm07({typed:t,DenseMatrix:n}),o=createAlgorithm12({typed:t,DenseMatrix:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3u,{"number, number":bitXorNumber,"BigNumber, BigNumber":bitXor$1,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3t="arg",dependencies$3t=["typed"],createArg=factory(name$3t,dependencies$3t,(e=>{var{typed:t}=e;return t(name$3t,{number:function(e){return Math.atan2(0,e)},BigNumber:function(e){return e.constructor.atan2(0,e)},Complex:function(e){return e.arg()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3s="conj",dependencies$3s=["typed"],createConj=factory(name$3s,dependencies$3s,(e=>{var{typed:t}=e;return t(name$3s,{number:function(e){return e},BigNumber:function(e){return e},Complex:function(e){return e.conjugate()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3r="im",dependencies$3r=["typed"],createIm=factory(name$3r,dependencies$3r,(e=>{var{typed:t}=e;return t(name$3r,{number:function(e){return 0},BigNumber:function(e){return e.mul(0)},Fraction:function(e){return e.mul(0)},Complex:function(e){return e.im},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3q="re",dependencies$3q=["typed"],createRe=factory(name$3q,dependencies$3q,(e=>{var{typed:t}=e;return t(name$3q,{number:function(e){return e},BigNumber:function(e){return e},Fraction:function(e){return e},Complex:function(e){return e.re},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3p="not",dependencies$3p=["typed"],createNot=factory(name$3p,dependencies$3p,(e=>{var{typed:t}=e;return t(name$3p,{number:notNumber,Complex:function(e){return 0===e.re&&0===e.im},BigNumber:function(e){return e.isZero()||e.isNaN()},Unit:function(e){return null===e.value||this(e.value)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3o="or",dependencies$3o=["typed","matrix","equalScalar","DenseMatrix"],createOr=factory(name$3o,dependencies$3o,(e=>{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm05({typed:t,equalScalar:n}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3o,{"number, number":orNumber,"Complex, Complex":function(e,t){return 0!==e.re||0!==e.im||0!==t.re||0!==t.im},"BigNumber, BigNumber":function(e,t){return!e.isZero()&&!e.isNaN()||!t.isZero()&&!t.isNaN()},"Unit, Unit":function(e,t){return this(e.value||0,t.value||0)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$3n="xor",dependencies$3n=["typed","matrix","DenseMatrix"],createXor=factory(name$3n,dependencies$3n,(e=>{var{typed:t,matrix:r,DenseMatrix:n}=e,i=createAlgorithm03({typed:t}),a=createAlgorithm07({typed:t,DenseMatrix:n}),o=createAlgorithm12({typed:t,DenseMatrix:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3n,{"number, number":xorNumber,"Complex, Complex":function(e,t){return(0!==e.re||0!==e.im)!=(0!==t.re||0!==t.im)},"BigNumber, BigNumber":function(e,t){return(!e.isZero()&&!e.isNaN())!=(!t.isZero()&&!t.isNaN())},"Unit, Unit":function(e,t){return this(e.value||0,t.value||0)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3m="concat",dependencies$3m=["typed","matrix","isInteger"],createConcat=factory(name$3m,dependencies$3m,(e=>{var{typed:t,matrix:r,isInteger:n}=e;return t(name$3m,{"...Array | Matrix | number | BigNumber":function(e){var t,i,a=e.length,o=-1,s=!1,u=[];for(t=0;t0&&o>i)throw new IndexError(o,i+1)}else{var l=clone$3(c).valueOf(),f=arraySize(l);if(u[t]=l,i=o,o=f.length-1,t>0&&o!==i)throw new DimensionError(i+1,o+1)}}if(0===u.length)throw new SyntaxError("At least one matrix expected");for(var p=u.shift();u.length;)p=_concat(p,u.shift(),o,0);return s?r(p):p},"...string":function(e){return e.join("")}})}));function _concat(e,t,r,n){if(n{var{typed:t,Index:r,matrix:n,range:i}=e;return t(name$3l,{"Matrix, number":a,"Array, number":function(e,t){return a(n(clone$3(e)),t).valueOf()}});function a(e,t){if(2!==e.size().length)throw new Error("Only two dimensional matrix is supported");validateIndex(t,e.size()[1]);var n=i(0,e.size()[0]),a=new r(n,t);return e.subset(a)}})),name$3k="count",dependencies$3k=["typed","size","prod"],createCount=factory(name$3k,dependencies$3k,(e=>{var{typed:t,size:r,prod:n}=e;return t(name$3k,{string:function(e){return e.length},"Matrix | Array":function(e){return n(r(e))}})})),name$3j="cross",dependencies$3j=["typed","matrix","subtract","multiply"],createCross=factory(name$3j,dependencies$3j,(e=>{var{typed:t,matrix:r,subtract:n,multiply:i}=e;return t(name$3j,{"Matrix, Matrix":function(e,t){return r(a(e.toArray(),t.toArray()))},"Matrix, Array":function(e,t){return r(a(e.toArray(),t))},"Array, Matrix":function(e,t){return r(a(e,t.toArray()))},"Array, Array":a});function a(e,t){var r=Math.max(arraySize(e).length,arraySize(t).length);e=squeeze$1(e),t=squeeze$1(t);var a=arraySize(e),o=arraySize(t);if(1!==a.length||1!==o.length||3!==a[0]||3!==o[0])throw new RangeError("Vectors with length 3 expected (Size A = ["+a.join(", ")+"], B = ["+o.join(", ")+"])");var s=[n(i(e[1],t[2]),i(e[2],t[1])),n(i(e[2],t[0]),i(e[0],t[2])),n(i(e[0],t[1]),i(e[1],t[0]))];return r>1?[s]:s}})),name$3i="diag",dependencies$3i=["typed","matrix","DenseMatrix","SparseMatrix"],createDiag=factory(name$3i,dependencies$3i,(e=>{var{typed:t,matrix:r,DenseMatrix:n,SparseMatrix:i}=e;return t(name$3i,{Array:function(e){return a(e,0,arraySize(e),null)},"Array, number":function(e,t){return a(e,t,arraySize(e),null)},"Array, BigNumber":function(e,t){return a(e,t.toNumber(),arraySize(e),null)},"Array, string":function(e,t){return a(e,0,arraySize(e),t)},"Array, number, string":function(e,t,r){return a(e,t,arraySize(e),r)},"Array, BigNumber, string":function(e,t,r){return a(e,t.toNumber(),arraySize(e),r)},Matrix:function(e){return a(e,0,e.size(),e.storage())},"Matrix, number":function(e,t){return a(e,t,e.size(),e.storage())},"Matrix, BigNumber":function(e,t){return a(e,t.toNumber(),e.size(),e.storage())},"Matrix, string":function(e,t){return a(e,0,e.size(),t)},"Matrix, number, string":function(e,t,r){return a(e,t,e.size(),r)},"Matrix, BigNumber, string":function(e,t,r){return a(e,t.toNumber(),e.size(),r)}});function a(e,t,a,o){if(!isInteger$1(t))throw new TypeError("Second parameter in function diag must be an integer");var s=t>0?t:0,u=t<0?-t:0;switch(a.length){case 1:return function(e,t,r,a,o,s){var u=[a+o,a+s];if(r&&"sparse"!==r&&"dense"!==r)throw new TypeError("Unknown matrix type ".concat(r,'"'));var c="sparse"===r?i.diagonal(u,e,t):n.diagonal(u,e,t);return null!==r?c:c.valueOf()}(e,t,o,a[0],u,s);case 2:return function(e,t,n,i,a,o){if(isMatrix(e)){var s=e.diagonal(t);return null!==n?n!==s.storage()?r(s,n):s:s.valueOf()}for(var u=Math.min(i[0]-a,i[1]-o),c=[],l=0;l1&&void 0!==arguments[1]?arguments[1]:{};return r=null==r?Number.POSITIVE_INFINITY:r,t=null==t?JSON.stringify:t,function n(){"object"!=typeof n.cache&&(n.cache={values:new Map,lru:lruQueue(r||Number.POSITIVE_INFINITY)});for(var i=[],a=0;a{var{typed:t}=e;return t("filter",{"Array, function":_filterCallback,"Matrix, function":function(e,t){return e.create(_filterCallback(e.toArray(),t))},"Array, RegExp":filterRegExp,"Matrix, RegExp":function(e,t){return e.create(filterRegExp(e.toArray(),t))}})}));function _filterCallback(e,t){var r=maxArgumentCount(t);return filter$2(e,(function(e,n,i){return 1===r?t(e):2===r?t(e,[n]):t(e,[n],i)}))}var name$3g="flatten",dependencies$3g=["typed","matrix"],createFlatten=factory(name$3g,dependencies$3g,(e=>{var{typed:t,matrix:r}=e;return t(name$3g,{Array:function(e){return flatten$4(clone$3(e))},Matrix:function(e){var t=flatten$4(clone$3(e.toArray()));return r(t)}})})),name$3f="forEach",dependencies$3f=["typed"],createForEach=factory(name$3f,dependencies$3f,(e=>{var{typed:t}=e;return t(name$3f,{"Array, function":_forEach,"Matrix, function":function(e,t){return e.forEach(t)}})}));function _forEach(e,t){var r=maxArgumentCount(t);!function n(i,a){Array.isArray(i)?forEach$1(i,(function(e,t){n(e,a.concat(t))})):1===r?t(i):2===r?t(i,a):t(i,a,e)}(e,[])}var name$3e="getMatrixDataType",dependencies$3e=["typed"],createGetMatrixDataType=factory(name$3e,dependencies$3e,(e=>{var{typed:t}=e;return t(name$3e,{Array:function(e){return getArrayDataType(e,typeOf$1)},Matrix:function(e){return e.getDataType()}})})),name$3d="identity",dependencies$3d=["typed","config","matrix","BigNumber","DenseMatrix","SparseMatrix"],createIdentity=factory(name$3d,dependencies$3d,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i,DenseMatrix:a,SparseMatrix:o}=e;return t(name$3d,{"":function(){return"Matrix"===r.matrix?n([]):[]},string:function(e){return n(e)},"number | BigNumber":function(e){return u(e,e,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber, string":function(e,t){return u(e,e,t)},"number | BigNumber, number | BigNumber":function(e,t){return u(e,t,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber, number | BigNumber, string":function(e,t,r){return u(e,t,r)},Array:function(e){return s(e)},"Array, string":function(e,t){return s(e,t)},Matrix:function(e){return s(e.valueOf(),e.storage())},"Matrix, string":function(e,t){return s(e.valueOf(),t)}});function s(e,t){switch(e.length){case 0:return t?n(t):[];case 1:return u(e[0],e[0],t);case 2:return u(e[0],e[1],t);default:throw new Error("Vector containing two values expected")}}function u(e,t,r){var n=isBigNumber(e)||isBigNumber(t)?i:null;if(isBigNumber(e)&&(e=e.toNumber()),isBigNumber(t)&&(t=t.toNumber()),!isInteger$1(e)||e<1)throw new Error("Parameters in function identity must be positive integers");if(!isInteger$1(t)||t<1)throw new Error("Parameters in function identity must be positive integers");var s=n?new i(1):1,u=n?new n(0):0,c=[e,t];if(r){if("sparse"===r)return o.diagonal(c,s,0,u);if("dense"===r)return a.diagonal(c,s,0,u);throw new TypeError('Unknown matrix type "'.concat(r,'"'))}for(var l=resize$1([],c,u),f=e{var{typed:t,matrix:r,multiplyScalar:n}=e;return t(name$3c,{"Matrix, Matrix":function(e,t){return r(i(e.toArray(),t.toArray()))},"Matrix, Array":function(e,t){return r(i(e.toArray(),t))},"Array, Matrix":function(e,t){return r(i(e,t.toArray()))},"Array, Array":i});function i(e,t){if(1===arraySize(e).length&&(e=[e]),1===arraySize(t).length&&(t=[t]),arraySize(e).length>2||arraySize(t).length>2)throw new RangeError("Vectors with dimensions greater then 2 are not supported expected (Size x = "+JSON.stringify(e.length)+", y = "+JSON.stringify(t.length)+")");var r=[],i=[];return e.map((function(e){return t.map((function(t){return i=[],r.push(i),e.map((function(e){return t.map((function(t){return i.push(n(e,t))}))}))}))}))&&r}})),name$3b="map",dependencies$3b=["typed"],createMap=factory(name$3b,dependencies$3b,(e=>{var{typed:t}=e;return t(name$3b,{"Array, function":_map$1,"Matrix, function":function(e,t){return e.map(t)}})}));function _map$1(e,t){var r=maxArgumentCount(t);return function n(i,a){if(Array.isArray(i))return i.map((function(e,t){return n(e,a.concat(t))}));try{return 1===r?t(i):2===r?t(i,a):t(i,a,e)}catch(t){if(t instanceof TypeError&&"data"in t&&"wrongType"===t.data.category){var o="map attempted to call '".concat(t.data.fn,"(").concat(i),s=JSON.stringify(a);throw 2===r?o+=","+s:1!==r&&(o+=",".concat(s,",").concat(e)),o+=")' but argument ".concat(t.data.index+1," of type "),o+="".concat(t.data.actual," does not match expected type "),o+=t.data.expected.join(" or "),new TypeError(o)}throw t}}(e,[])}var name$3a="diff",dependencies$3a=["typed","matrix","subtract","number"],createDiff=factory(name$3a,dependencies$3a,(e=>{var{typed:t,matrix:r,subtract:n,number:i}=e;return t(name$3a,{"Array | Matrix":function(e){return isMatrix(e)?r(o(e.toArray())):o(e)},"Array | Matrix, number":function(e,t){if(!isInteger$1(t))throw new RangeError("Dimension must be a whole number");return isMatrix(e)?r(a(e.toArray(),t)):a(e,t)},"Array | Matrix, BigNumber":function(e,t){return this(e,i(t))}});function a(e,t){if(isMatrix(e)&&(e=e.toArray()),!Array.isArray(e))throw RangeError("Array/Matrix does not have that many dimensions");if(t>0){var r=[];return e.forEach((e=>{r.push(a(e,t-1))})),r}if(0===t)return o(e);throw RangeError("Cannot have negative dimension")}function o(e){var t=[],r=e.length;if(r<2)return e;for(var n=1;n{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t("ones",{"":function(){return"Array"===r.matrix?a([]):a([],"default")},"...number | BigNumber | string":function(e){if("string"==typeof e[e.length-1]){var t=e.pop();return a(e,t)}return"Array"===r.matrix?a(e):a(e,"default")},Array:a,Matrix:function(e){var t=e.storage();return a(e.valueOf(),t)},"Array | Matrix, string":function(e,t){return a(e.valueOf(),t)}});function a(e,t){var r=function(e){var t=!1;return e.forEach((function(e,r,n){isBigNumber(e)&&(t=!0,n[r]=e.toNumber())})),t}(e),a=r?new i(1):1;if(function(e){e.forEach((function(e){if("number"!=typeof e||!isInteger$1(e)||e<0)throw new Error("Parameters in function ones must be positive integers")}))}(e),t){var o=n(t);return e.length>0?o.resize(e,a):o}var s=[];return e.length>0?resize$1(s,e,a):s}}));function noBignumber(){throw new Error('No "bignumber" implementation available')}function noFraction(){throw new Error('No "fraction" implementation available')}function noMatrix(){throw new Error('No "matrix" implementation available')}var name$38="range",dependencies$38=["typed","config","?matrix","?bignumber","smaller","smallerEq","larger","largerEq"],createRange=factory(name$38,dependencies$38,(e=>{var{typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u}=e;return t(name$38,{string:l,"string, boolean":l,"number, number":function(e,t){return c(f(e,t,1))},"number, number, number":function(e,t,r){return c(f(e,t,r))},"number, number, boolean":function(e,t,r){return c(r?p(e,t,1):f(e,t,1))},"number, number, number, boolean":function(e,t,r,n){return c(n?p(e,t,r):f(e,t,r))},"BigNumber, BigNumber":function(e,t){return c(m(e,t,new(0,e.constructor)(1)))},"BigNumber, BigNumber, BigNumber":function(e,t,r){return c(m(e,t,r))},"BigNumber, BigNumber, boolean":function(e,t,r){var n=e.constructor;return c(r?d(e,t,new n(1)):m(e,t,new n(1)))},"BigNumber, BigNumber, BigNumber, boolean":function(e,t,r,n){return c(n?d(e,t,r):m(e,t,r))}});function c(e){return"Matrix"===r.matrix?n?n(e):noMatrix():e}function l(e,t){var n=function(e){var t=e.split(":"),r=t.map((function(e){return Number(e)}));if(r.some((function(e){return isNaN(e)})))return null;switch(r.length){case 2:return{start:r[0],end:r[1],step:1};case 3:return{start:r[0],end:r[2],step:r[1]};default:return null}}(e);if(!n)throw new SyntaxError('String "'+e+'" is no valid range');return"BigNumber"===r.number?(void 0===i&&noBignumber(),c((t?d:m)(i(n.start),i(n.end),i(n.step)))):c((t?p:f)(n.start,n.end,n.step))}function f(e,t,r){var n=[],i=e;if(r>0)for(;a(i,t);)n.push(i),i+=r;else if(r<0)for(;s(i,t);)n.push(i),i+=r;return n}function p(e,t,r){var n=[],i=e;if(r>0)for(;o(i,t);)n.push(i),i+=r;else if(r<0)for(;u(i,t);)n.push(i),i+=r;return n}function m(e,t,r){var n=i(0),o=[],u=e;if(r.gt(n))for(;a(u,t);)o.push(u),u=u.plus(r);else if(r.lt(n))for(;s(u,t);)o.push(u),u=u.plus(r);return o}function d(e,t,r){var n=i(0),a=[],s=e;if(r.gt(n))for(;o(s,t);)a.push(s),s=s.plus(r);else if(r.lt(n))for(;u(s,t);)a.push(s),s=s.plus(r);return a}})),name$37="reshape",dependencies$37=["typed","isInteger","matrix"],createReshape=factory(name$37,dependencies$37,(e=>{var{typed:t,isInteger:r}=e;return t(name$37,{"Matrix, Array":function(e,t){return e.reshape(t)},"Array, Array":function(e,t){return t.forEach((function(e){if(!r(e))throw new TypeError("Invalid size for dimension: "+e)})),reshape$1(e,t)}})}));function ArgumentsError(e,t,r,n){if(!(this instanceof ArgumentsError))throw new SyntaxError("Constructor must be called with the new operator");this.fn=e,this.count=t,this.min=r,this.max=n,this.message="Wrong number of arguments in function "+e+" ("+t+" provided, "+r+(null!=n?"-"+n:"")+" expected)",this.stack=(new Error).stack}ArgumentsError.prototype=new Error,ArgumentsError.prototype.constructor=Error,ArgumentsError.prototype.name="ArgumentsError",ArgumentsError.prototype.isArgumentsError=!0;var name$36="resize",dependencies$36=["config","matrix"],createResize=factory(name$36,dependencies$36,(e=>{var{config:t,matrix:r}=e;return function(e,n,i){if(2!==arguments.length&&3!==arguments.length)throw new ArgumentsError("resize",arguments.length,2,3);if(isMatrix(n)&&(n=n.valueOf()),isBigNumber(n[0])&&(n=n.map((function(e){return isBigNumber(e)?e.toNumber():e}))),isMatrix(e))return e.resize(n,i,!0);if("string"==typeof e)return function(e,t,r){if(void 0!==r){if("string"!=typeof r||1!==r.length)throw new TypeError("Single character expected as defaultValue")}else r=" ";if(1!==t.length)throw new DimensionError(t.length,1);var n=t[0];if("number"!=typeof n||!isInteger$1(n))throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(t)+")");if(e.length>n)return e.substring(0,n);if(e.length{var{typed:t,multiply:r,rotationMatrix:n}=e;return t(name$35,{"Array , number | BigNumber | Complex | Unit":function(e,t){return i(e,2),r(n(t),e).toArray()},"Matrix , number | BigNumber | Complex | Unit":function(e,t){return i(e,2),r(n(t),e)},"Array, number | BigNumber | Complex | Unit, Array | Matrix":function(e,t,a){return i(e,3),r(n(t,a),e)},"Matrix, number | BigNumber | Complex | Unit, Array | Matrix":function(e,t,a){return i(e,3),r(n(t,a),e)}});function i(e,t){var r=Array.isArray(e)?arraySize(e):e.size();if(r.length>2)throw new RangeError("Vector must be of dimensions 1x".concat(t));if(2===r.length&&1!==r[1])throw new RangeError("Vector must be of dimensions 1x".concat(t));if(r[0]!==t)throw new RangeError("Vector must be of dimensions 1x".concat(t))}})),name$34="rotationMatrix",dependencies$34=["typed","config","multiplyScalar","addScalar","unaryMinus","norm","matrix","BigNumber","DenseMatrix","SparseMatrix","cos","sin"],createRotationMatrix=factory(name$34,dependencies$34,(e=>{var{typed:t,config:r,multiplyScalar:n,addScalar:i,unaryMinus:a,norm:o,BigNumber:s,matrix:u,DenseMatrix:c,SparseMatrix:l,cos:f,sin:p}=e;return t(name$34,{"":function(){return"Matrix"===r.matrix?u([]):[]},string:function(e){return u(e)},"number | BigNumber | Complex | Unit":function(e){return m(e,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber | Complex | Unit, string":function(e,t){return m(e,t)},"number | BigNumber | Complex | Unit, Array":function(e,t){var r=u(t);return d(r),g(e,r,void 0)},"number | BigNumber | Complex | Unit, Matrix":function(e,t){d(t);var n=t.storage()||("Matrix"===r.matrix?"dense":void 0);return g(e,t,n)},"number | BigNumber | Complex | Unit, Array, string":function(e,t,r){var n=u(t);return d(n),g(e,n,r)},"number 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o,s=typeOf$1(e),u=typeOf$1(t);if(!("number"!==s&&"BigNumber"!==s&&"Fraction"!==s||"number"!==u&&"BigNumber"!==u&&"Fraction"!==u))return"0"!==(o=r(e,t)).toString()?o>0?1:-1:naturalSort(s,u);if("Array"===s||"Matrix"===s||"Array"===u||"Matrix"===u)return 0!==(o=i(this,e,t))?o:naturalSort(s,u);if(s!==u)return naturalSort(s,u);if("Complex"===s)return compareComplexNumbers(e,t);if("Unit"===s)return e.equalBase(t)?this(e.value,t.value):a(this,e.formatUnits(),t.formatUnits());if("boolean"===s)return n(e,t);if("string"===s)return naturalSort(e,t);if("Object"===s)return function(e,t,r){var n=Object.keys(t),i=Object.keys(r);n.sort(naturalSort),i.sort(naturalSort);var o=a(e,n,i);if(0!==o)return o;for(var s=0;sr.length?1:t.lengtht.re?1:e.ret.im?1:e.im{var{typed:t,matrix:r}=e,n=createAlgorithm13({typed:t}),i=createAlgorithm14({typed:t});return t(name$2s,{"any, any":compareText$1,"DenseMatrix, DenseMatrix":function(e,t){return n(e,t,compareText$1)},"Array, Array":function(e,t){return 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name$2q="equalText",dependencies$2q=["typed","compareText","isZero"],createEqualText=factory(name$2q,dependencies$2q,(e=>{var{typed:t,compareText:r,isZero:n}=e;return t(name$2q,{"any, any":function(e,t){return n(r(e,t))}})})),name$2p="smaller",dependencies$2p=["typed","config","matrix","DenseMatrix"],createSmaller=factory(name$2p,dependencies$2p,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2p,{"boolean, boolean":function(e,t){return e{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2o,{"boolean, boolean":function(e,t){return e<=t},"number, number":function(e,t){return e<=t||nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.lte(t)||nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return 1!==e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2n="larger",dependencies$2n=["typed","config","matrix","DenseMatrix"],createLarger=factory(name$2n,dependencies$2n,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2n,{"boolean, boolean":function(e,t){return e>t},"number, number":function(e,t){return e>t&&!nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.gt(t)&&!nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return 1===e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2m="largerEq",dependencies$2m=["typed","config","matrix","DenseMatrix"],createLargerEq=factory(name$2m,dependencies$2m,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2m,{"boolean, boolean":function(e,t){return e>=t},"number, number":function(e,t){return e>=t||nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.gte(t)||nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return-1!==e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2l="deepEqual",dependencies$2l=["typed","equal"],createDeepEqual=factory(name$2l,dependencies$2l,(e=>{var{typed:t,equal:r}=e;return t(name$2l,{"any, any":function(e,t){return n(e.valueOf(),t.valueOf())}});function n(e,t){if(Array.isArray(e)){if(Array.isArray(t)){var i=e.length;if(i!==t.length)return!1;for(var a=0;a{var{typed:t,config:r,equalScalar:n,matrix:i,DenseMatrix:a}=e,o=createAlgorithm03({typed:t}),s=createAlgorithm07({typed:t,DenseMatrix:a}),u=createAlgorithm12({typed:t,DenseMatrix:a}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t});return t("unequal",{"any, any":function(e,t){return null===e?null!==t:null===t?null!==e:void 0===e?void 0!==t:void 0===t?void 0!==e:f(e,t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,f)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,f,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,f,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,f)},"Array, Array":function(e,t){return this(i(e),i(t)).valueOf()},"Array, Matrix":function(e,t){return this(i(e),t)},"Matrix, Array":function(e,t){return this(e,i(t))},"SparseMatrix, any":function(e,t){return u(e,t,f,!1)},"DenseMatrix, any":function(e,t){return l(e,t,f,!1)},"any, SparseMatrix":function(e,t){return u(t,e,f,!0)},"any, DenseMatrix":function(e,t){return l(t,e,f,!0)},"Array, any":function(e,t){return l(i(e),t,f,!1).valueOf()},"any, Array":function(e,t){return l(i(t),e,f,!0).valueOf()}});function f(e,t){return!n(e,t)}}));factory(name$2k,["typed","equalScalar"],(e=>{var{typed:t,equalScalar:r}=e;return t(name$2k,{"any, any":function(e,t){return null===e?null!==t:null===t?null!==e:void 0===e?void 0!==t:void 0===t?void 0!==e:!r(e,t)}})}));var name$2j="partitionSelect",dependencies$2j=["typed","isNumeric","isNaN","compare"],createPartitionSelect=factory(name$2j,dependencies$2j,(e=>{var{typed:t,isNumeric:r,isNaN:n,compare:i}=e,a=i,o=(e,t)=>-i(e,t);return t(name$2j,{"Array | Matrix, number":function(e,t){return s(e,t,a)},"Array | Matrix, number, string":function(e,t,r){if("asc"===r)return s(e,t,a);if("desc"===r)return s(e,t,o);throw new Error('Compare string must be "asc" or "desc"')},"Array | Matrix, number, function":s});function s(e,t,r){if(!isInteger$1(t)||t<0)throw new Error("k must be a non-negative integer");if(isMatrix(e)){if(e.size().length>1)throw new Error("Only one dimensional matrices supported");return u(e.valueOf(),t,r)}if(Array.isArray(e))return u(e,t,r)}function u(e,t,i){if(t>=e.length)throw new Error("k out of bounds");for(var a=0;a=0){var f=e[c];e[c]=e[u],e[u]=f,--c}else++u;i(e[u],l)>0&&--u,t<=u?s=u:o=u+1}return e[t]}})),name$2i="sort",dependencies$2i=["typed","matrix","compare","compareNatural"],createSort=factory(name$2i,dependencies$2i,(e=>{var{typed:t,matrix:r,compare:n,compareNatural:i}=e,a=n,o=(e,t)=>-n(e,t);return t(name$2i,{Array:function(e){return u(e),e.sort(a)},Matrix:function(e){return c(e),r(e.toArray().sort(a),e.storage())},"Array, function":function(e,t){return u(e),e.sort(t)},"Matrix, function":function(e,t){return c(e),r(e.toArray().sort(t),e.storage())},"Array, string":function(e,t){return u(e),e.sort(s(t))},"Matrix, string":function(e,t){return c(e),r(e.toArray().sort(s(t)),e.storage())}});function s(e){if("asc"===e)return a;if("desc"===e)return o;if("natural"===e)return i;throw new Error('String "asc", "desc", or "natural" expected')}function u(e){if(1!==arraySize(e).length)throw new Error("One dimensional array expected")}function c(e){if(1!==e.size().length)throw new Error("One dimensional matrix expected")}})),name$2h="max",dependencies$2h=["typed","config","numeric","larger"],createMax=factory(name$2h,dependencies$2h,(e=>{var{typed:t,config:r,numeric:n,larger:i}=e;return t(name$2h,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return reduce$2(e,t.valueOf(),a)},"...":function(e){if(containsCollections(e))throw new TypeError("Scalar values expected in function max");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw improveErrorMessage(e,"max",t)}}function o(e){var t;if(deepForEach(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw improveErrorMessage(t,"max",e)}})),void 0===t)throw new Error("Cannot calculate max of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),name$2g="min",dependencies$2g=["typed","config","numeric","smaller"],createMin=factory(name$2g,dependencies$2g,(e=>{var{typed:t,config:r,numeric:n,smaller:i}=e;return t(name$2g,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return reduce$2(e,t.valueOf(),a)},"...":function(e){if(containsCollections(e))throw new TypeError("Scalar values expected in function min");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw improveErrorMessage(e,"min",t)}}function o(e){var t;if(deepForEach(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw improveErrorMessage(t,"min",e)}})),void 0===t)throw new Error("Cannot calculate min of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),name$2f="ImmutableDenseMatrix",dependencies$2f=["smaller","DenseMatrix"],createImmutableDenseMatrixClass=factory(name$2f,dependencies$2f,(e=>{var{smaller:t,DenseMatrix:r}=e;function n(e,t){if(!(this instanceof n))throw new SyntaxError("Constructor must be called with the new operator");if(t&&!isString$1(t))throw new Error("Invalid datatype: "+t);if(isMatrix(e)||isArray$1(e)){var i=new r(e,t);this._data=i._data,this._size=i._size,this._datatype=i._datatype,this._min=null,this._max=null}else if(e&&isArray$1(e.data)&&isArray$1(e.size))this._data=e.data,this._size=e.size,this._datatype=e.datatype,this._min=void 0!==e.min?e.min:null,this._max=void 0!==e.max?e.max:null;else{if(e)throw new TypeError("Unsupported type of data ("+typeOf$1(e)+")");this._data=[],this._size=[0],this._datatype=t,this._min=null,this._max=null}}return n.prototype=new r,n.prototype.type="ImmutableDenseMatrix",n.prototype.isImmutableDenseMatrix=!0,n.prototype.subset=function(e){switch(arguments.length){case 1:var t=r.prototype.subset.call(this,e);return isMatrix(t)?new n({data:t._data,size:t._size,datatype:t._datatype}):t;case 2:case 3:throw new Error("Cannot invoke set subset on an Immutable Matrix instance");default:throw new SyntaxError("Wrong number of arguments")}},n.prototype.set=function(){throw new Error("Cannot invoke set on an Immutable Matrix instance")},n.prototype.resize=function(){throw new Error("Cannot invoke resize on an Immutable Matrix instance")},n.prototype.reshape=function(){throw new Error("Cannot invoke reshape on an Immutable Matrix instance")},n.prototype.clone=function(){return new n({data:clone$3(this._data),size:clone$3(this._size),datatype:this._datatype})},n.prototype.toJSON=function(){return{mathjs:"ImmutableDenseMatrix",data:this._data,size:this._size,datatype:this._datatype}},n.fromJSON=function(e){return new n(e)},n.prototype.swapRows=function(){throw new Error("Cannot invoke swapRows on an Immutable Matrix instance")},n.prototype.min=function(){if(null===this._min){var e=null;this.forEach((function(r){(null===e||t(r,e))&&(e=r)})),this._min=null!==e?e:void 0}return this._min},n.prototype.max=function(){if(null===this._max){var e=null;this.forEach((function(r){(null===e||t(e,r))&&(e=r)})),this._max=null!==e?e:void 0}return this._max},n}),{isClass:!0}),name$2e="Index",dependencies$2e=["ImmutableDenseMatrix"],createIndexClass=factory(name$2e,dependencies$2e,(e=>{var{ImmutableDenseMatrix:t}=e;function r(e){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");this._dimensions=[],this._isScalar=!0;for(var t=0,i=arguments.length;t{var{smaller:t,larger:r}=e,n=1/Math.log((1+Math.sqrt(5))/2);function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._minimum=null,this._size=0}function a(e,t,r){t.left.right=t.right,t.right.left=t.left,r.degree--,r.child===t&&(r.child=t.right),0===r.degree&&(r.child=null),t.left=e,t.right=e.right,e.right=t,t.right.left=t,t.parent=null,t.mark=!1}function o(e,t){var r=t.parent;r&&(t.mark?(a(e,t,r),o(r)):t.mark=!0)}i.prototype.type="FibonacciHeap",i.prototype.isFibonacciHeap=!0,i.prototype.insert=function(e,r){var n={key:e,value:r,degree:0};if(this._minimum){var i=this._minimum;n.left=i,n.right=i.right,i.right=n,n.right.left=n,t(e,i.key)&&(this._minimum=n)}else n.left=n,n.right=n,this._minimum=n;return this._size++,n},i.prototype.size=function(){return this._size},i.prototype.clear=function(){this._minimum=null,this._size=0},i.prototype.isEmpty=function(){return 0===this._size},i.prototype.extractMinimum=function(){var e=this._minimum;if(null===e)return e;for(var i=this._minimum,a=e.degree,o=e.child;a>0;){var u=o.right;o.left.right=o.right,o.right.left=o.left,o.left=i,o.right=i.right,i.right=o,o.right.left=o,o.parent=null,o=u,a--}return 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i=this._heap,a=this._values,o=[],s=i.extractMinimum();for(s&&o.push(s);s&&s.key<=t;)s.key>=e&&(r(s.value,0)||n(s.key,s.value,this)),(s=i.extractMinimum())&&o.push(s);for(var u=0;u{var t,r,n,{on:i,config:a,addScalar:o,subtract:s,multiplyScalar:u,divideScalar:c,pow:l,abs:f,fix:p,round:m,equal:d,isNumeric:h,format:y,number:g,Complex:v,BigNumber:x,Fraction:b}=e,_=g;function w(e,t){if(!(this instanceof w))throw new Error("Constructor must be called with the new operator");if(null!=e&&!h(e)&&!isComplex(e))throw new TypeError("First parameter in Unit constructor must be number, BigNumber, Fraction, Complex, or undefined");if(void 0!==t&&("string"!=typeof t||""===t))throw new TypeError("Second parameter in Unit constructor must be a string");if(void 0!==t){var r=w.parse(t);this.units=r.units,this.dimensions=r.dimensions}else{this.units=[{unit:z,prefix:k.NONE,power:0}],this.dimensions=[];for(var n=0;n="0"&&e<="9"}function A(){r++,n=t.charAt(r)}function M(e){r=e,n=t.charAt(r)}function S(){var 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this.properties)hasOwnProperty$2(this.properties,t)&&(e[t]=this.properties[t]);return new r(e)},r.prototype._toString=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push(stringify(r)+": "+this.properties[r].toString(e));return"{"+t.join(", ")+"}"},r.prototype.toJSON=function(){return{mathjs:"ObjectNode",properties:this.properties}},r.fromJSON=function(e){return new r(e.properties)},r.prototype.toHTML=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push(''+escape$1(r)+':'+this.properties[r].toHTML(e));return'{'+t.join(',')+'}'},r.prototype._toTex=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push("\\mathbf{"+r+":} & 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n.map((function(e){switch(e.getContent().type){case"ArrayNode":case"ConstantNode":case"SymbolNode":case"ParenthesisNode":return!1;default:return!0}}));switch(n.length){case 0:a=[];break;case 1:var u=getPrecedence(n[0],t);if(i&&null!==u){var c,l;if("keep"===t?(c=n[0].getIdentifier(),l=e.getIdentifier()):(c=n[0].getContent().getIdentifier(),l=e.getContent().getIdentifier()),!1===properties[o][l].latexLeftParens){a=[!1];break}if(!1===properties[u][c].latexParens){a=[!1];break}}if(null===u){a=[!1];break}if(u<=o){a=[!0];break}a=[!1];break;case 2:var f,p,m=getPrecedence(n[0],t),d=isAssociativeWith(e,n[0],t);f=null!==m&&(m===o&&"right"===s&&!d||m=2&&"OperatorNode:multiply"===e.getIdentifier()&&e.implicit&&"auto"===t&&"hide"===r&&(a=n.map((function(e,t){var r="ParenthesisNode"===e.getIdentifier();return!(!a[t]&&!r)}))),a}return r.prototype=new t,r.prototype.type="OperatorNode",r.prototype.isOperatorNode=!0,r.prototype._compile=function(e,t){if("string"!=typeof this.fn||!isSafeMethod(e,this.fn))throw e[this.fn]?new Error('No access to function "'+this.fn+'"'):new Error("Function "+this.fn+' missing in provided namespace "math"');var r=getSafeProperty(e,this.fn),n=map$2(this.args,(function(r){return r._compile(e,t)}));if(1===n.length){var i=n[0];return function(e,t,n){return r(i(e,t,n))}}if(2===n.length){var a=n[0],o=n[1];return function(e,t,n){return r(a(e,t,n),o(e,t,n))}}return function(e,t,i){return r.apply(null,map$2(n,(function(r){return r(e,t,i)})))}},r.prototype.forEach=function(e){for(var t=0;t2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())){var f=i.map((function(t,r){return t=t.toString(e),a[r]&&(t="("+t+")"),t}));return this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?f.join(" "):f.join(" "+this.op+" ")}return this.fn+"("+this.args.join(", 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i.length>2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())?this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?l.join(''):l.join(''+escape$1(this.op)+""):''+escape$1(this.fn)+'('+l.join(',')+')'},r.prototype._toTex=function(e){var t=e&&e.parenthesis?e.parenthesis:"keep",r=e&&e.implicit?e.implicit:"hide",i=this.args,a=n(this,t,r,i,!0),o=latexOperators[this.fn];if(o=void 0===o?this.op:o,1===i.length){var s=getAssociativity(this,t),u=i[0].toTex(e);return a[0]&&(u="\\left(".concat(u,"\\right)")),"right"===s?o+u:u+o}if(2===i.length){var c=i[0],l=c.toTex(e);a[0]&&(l="\\left(".concat(l,"\\right)"));var f,p=i[1].toTex(e);switch(a[1]&&(p="\\left(".concat(p,"\\right)")),f="keep"===t?c.getIdentifier():c.getContent().getIdentifier(),this.getIdentifier()){case"OperatorNode:divide":return 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If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]},log10Docs={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]},log1pDocs={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]},log2Docs={name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]},modDocs={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]},multiplyDocs={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]},normDocs={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']},nthRootDocs={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]},nthRootsDocs={name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]},powDocs={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)","math.pow([[1, 2], [4, 3]], 2)","math.pow([[1, 2], [4, 3]], -1)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]},roundDocs={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)"],seealso:["ceil","floor","fix"]},signDocs={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]},sqrtDocs={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]},sqrtmDocs={name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[1, 2], [3, 4]])"],seealso:["sqrt","abs","square","multiply"]},squareDocs={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]},subtractDocs={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]},unaryMinusDocs={name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]},unaryPlusDocs={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]},xgcdDocs={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]},bitAndDocs={name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitNotDocs={name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitOrDocs={name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]},bitXorDocs={name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]},leftShiftDocs={name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]},rightArithShiftDocs={name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]},rightLogShiftDocs={name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]},bellNumbersDocs={name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]},catalanDocs={name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]},compositionDocs={name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]},stirlingS2Docs={name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]},argDocs={name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]},conjDocs={name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]},imDocs={name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]},reDocs={name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]},evaluateDocs={name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(" + 4 + ")")'],seealso:[]},helpDocs={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]},distanceDocs={name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]},intersectDocs={name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])"],seealso:[]},andDocs={name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]},notDocs={name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]},orDocs={name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]},xorDocs={name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]},columnDocs={name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row","matrixFromColumns"]},concatDocs={name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},countDocs={name:"count",category:"Matrix",syntax:["count(x)"],description:"Count the number of elements of a matrix, array or string.",examples:["a = [1, 2; 3, 4; 5, 6]","count(a)","size(a)",'count("hello world")'],seealso:["size"]},crossDocs={name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0], [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4], [5, 6, 7])"],seealso:["multiply","dot"]},ctransposeDocs={name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},detDocs={name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diagDocs={name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diffDocs={name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["diff([1, 2, 4, 7, 0])","diff([1, 2, 4, 7, 0], 0)","diff(matrix([1, 2, 4, 7, 0]))","diff([[1, 2], [3, 4]])","diff([[1, 2], [3, 4]], 0)","diff([[1, 2], [3, 4]], 1)","diff([[1, 2], [3, 4]], bignumber(1))","diff(matrix([[1, 2], [3, 4]]), 1)","diff([[1, 2], matrix([3, 4])], 1)"],seealso:["subtract","partitionSelect"]},dotDocs={name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]},eigsDocs={name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and eigenvectors of a real symmetric matrix",examples:["eigs([[5, 2.3], [2.3, 1]])"],seealso:["inv"]},filterDocs={name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]},flattenDocs={name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]},forEachDocs={name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["numberOfPets = {}","addPet(n) = numberOfPets[n] = (numberOfPets[n] ? numberOfPets[n]:0 ) + 1;",'forEach(["Dog","Cat","Cat"], addPet)',"numberOfPets"],seealso:["map","sort","filter"]},getMatrixDataTypeDocs={name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeOf"]},identityDocs={name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},invDocs={name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]},pinvDocs={name:"pinv",category:"Matrix",syntax:["pinv(x)"],description:"Calculate the Moore–Penrose inverse of a matrix",examples:["pinv([1, 2; 3, 4])","pinv([[1, 0], [0, 1], [0, 1]])","pinv(4)"],seealso:["inv"]},kronDocs={name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]},mapDocs={name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]},matrixFromColumnsDocs={name:"matrixFromColumns",category:"Matrix",syntax:["math.matrixFromColumns(...arr)","math.matrixFromColumns(row1, row2)","math.matrixFromColumns(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual columns.",examples:["matrixFromColumns([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromRows","matrixFromFunction","zeros"]},matrixFromFunctionDocs={name:"matrixFromFunction",category:"Matrix",syntax:["math.matrixFromFunction(size, fn)","math.matrixFromFunction(size, fn, format)","math.matrixFromFunction(size, fn, format, datatype)","math.matrixFromFunction(size, format, fn)","math.matrixFromFunction(size, format, datatype, fn)"],description:"Create a matrix by evaluating a generating function at each index.",examples:["f(I) = I[1] - I[2]","matrixFromFunction([3,3], f)","g(I) = I[1] - I[2] == 1 ? 4 : 0",'matrixFromFunction([100, 100], "sparse", g)',"matrixFromFunction([5], random)"],seealso:["matrix","matrixFromRows","matrixFromColumns","zeros"]},matrixFromRowsDocs={name:"matrixFromRows",category:"Matrix",syntax:["math.matrixFromRows(...arr)","math.matrixFromRows(row1, row2)","math.matrixFromRows(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual rows.",examples:["matrixFromRows([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromColumns","matrixFromFunction","zeros"]},onesDocs={name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]},partitionSelectDocs={name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1)'],seealso:["sort"]},rangeDocs={name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]},reshapeDocs={name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])"],seealso:["size","squeeze","resize"]},resizeDocs={name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]},rotateDocs={name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], math.pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]},rotationMatrixDocs={name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]},rowDocs={name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column","matrixFromRows"]},sizeDocs={name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","count","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]},sortDocs={name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"])',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]},squeezeDocs={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]},subsetDocs={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of the entries of a matrix or characters of a string. Indexes are one-based. There should be one index specification for each dimension of the target. Each specification can be a single index, a list of indices, or a range in colon notation `l:u`. In a range, both the lower bound l and upper bound u are included; and if a bound is omitted it defaults to the most extreme valid value. The cartesian product of the indices specified in each dimension determines the target of the operation.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]","f[[1,2], [1,3]] = [9, 10; 11, 12]","f"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]},traceDocs={name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]},transposeDocs={name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},zerosDocs={name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]},fftDocs={name:"fft",category:"Matrix",syntax:["fft(x)"],description:"Calculate N-dimensional fourier transform",examples:["fft([[1, 0], [1, 0]])"],seealso:["ifft"]},ifftDocs={name:"ifft",category:"Matrix",syntax:["ifft(x)"],description:"Calculate N-dimensional inverse fourier transform",examples:["ifft([[2, 2], [0, 0]])"],seealso:["fft"]},combinationsDocs={name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]},combinationsWithRepDocs={name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]},factorialDocs={name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]},gammaDocs={name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]},lgammaDocs={name:"lgamma",category:"Probability",syntax:["lgamma(n)"],description:"Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers.",examples:["lgamma(4)","lgamma(1/2)","lgamma(math.i)","lgamma(complex(1.1, 2))"],seealso:["gamma"]},kldivergenceDocs={name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]},multinomialDocs={name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]},permutationsDocs={name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]},pickRandomDocs={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]},randomDocs={name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]},randomIntDocs={name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]},compareDocs={name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]},compareNaturalDocs={name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]},compareTextDocs={name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]},deepEqualDocs={name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]},equalDocs={name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]},equalTextDocs={name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]},largerDocs={name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]},largerEqDocs={name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]},smallerDocs={name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]},smallerEqDocs={name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]},unequalDocs={name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]},setCartesianDocs={name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]},setDifferenceDocs={name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]},setDistinctDocs={name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]},setIntersectDocs={name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]},setIsSubsetDocs={name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]},setMultiplicityDocs={name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]},setPowersetDocs={name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]},setSizeDocs={name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]},setSymDifferenceDocs={name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]},setUnionDocs={name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]},erfDocs={name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]},madDocs={name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]},maxDocs={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]},meanDocs={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]},medianDocs={name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]},minDocs={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]},modeDocs={name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]},prodDocs={name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]},quantileSeqDocs={name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.",examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","variance"]},stdDocs={name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","prod","sum","variance"]},cumSumDocs={name:"cumsum",category:"Statistics",syntax:["cumsum(a, b, c, ...)","cumsum(A)"],description:"Compute the cumulative sum of all values.",examples:["cumsum(2, 3, 4, 1)","cumsum([2, 3, 4, 1])","cumsum([1, 2; 3, 4])","cumsum([1, 2; 3, 4], 1)","cumsum([1, 2; 3, 4], 2)"],seealso:["max","mean","median","min","prod","std","sum","variance"]},sumDocs={name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","variance"]},varianceDocs={name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, normalization)"],description:'Compute the variance of all values. 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N("^","pow",[e.args[0].cloneDeep(),new x(a-1)]);e=new N("*","multiply",[s,u])}else e=new N("*","multiply",[e.args[0],e.args[0].cloneDeep()]);i&&("content"===r?t.content=e:t.args[r]=e)}}if("ParenthesisNode"===n)S(e.content,e,"content");else if("ConstantNode"!==n&&"SymbolNode"!==n)for(var c=0;cn&&(t[c]=0),t[c]+=o.cte*("+"===o.oper?1:-1),void(n=Math.max(c,n))}o.cte=c,""===o.fire&&(t[0]+=o.cte*("+"===o.oper?1:-1))}}(e,null,r);for(var a,o=!0,s=n=t.length-1;s>=0;s--)if(0!==t[s]){var u=new x(o?t[s]:Math.abs(t[s])),c=t[s]<0?"-":"+";if(s>0){var l=new $(i);if(s>1){var f=new x(s);l=new N("^","pow",[l,f])}u=-1===t[s]&&o?new N("-","unaryMinus",[l]):1===Math.abs(t[s])?l:new N("*","multiply",[u,l])}a=o?u:"+"===c?new N("+","add",[a,u]):new N("-","subtract",[a,u]),o=!1}return o?new x(0):a}})),name$j="reviver",dependencies$j=["classes"],createReviver=factory(name$j,dependencies$j,(e=>{var{classes:t}=e;return function(e,r){var n=t[r&&r.mathjs];return n&&"function"==typeof n.fromJSON?n.fromJSON(r):r}})),name$i="replacer",dependencies$i=[],createReplacer=factory(name$i,dependencies$i,(()=>function(e,t){return"number"!=typeof t||isFinite(t)&&!isNaN(t)?t:{mathjs:"number",value:String(t)}})),version$2="10.6.4",createTrue=factory("true",[],(()=>!0)),createFalse=factory("false",[],(()=>!1)),createNull=factory("null",[],(()=>null)),createInfinity=recreateFactory("Infinity",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1/0):1/0})),createNaN=recreateFactory("NaN",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(NaN):NaN})),createPi=recreateFactory("pi",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberPi(r):pi$1})),createTau=recreateFactory("tau",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberTau(r):tau$1})),createE=recreateFactory("e",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberE(r):e$1})),createPhi=recreateFactory("phi",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberPhi(r):phi$1})),createLN2=recreateFactory("LN2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(2).ln():Math.LN2})),createLN10=recreateFactory("LN10",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(10).ln():Math.LN10})),createLOG2E=recreateFactory("LOG2E",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1).div(new r(2).ln()):Math.LOG2E})),createLOG10E=recreateFactory("LOG10E",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1).div(new r(10).ln()):Math.LOG10E})),createSQRT1_2=recreateFactory("SQRT1_2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r("0.5").sqrt():Math.SQRT1_2})),createSQRT2=recreateFactory("SQRT2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(2).sqrt():Math.SQRT2})),createI=recreateFactory("i",["Complex"],(e=>{var{Complex:t}=e;return t.I})),createUppercasePi=factory("PI",["pi"],(e=>{var{pi:t}=e;return t})),createUppercaseE=factory("E",["e"],(e=>{var{e:t}=e;return t})),createVersion=factory("version",[],(()=>version$2));function recreateFactory(e,t,r){return factory(e,t,r,{recreateOnConfigChange:!0})}var createSpeedOfLight=unitFactory("speedOfLight","299792458","m s^-1"),createGravitationConstant=unitFactory("gravitationConstant","6.67430e-11","m^3 kg^-1 s^-2"),createPlanckConstant=unitFactory("planckConstant","6.62607015e-34","J s"),createReducedPlanckConstant=unitFactory("reducedPlanckConstant","1.0545718176461565e-34","J s"),createMagneticConstant=unitFactory("magneticConstant","1.25663706212e-6","N A^-2"),createElectricConstant=unitFactory("electricConstant","8.8541878128e-12","F m^-1"),createVacuumImpedance=unitFactory("vacuumImpedance","376.730313667","ohm"),createCoulomb=unitFactory("coulomb","8.987551792261171e9","N m^2 C^-2"),createElementaryCharge=unitFactory("elementaryCharge","1.602176634e-19","C"),createBohrMagneton=unitFactory("bohrMagneton","9.2740100783e-24","J T^-1"),createConductanceQuantum=unitFactory("conductanceQuantum","7.748091729863649e-5","S"),createInverseConductanceQuantum=unitFactory("inverseConductanceQuantum","12906.403729652257","ohm"),createMagneticFluxQuantum=unitFactory("magneticFluxQuantum","2.0678338484619295e-15","Wb"),createNuclearMagneton=unitFactory("nuclearMagneton","5.0507837461e-27","J T^-1"),createKlitzing=unitFactory("klitzing","25812.807459304513","ohm"),createBohrRadius=unitFactory("bohrRadius","5.29177210903e-11","m"),createClassicalElectronRadius=unitFactory("classicalElectronRadius","2.8179403262e-15","m"),createElectronMass=unitFactory("electronMass","9.1093837015e-31","kg"),createFermiCoupling=unitFactory("fermiCoupling","1.1663787e-5","GeV^-2"),createFineStructure=numberFactory("fineStructure",.0072973525693),createHartreeEnergy=unitFactory("hartreeEnergy","4.3597447222071e-18","J"),createProtonMass=unitFactory("protonMass","1.67262192369e-27","kg"),createDeuteronMass=unitFactory("deuteronMass","3.3435830926e-27","kg"),createNeutronMass=unitFactory("neutronMass","1.6749271613e-27","kg"),createQuantumOfCirculation=unitFactory("quantumOfCirculation","3.6369475516e-4","m^2 s^-1"),createRydberg=unitFactory("rydberg","10973731.568160","m^-1"),createThomsonCrossSection=unitFactory("thomsonCrossSection","6.6524587321e-29","m^2"),createWeakMixingAngle=numberFactory("weakMixingAngle",.2229),createEfimovFactor=numberFactory("efimovFactor",22.7),createAtomicMass=unitFactory("atomicMass","1.66053906660e-27","kg"),createAvogadro=unitFactory("avogadro","6.02214076e23","mol^-1"),createBoltzmann=unitFactory("boltzmann","1.380649e-23","J K^-1"),createFaraday=unitFactory("faraday","96485.33212331001","C mol^-1"),createFirstRadiation=unitFactory("firstRadiation","3.7417718521927573e-16","W m^2"),createLoschmidt=unitFactory("loschmidt","2.686780111798444e25","m^-3"),createGasConstant=unitFactory("gasConstant","8.31446261815324","J K^-1 mol^-1"),createMolarPlanckConstant=unitFactory("molarPlanckConstant","3.990312712893431e-10","J s mol^-1"),createMolarVolume=unitFactory("molarVolume","0.022413969545014137","m^3 mol^-1"),createSackurTetrode=numberFactory("sackurTetrode",-1.16487052358),createSecondRadiation=unitFactory("secondRadiation","0.014387768775039337","m K"),createStefanBoltzmann=unitFactory("stefanBoltzmann","5.67037441918443e-8","W m^-2 K^-4"),createWienDisplacement=unitFactory("wienDisplacement","2.897771955e-3","m K"),createMolarMass=unitFactory("molarMass","0.99999999965e-3","kg mol^-1"),createMolarMassC12=unitFactory("molarMassC12","11.9999999958e-3","kg mol^-1"),createGravity=unitFactory("gravity","9.80665","m s^-2"),createPlanckLength=unitFactory("planckLength","1.616255e-35","m"),createPlanckMass=unitFactory("planckMass","2.176435e-8","kg"),createPlanckTime=unitFactory("planckTime","5.391245e-44","s"),createPlanckCharge=unitFactory("planckCharge","1.87554603778e-18","C"),createPlanckTemperature=unitFactory("planckTemperature","1.416785e+32","K");function unitFactory(e,t,r){return factory(e,["config","Unit","BigNumber"],(e=>{var{config:n,Unit:i,BigNumber:a}=e,o=new i("BigNumber"===n.number?new a(t):parseFloat(t),r);return o.fixPrefix=!0,o}))}function numberFactory(e,t){return factory(e,["config","BigNumber"],(e=>{var{config:r,BigNumber:n}=e;return"BigNumber"===r.number?new n(t):t}))}var name$h="apply",dependencies$h=["typed","isInteger"],createApplyTransform=factory(name$h,dependencies$h,(e=>{var{typed:t,isInteger:r}=e,n=createApply({typed:t,isInteger:r});return t("apply",{"...any":function(e){var t=e[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1));try{return n.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$g="column",dependencies$g=["typed","Index","matrix","range"],createColumnTransform=factory(name$g,dependencies$g,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e,a=createColumn({typed:t,Index:r,matrix:n,range:i});return t("column",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)&&(e[t]=r-1);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0});function compileInlineExpression(e,t,r){var n=e.filter((function(e){return isSymbolNode(e)&&!(e.name in t)&&!r.has(e.name)}))[0];if(!n)throw new Error('No undefined variable found in inline expression "'+e+'"');var i=n.name,a=createSubScope(r),o=e.compile();return function(e){return a.set(i,e),o.evaluate(a)}}var name$f="filter",dependencies$f=["typed"],createFilterTransform=factory(name$f,dependencies$f,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("filter",{"Array, function":_filter,"Matrix, function":function(e,t){return e.create(_filter(e.toArray(),t))},"Array, RegExp":filterRegExp,"Matrix, RegExp":function(e,t){return e.create(filterRegExp(e.toArray(),t))}});return r}),{isTransformFunction:!0});function _filter(e,t){var r=maxArgumentCount(t);return filter$2(e,(function(e,n,i){return 1===r?t(e):2===r?t(e,[n+1]):t(e,[n+1],i)}))}var name$e="forEach",dependencies$e=["typed"],createForEachTransform=factory(name$e,dependencies$e,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("forEach",{"Array | Matrix, function":function(e,t){var r=maxArgumentCount(t);!function n(i,a){Array.isArray(i)?forEach$1(i,(function(e,t){n(e,a.concat(t+1))})):1===r?t(i):2===r?t(i,a):t(i,a,e)}(e.valueOf(),[])}});return r}),{isTransformFunction:!0}),name$d="index",dependencies$d=["Index"],createIndexTransform=factory(name$d,dependencies$d,(e=>{var{Index:t}=e;return function(){for(var e=[],r=0,n=arguments.length;r0?0:2;else if(i&&!0===i.isSet)i=i.map((function(e){return e-1}));else if(isArray$1(i)||isMatrix(i))i=i.map((function(e){return e-1}));else if(isNumber$1(i))i--;else if(isBigNumber(i))i=i.toNumber()-1;else if("string"!=typeof i)throw new TypeError("Dimension must be an Array, Matrix, number, string, or Range");e[r]=i}var a=new t;return t.apply(a,e),a}}),{isTransformFunction:!0}),name$c="map",dependencies$c=["typed"],createMapTransform=factory(name$c,dependencies$c,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("map",{"Array, function":function(e,t){return _map(e,t,e)},"Matrix, function":function(e,t){return e.create(_map(e.valueOf(),t,e))}});return r}),{isTransformFunction:!0});function _map(e,t,r){var n=maxArgumentCount(t);return function e(i,a){return Array.isArray(i)?map$2(i,(function(t,r){return e(t,a.concat(r+1))})):1===n?t(i):2===n?t(i,a):t(i,a,r)}(e,[])}function lastDimToZeroBase(e){if(2===e.length&&isCollection(e[0])){var t=(e=e.slice())[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1))}return e}var name$b="max",dependencies$b=["typed","config","numeric","larger"],createMaxTransform=factory(name$b,dependencies$b,(e=>{var{typed:t,config:r,numeric:n,larger:i}=e,a=createMax({typed:t,config:r,numeric:n,larger:i});return t("max",{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$a="mean",dependencies$a=["typed","add","divide"],createMeanTransform=factory(name$a,dependencies$a,(e=>{var{typed:t,add:r,divide:n}=e,i=createMean({typed:t,add:r,divide:n});return t("mean",{"...any":function(e){e=lastDimToZeroBase(e);try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$9="min",dependencies$9=["typed","config","numeric","smaller"],createMinTransform=factory(name$9,dependencies$9,(e=>{var{typed:t,config:r,numeric:n,smaller:i}=e,a=createMin({typed:t,config:r,numeric:n,smaller:i});return t("min",{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$8="range",dependencies$8=["typed","config","?matrix","?bignumber","smaller","smallerEq","larger","largerEq"],createRangeTransform=factory(name$8,dependencies$8,(e=>{var{typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u}=e,c=createRange({typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u});return t("range",{"...any":function(e){return"boolean"!=typeof e[e.length-1]&&e.push(!0),c.apply(null,e)}})}),{isTransformFunction:!0}),name$7="row",dependencies$7=["typed","Index","matrix","range"],createRowTransform=factory(name$7,dependencies$7,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e,a=createRow({typed:t,Index:r,matrix:n,range:i});return t("row",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)&&(e[t]=r-1);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$6="subset",dependencies$6=["typed","matrix"],createSubsetTransform=factory(name$6,dependencies$6,(e=>{var{typed:t,matrix:r}=e,n=createSubset({typed:t,matrix:r});return t("subset",{"...any":function(e){try{return n.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$5="concat",dependencies$5=["typed","matrix","isInteger"],createConcatTransform=factory(name$5,dependencies$5,(e=>{var{typed:t,matrix:r,isInteger:n}=e,i=createConcat({typed:t,matrix:r,isInteger:n});return t("concat",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)?e[t]=r-1:isBigNumber(r)&&(e[t]=r.minus(1));try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$4="diff",dependencies$4=["typed","matrix","subtract","number","bignumber"],createDiffTransform=factory(name$4,dependencies$4,(e=>{var{typed:t,matrix:r,subtract:n,number:i,bignumber:a}=e,o=createDiff({typed:t,matrix:r,subtract:n,number:i,bignumber:a});return t(name$4,{"...any":function(e){e=lastDimToZeroBase(e);try{return o.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$3="std",dependencies$3=["typed","sqrt","variance"],createStdTransform=factory(name$3,dependencies$3,(e=>{var{typed:t,sqrt:r,variance:n}=e,i=createStd({typed:t,sqrt:r,variance:n});return t("std",{"...any":function(e){e=lastDimToZeroBase(e);try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$2="sum",dependencies$2=["typed","config","add","numeric"],createSumTransform=factory(name$2,dependencies$2,(e=>{var{typed:t,config:r,add:n,numeric:i}=e,a=createSum({typed:t,config:r,add:n,numeric:i});return t(name$2,{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$1="cumsum",dependencies$1=["typed","add","unaryPlus"],createCumSumTransform=factory(name$1,dependencies$1,(e=>{var{typed:t,add:r,unaryPlus:n}=e,i=createCumSum({typed:t,add:r,unaryPlus:n});return t(name$1,{"...any":function(e){if(2===e.length&&isCollection(e[0])){var t=e[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1))}try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name="variance",dependencies=["typed","add","subtract","multiply","divide","apply","isNaN"],createVarianceTransform=factory(name,dependencies,(e=>{var{typed:t,add:r,subtract:n,multiply:i,divide:a,apply:o,isNaN:s}=e,u=createVariance({typed:t,add:r,subtract:n,multiply:i,divide:a,apply:o,isNaN:s});return t(name,{"...any":function(e){e=lastDimToZeroBase(e);try{return u.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),allFactories=Object.freeze({__proto__:null,createTyped:createTyped,createResultSet:createResultSet,createBigNumberClass:createBigNumberClass,createComplexClass:createComplexClass,createFractionClass:createFractionClass,createRangeClass:createRangeClass,createMatrixClass:createMatrixClass,createDenseMatrixClass:createDenseMatrixClass,createClone:createClone,createIsInteger:createIsInteger,createIsNegative:createIsNegative,createIsNumeric:createIsNumeric,createHasNumericValue:createHasNumericValue,createIsPositive:createIsPositive,createIsZero:createIsZero,createIsNaN:createIsNaN,createTypeOf:createTypeOf,createEqualScalar:createEqualScalar,createSparseMatrixClass:createSparseMatrixClass,createNumber:createNumber,createString:createString,createBoolean:createBoolean,createBignumber:createBignumber,createComplex:createComplex,createFraction:createFraction,createMatrix:createMatrix,createMatrixFromFunction:createMatrixFromFunction,createMatrixFromRows:createMatrixFromRows,createMatrixFromColumns:createMatrixFromColumns,createSplitUnit:createSplitUnit,createUnaryMinus:createUnaryMinus,createUnaryPlus:createUnaryPlus,createAbs:createAbs,createApply:createApply,createAddScalar:createAddScalar,createCbrt:createCbrt,createCeil:createCeil,createCube:createCube,createExp:createExp,createExpm1:createExpm1,createFix:createFix,createFloor:createFloor,createGcd:createGcd,createLcm:createLcm,createLog10:createLog10,createLog2:createLog2,createMod:createMod,createMultiplyScalar:createMultiplyScalar,createMultiply:createMultiply,createNthRoot:createNthRoot,createSign:createSign,createSqrt:createSqrt,createSquare:createSquare,createSubtract:createSubtract,createXgcd:createXgcd,createInvmod:createInvmod,createDotMultiply:createDotMultiply,createBitAnd:createBitAnd,createBitNot:createBitNot,createBitOr:createBitOr,createBitXor:createBitXor,createArg:createArg,createConj:createConj,createIm:createIm,createRe:createRe,createNot:createNot,createOr:createOr,createXor:createXor,createConcat:createConcat,createColumn:createColumn,createCount:createCount,createCross:createCross,createDiag:createDiag,createFilter:createFilter,createFlatten:createFlatten,createForEach:createForEach,createGetMatrixDataType:createGetMatrixDataType,createIdentity:createIdentity,createKron:createKron,createMap:createMap,createDiff:createDiff,createOnes:createOnes,createRange:createRange,createReshape:createReshape,createResize:createResize,createRotate:createRotate,createRotationMatrix:createRotationMatrix,createRow:createRow,createSize:createSize,createSqueeze:createSqueeze,createSubset:createSubset,createTranspose:createTranspose,createCtranspose:createCtranspose,createZeros:createZeros,createFft:createFft,createIfft:createIfft,createErf:createErf,createMode:createMode,createProd:createProd,createFormat:createFormat,createBin:createBin,createOct:createOct,createHex:createHex,createPrint:createPrint,createTo:createTo,createIsPrime:createIsPrime,createNumeric:createNumeric,createDivideScalar:createDivideScalar,createPow:createPow,createRound:createRound,createLog:createLog,createLog1p:createLog1p,createNthRoots:createNthRoots,createDotPow:createDotPow,createDotDivide:createDotDivide,createLsolve:createLsolve,createUsolve:createUsolve,createLsolveAll:createLsolveAll,createUsolveAll:createUsolveAll,createLeftShift:createLeftShift,createRightArithShift:createRightArithShift,createRightLogShift:createRightLogShift,createAnd:createAnd,createCompare:createCompare,createCompareNatural:createCompareNatural,createCompareText:createCompareText,createEqual:createEqual,createEqualText:createEqualText,createSmaller:createSmaller,createSmallerEq:createSmallerEq,createLarger:createLarger,createLargerEq:createLargerEq,createDeepEqual:createDeepEqual,createUnequal:createUnequal,createPartitionSelect:createPartitionSelect,createSort:createSort,createMax:createMax,createMin:createMin,createImmutableDenseMatrixClass:createImmutableDenseMatrixClass,createIndexClass:createIndexClass,createFibonacciHeapClass:createFibonacciHeapClass,createSpaClass:createSpaClass,createUnitClass:createUnitClass,createUnitFunction:createUnitFunction,createSparse:createSparse,createCreateUnit:createCreateUnit,createAcos:createAcos,createAcosh:createAcosh,createAcot:createAcot,createAcoth:createAcoth,createAcsc:createAcsc,createAcsch:createAcsch,createAsec:createAsec,createAsech:createAsech,createAsin:createAsin,createAsinh:createAsinh,createAtan:createAtan,createAtan2:createAtan2,createAtanh:createAtanh,createCos:createCos,createCosh:createCosh,createCot:createCot,createCoth:createCoth,createCsc:createCsc,createCsch:createCsch,createSec:createSec,createSech:createSech,createSin:createSin,createSinh:createSinh,createTan:createTan,createTanh:createTanh,createSetCartesian:createSetCartesian,createSetDifference:createSetDifference,createSetDistinct:createSetDistinct,createSetIntersect:createSetIntersect,createSetIsSubset:createSetIsSubset,createSetMultiplicity:createSetMultiplicity,createSetPowerset:createSetPowerset,createSetSize:createSetSize,createSetSymDifference:createSetSymDifference,createSetUnion:createSetUnion,createAdd:createAdd,createHypot:createHypot,createNorm:createNorm,createDot:createDot,createTrace:createTrace,createIndex:createIndex,createNode:createNode,createAccessorNode:createAccessorNode,createArrayNode:createArrayNode,createAssignmentNode:createAssignmentNode,createBlockNode:createBlockNode,createConditionalNode:createConditionalNode,createConstantNode:createConstantNode,createFunctionAssignmentNode:createFunctionAssignmentNode,createIndexNode:createIndexNode,createObjectNode:createObjectNode,createOperatorNode:createOperatorNode,createParenthesisNode:createParenthesisNode,createRangeNode:createRangeNode,createRelationalNode:createRelationalNode,createSymbolNode:createSymbolNode,createFunctionNode:createFunctionNode,createParse:createParse,createCompile:createCompile,createEvaluate:createEvaluate,createParserClass:createParserClass,createParser:createParser,createLup:createLup,createQr:createQr,createSlu:createSlu,createLusolve:createLusolve,createHelpClass:createHelpClass,createChainClass:createChainClass,createHelp:createHelp,createChain:createChain,createDet:createDet,createInv:createInv,createPinv:createPinv,createEigs:createEigs,createExpm:createExpm,createSqrtm:createSqrtm,createDivide:createDivide,createDistance:createDistance,createIntersect:createIntersect,createSum:createSum,createCumSum:createCumSum,createMean:createMean,createMedian:createMedian,createMad:createMad,createVariance:createVariance,createQuantileSeq:createQuantileSeq,createStd:createStd,createCombinations:createCombinations,createCombinationsWithRep:createCombinationsWithRep,createGamma:createGamma,createLgamma:createLgamma,createFactorial:createFactorial,createKldivergence:createKldivergence,createMultinomial:createMultinomial,createPermutations:createPermutations,createPickRandom:createPickRandom,createRandom:createRandom,createRandomInt:createRandomInt,createStirlingS2:createStirlingS2,createBellNumbers:createBellNumbers,createCatalan:createCatalan,createComposition:createComposition,createLeafCount:createLeafCount,createSimplify:createSimplify,createSimplifyCore:createSimplifyCore,createResolve:createResolve,createSymbolicEqual:createSymbolicEqual,createDerivative:createDerivative,createRationalize:createRationalize,createReviver:createReviver,createReplacer:createReplacer,createE:createE,createUppercaseE:createUppercaseE,createFalse:createFalse,createI:createI,createInfinity:createInfinity,createLN10:createLN10,createLN2:createLN2,createLOG10E:createLOG10E,createLOG2E:createLOG2E,createNaN:createNaN,createNull:createNull,createPhi:createPhi,createPi:createPi,createUppercasePi:createUppercasePi,createSQRT1_2:createSQRT1_2,createSQRT2:createSQRT2,createTau:createTau,createTrue:createTrue,createVersion:createVersion,createAtomicMass:createAtomicMass,createAvogadro:createAvogadro,createBohrMagneton:createBohrMagneton,createBohrRadius:createBohrRadius,createBoltzmann:createBoltzmann,createClassicalElectronRadius:createClassicalElectronRadius,createConductanceQuantum:createConductanceQuantum,createCoulomb:createCoulomb,createDeuteronMass:createDeuteronMass,createEfimovFactor:createEfimovFactor,createElectricConstant:createElectricConstant,createElectronMass:createElectronMass,createElementaryCharge:createElementaryCharge,createFaraday:createFaraday,createFermiCoupling:createFermiCoupling,createFineStructure:createFineStructure,createFirstRadiation:createFirstRadiation,createGasConstant:createGasConstant,createGravitationConstant:createGravitationConstant,createGravity:createGravity,createHartreeEnergy:createHartreeEnergy,createInverseConductanceQuantum:createInverseConductanceQuantum,createKlitzing:createKlitzing,createLoschmidt:createLoschmidt,createMagneticConstant:createMagneticConstant,createMagneticFluxQuantum:createMagneticFluxQuantum,createMolarMass:createMolarMass,createMolarMassC12:createMolarMassC12,createMolarPlanckConstant:createMolarPlanckConstant,createMolarVolume:createMolarVolume,createNeutronMass:createNeutronMass,createNuclearMagneton:createNuclearMagneton,createPlanckCharge:createPlanckCharge,createPlanckConstant:createPlanckConstant,createPlanckLength:createPlanckLength,createPlanckMass:createPlanckMass,createPlanckTemperature:createPlanckTemperature,createPlanckTime:createPlanckTime,createProtonMass:createProtonMass,createQuantumOfCirculation:createQuantumOfCirculation,createReducedPlanckConstant:createReducedPlanckConstant,createRydberg:createRydberg,createSackurTetrode:createSackurTetrode,createSecondRadiation:createSecondRadiation,createSpeedOfLight:createSpeedOfLight,createStefanBoltzmann:createStefanBoltzmann,createThomsonCrossSection:createThomsonCrossSection,createVacuumImpedance:createVacuumImpedance,createWeakMixingAngle:createWeakMixingAngle,createWienDisplacement:createWienDisplacement,createApplyTransform:createApplyTransform,createColumnTransform:createColumnTransform,createFilterTransform:createFilterTransform,createForEachTransform:createForEachTransform,createIndexTransform:createIndexTransform,createMapTransform:createMapTransform,createMaxTransform:createMaxTransform,createMeanTransform:createMeanTransform,createMinTransform:createMinTransform,createRangeTransform:createRangeTransform,createRowTransform:createRowTransform,createSubsetTransform:createSubsetTransform,createConcatTransform:createConcatTransform,createDiffTransform:createDiffTransform,createStdTransform:createStdTransform,createSumTransform:createSumTransform,createCumSumTransform:createCumSumTransform,createVarianceTransform:createVarianceTransform}),BigNumber=createBigNumberClass({config:config$2}),Complex=createComplexClass({}),e=createE({BigNumber:BigNumber,config:config$2}),_false=createFalse({}),fineStructure=createFineStructure({BigNumber:BigNumber,config:config$2}),Fraction=createFractionClass({}),i=createI({Complex:Complex}),_Infinity=createInfinity({BigNumber:BigNumber,config:config$2}),LN10=createLN10({BigNumber:BigNumber,config:config$2}),LOG10E=createLOG10E({BigNumber:BigNumber,config:config$2}),Matrix=createMatrixClass({}),_NaN=createNaN({BigNumber:BigNumber,config:config$2}),_null=createNull({}),phi=createPhi({BigNumber:BigNumber,config:config$2}),Range=createRangeClass({}),ResultSet=createResultSet({}),SQRT1_2=createSQRT1_2({BigNumber:BigNumber,config:config$2}),sackurTetrode=createSackurTetrode({BigNumber:BigNumber,config:config$2}),tau=createTau({BigNumber:BigNumber,config:config$2}),_true=createTrue({}),version$1=createVersion({}),DenseMatrix=createDenseMatrixClass({Matrix:Matrix}),efimovFactor=createEfimovFactor({BigNumber:BigNumber,config:config$2}),LN2=createLN2({BigNumber:BigNumber,config:config$2}),pi=createPi({BigNumber:BigNumber,config:config$2}),replacer=createReplacer({}),SQRT2=createSQRT2({BigNumber:BigNumber,config:config$2}),typed=createTyped({BigNumber:BigNumber,Complex:Complex,DenseMatrix:DenseMatrix,Fraction:Fraction}),unaryPlus=createUnaryPlus({BigNumber:BigNumber,config:config$2,typed:typed}),weakMixingAngle=createWeakMixingAngle({BigNumber:BigNumber,config:config$2}),abs$1=createAbs({typed:typed}),acos$1=createAcos({Complex:Complex,config:config$2,typed:typed}),acot$1=createAcot({BigNumber:BigNumber,typed:typed}),acsc$1=createAcsc({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),addScalar=createAddScalar({typed:typed}),arg=createArg({typed:typed}),asech$1=createAsech({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),asinh$1=createAsinh({typed:typed}),atan$1=createAtan({typed:typed}),atanh$1=createAtanh({Complex:Complex,config:config$2,typed:typed}),bignumber=createBignumber({BigNumber:BigNumber,typed:typed}),bitNot=createBitNot({typed:typed}),boolean=createBoolean({typed:typed}),clone$1=createClone({typed:typed}),combinations=createCombinations({typed:typed}),complex=createComplex({Complex:Complex,typed:typed}),conj$1=createConj({typed:typed}),cosh$1=createCosh({typed:typed}),coth$1=createCoth({BigNumber:BigNumber,typed:typed}),csc$1=createCsc({BigNumber:BigNumber,typed:typed}),cube=createCube({typed:typed}),equalScalar=createEqualScalar({config:config$2,typed:typed}),erf$1=createErf({typed:typed}),exp$1=createExp({typed:typed}),expm1=createExpm1({Complex:Complex,typed:typed}),filter$1=createFilter({typed:typed}),forEach=createForEach({typed:typed}),format=createFormat({typed:typed}),getMatrixDataType=createGetMatrixDataType({typed:typed}),hex=createHex({format:format,typed:typed}),im$1=createIm({typed:typed}),isInteger=createIsInteger({typed:typed}),isNegative=createIsNegative({typed:typed}),isPositive=createIsPositive({typed:typed}),isZero=createIsZero({typed:typed}),LOG2E=createLOG2E({BigNumber:BigNumber,config:config$2}),lgamma=createLgamma({Complex:Complex,typed:typed}),log10$1=createLog10({Complex:Complex,config:config$2,typed:typed}),log2=createLog2({Complex:Complex,config:config$2,typed:typed}),map$1=createMap({typed:typed}),multiplyScalar=createMultiplyScalar({typed:typed}),not=createNot({typed:typed}),number=createNumber({typed:typed}),oct=createOct({format:format,typed:typed}),pickRandom=createPickRandom({config:config$2,typed:typed}),print=createPrint({typed:typed}),random$1=createRandom({config:config$2,typed:typed}),re$1=createRe({typed:typed}),sec$1=createSec({BigNumber:BigNumber,typed:typed}),sign$1=createSign({BigNumber:BigNumber,Fraction:Fraction,complex:complex,typed:typed}),sin$1=createSin({typed:typed}),SparseMatrix=createSparseMatrixClass({Matrix:Matrix,equalScalar:equalScalar,typed:typed}),splitUnit=createSplitUnit({typed:typed}),square=createSquare({typed:typed}),string=createString({typed:typed}),tan$1=createTan({typed:typed}),typeOf=createTypeOf({typed:typed}),acosh$1=createAcosh({Complex:Complex,config:config$2,typed:typed}),acsch$1=createAcsch({BigNumber:BigNumber,typed:typed}),apply=createApply({isInteger:isInteger,typed:typed}),asec$1=createAsec({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),bin=createBin({format:format,typed:typed}),combinationsWithRep=createCombinationsWithRep({typed:typed}),cos$1=createCos({typed:typed}),csch$1=createCsch({BigNumber:BigNumber,typed:typed}),isNaN$2=createIsNaN({typed:typed}),isPrime=createIsPrime({typed:typed}),randomInt=createRandomInt({config:config$2,typed:typed}),sech$1=createSech({BigNumber:BigNumber,typed:typed}),sinh$1=createSinh({typed:typed}),sparse=createSparse({SparseMatrix:SparseMatrix,typed:typed}),sqrt$1=createSqrt({Complex:Complex,config:config$2,typed:typed}),tanh$1=createTanh({typed:typed}),unaryMinus=createUnaryMinus({typed:typed}),acoth$1=createAcoth({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),cot$1=createCot({BigNumber:BigNumber,typed:typed}),fraction=createFraction({Fraction:Fraction,typed:typed}),isNumeric=createIsNumeric({typed:typed}),matrix$2=createMatrix({DenseMatrix:DenseMatrix,Matrix:Matrix,SparseMatrix:SparseMatrix,typed:typed}),matrixFromFunction=createMatrixFromFunction({isZero:isZero,matrix:matrix$2,typed:typed}),mod$1=createMod({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),nthRoot=createNthRoot({BigNumber:BigNumber,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),numeric=createNumeric({bignumber:bignumber,fraction:fraction,number:number}),or=createOr({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),prod=createProd({config:config$2,multiplyScalar:multiplyScalar,numeric:numeric,typed:typed}),reshape=createReshape({isInteger:isInteger,matrix:matrix$2,typed:typed}),size$1=createSize({matrix:matrix$2,config:config$2,typed:typed}),smaller=createSmaller({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),squeeze=createSqueeze({matrix:matrix$2,typed:typed}),subset=createSubset({matrix:matrix$2,typed:typed}),subtract$1=createSubtract({DenseMatrix:DenseMatrix,addScalar:addScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed,unaryMinus:unaryMinus}),to=createTo({matrix:matrix$2,typed:typed}),transpose=createTranspose({matrix:matrix$2,typed:typed}),xgcd=createXgcd({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),zeros=createZeros({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),and=createAnd({equalScalar:equalScalar,matrix:matrix$2,not:not,typed:typed,zeros:zeros}),bitAnd=createBitAnd({equalScalar:equalScalar,matrix:matrix$2,typed:typed}),bitXor=createBitXor({DenseMatrix:DenseMatrix,matrix:matrix$2,typed:typed}),cbrt=createCbrt({BigNumber:BigNumber,Complex:Complex,Fraction:Fraction,config:config$2,isNegative:isNegative,matrix:matrix$2,typed:typed,unaryMinus:unaryMinus}),compare=createCompare({BigNumber:BigNumber,DenseMatrix:DenseMatrix,Fraction:Fraction,config:config$2,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),compareText=createCompareText({matrix:matrix$2,typed:typed}),concat=createConcat({isInteger:isInteger,matrix:matrix$2,typed:typed}),count=createCount({prod:prod,size:size$1,typed:typed}),ctranspose=createCtranspose({conj:conj$1,transpose:transpose,typed:typed}),diag=createDiag({DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,matrix:matrix$2,typed:typed}),divideScalar=createDivideScalar({numeric:numeric,typed:typed}),dotDivide=createDotDivide({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),equal$1=createEqual({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),fft=createFft({addScalar:addScalar,divideScalar:divideScalar,exp:exp$1,i:i,matrix:matrix$2,multiplyScalar:multiplyScalar,tau:tau,typed:typed}),flatten$3=createFlatten({matrix:matrix$2,typed:typed}),gcd=createGcd({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),hasNumericValue=createHasNumericValue({isNumeric:isNumeric,typed:typed}),hypot=createHypot({abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,isPositive:isPositive,multiplyScalar:multiplyScalar,smaller:smaller,sqrt:sqrt$1,typed:typed}),ifft=createIfft({conj:conj$1,dotDivide:dotDivide,fft:fft,typed:typed}),kron=createKron({matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),largerEq=createLargerEq({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),leftShift=createLeftShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),lsolve=createLsolve({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),matrixFromColumns=createMatrixFromColumns({flatten:flatten$3,matrix:matrix$2,size:size$1,typed:typed}),min$1=createMin({config:config$2,numeric:numeric,smaller:smaller,typed:typed}),mode=createMode({isNaN:isNaN$2,isNumeric:isNumeric,typed:typed}),nthRoots=createNthRoots({Complex:Complex,config:config$2,divideScalar:divideScalar,typed:typed}),ones=createOnes({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),partitionSelect=createPartitionSelect({compare:compare,isNaN:isNaN$2,isNumeric:isNumeric,typed:typed}),resize=createResize({config:config$2,matrix:matrix$2}),rightArithShift=createRightArithShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),round$1=createRound({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),smallerEq=createSmallerEq({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),unequal=createUnequal({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),usolve=createUsolve({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),xor=createXor({DenseMatrix:DenseMatrix,matrix:matrix$2,typed:typed}),add$1=createAdd({DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,addScalar:addScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),atan2$1=createAtan2({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),bitOr=createBitOr({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),catalan=createCatalan({addScalar:addScalar,combinations:combinations,divideScalar:divideScalar,isInteger:isInteger,isNegative:isNegative,multiplyScalar:multiplyScalar,typed:typed}),compareNatural=createCompareNatural({compare:compare,typed:typed}),cumsum=createCumSum({add:add$1,typed:typed,unaryPlus:unaryPlus}),deepEqual=createDeepEqual({equal:equal$1,typed:typed}),diff=createDiff({matrix:matrix$2,number:number,subtract:subtract$1,typed:typed}),dot=createDot({addScalar:addScalar,conj:conj$1,multiplyScalar:multiplyScalar,size:size$1,typed:typed}),equalText=createEqualText({compareText:compareText,isZero:isZero,typed:typed}),floor=createFloor({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,round:round$1,typed:typed,zeros:zeros}),identity$1=createIdentity({BigNumber:BigNumber,DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,config:config$2,matrix:matrix$2,typed:typed}),invmod=createInvmod({BigNumber:BigNumber,add:add$1,config:config$2,equal:equal$1,isInteger:isInteger,mod:mod$1,smaller:smaller,typed:typed,xgcd:xgcd}),larger=createLarger({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),log$1=createLog({Complex:Complex,config:config$2,divideScalar:divideScalar,typed:typed}),lsolveAll=createLsolveAll({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),matrixFromRows=createMatrixFromRows({flatten:flatten$3,matrix:matrix$2,size:size$1,typed:typed}),multiply$1=createMultiply({addScalar:addScalar,dot:dot,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),qr=createQr({addScalar:addScalar,complex:complex,conj:conj$1,divideScalar:divideScalar,equal:equal$1,identity:identity$1,isZero:isZero,matrix:matrix$2,multiplyScalar:multiplyScalar,sign:sign$1,sqrt:sqrt$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus,zeros:zeros}),range$1=createRange({bignumber:bignumber,matrix:matrix$2,config:config$2,larger:larger,largerEq:largerEq,smaller:smaller,smallerEq:smallerEq,typed:typed}),rightLogShift=createRightLogShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),setSize=createSetSize({compareNatural:compareNatural,typed:typed}),slu=createSlu({SparseMatrix:SparseMatrix,abs:abs$1,add:add$1,divideScalar:divideScalar,larger:larger,largerEq:largerEq,multiply:multiply$1,subtract:subtract$1,transpose:transpose,typed:typed}),sum=createSum({add:add$1,config:config$2,numeric:numeric,typed:typed}),trace=createTrace({add:add$1,matrix:matrix$2,typed:typed}),usolveAll=createUsolveAll({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),asin$1=createAsin({Complex:Complex,config:config$2,typed:typed}),ceil=createCeil({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,round:round$1,typed:typed,zeros:zeros}),composition=createComposition({addScalar:addScalar,combinations:combinations,isInteger:isInteger,isNegative:isNegative,isPositive:isPositive,larger:larger,typed:typed}),cross=createCross({matrix:matrix$2,multiply:multiply$1,subtract:subtract$1,typed:typed}),det=createDet({divideScalar:divideScalar,isZero:isZero,matrix:matrix$2,multiply:multiply$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),distance=createDistance({abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,multiplyScalar:multiplyScalar,sqrt:sqrt$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),dotMultiply=createDotMultiply({equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),FibonacciHeap=createFibonacciHeapClass({larger:larger,smaller:smaller}),fix=createFix({Complex:Complex,DenseMatrix:DenseMatrix,ceil:ceil,equalScalar:equalScalar,floor:floor,matrix:matrix$2,typed:typed,zeros:zeros}),ImmutableDenseMatrix=createImmutableDenseMatrixClass({DenseMatrix:DenseMatrix,smaller:smaller}),Index=createIndexClass({ImmutableDenseMatrix:ImmutableDenseMatrix}),intersect=createIntersect({abs:abs$1,add:add$1,addScalar:addScalar,config:config$2,divideScalar:divideScalar,equalScalar:equalScalar,flatten:flatten$3,isNumeric:isNumeric,isZero:isZero,matrix:matrix$2,multiply:multiply$1,multiplyScalar:multiplyScalar,smaller:smaller,subtract:subtract$1,typed:typed}),lcm=createLcm({equalScalar:equalScalar,matrix:matrix$2,typed:typed}),log1p=createLog1p({Complex:Complex,config:config$2,divideScalar:divideScalar,log:log$1,typed:typed}),max$1=createMax({config:config$2,larger:larger,numeric:numeric,typed:typed}),quantileSeq=createQuantileSeq({add:add$1,compare:compare,multiply:multiply$1,partitionSelect:partitionSelect,typed:typed}),row=createRow({Index:Index,matrix:matrix$2,range:range$1,typed:typed}),setCartesian=createSetCartesian({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setDistinct=createSetDistinct({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setIsSubset=createSetIsSubset({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setPowerset=createSetPowerset({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),sort=createSort({compare:compare,compareNatural:compareNatural,matrix:matrix$2,typed:typed}),column=createColumn({Index:Index,matrix:matrix$2,range:range$1,typed:typed}),index=createIndex({Index:Index,typed:typed}),inv=createInv({abs:abs$1,addScalar:addScalar,det:det,divideScalar:divideScalar,identity:identity$1,matrix:matrix$2,multiply:multiply$1,typed:typed,unaryMinus:unaryMinus}),pinv=createPinv({Complex:Complex,add:add$1,ctranspose:ctranspose,deepEqual:deepEqual,divideScalar:divideScalar,dot:dot,dotDivide:dotDivide,equal:equal$1,inv:inv,matrix:matrix$2,multiply:multiply$1,typed:typed}),pow$1=createPow({Complex:Complex,config:config$2,fraction:fraction,identity:identity$1,inv:inv,matrix:matrix$2,multiply:multiply$1,number:number,typed:typed}),setDifference=createSetDifference({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setMultiplicity=createSetMultiplicity({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),Spa=createSpaClass({FibonacciHeap:FibonacciHeap,addScalar:addScalar,equalScalar:equalScalar}),sqrtm=createSqrtm({abs:abs$1,add:add$1,identity:identity$1,inv:inv,max:max$1,multiply:multiply$1,size:size$1,sqrt:sqrt$1,subtract:subtract$1,typed:typed}),Unit=createUnitClass({BigNumber:BigNumber,Complex:Complex,Fraction:Fraction,abs:abs$1,addScalar:addScalar,config:config$2,divideScalar:divideScalar,equal:equal$1,fix:fix,format:format,isNumeric:isNumeric,multiplyScalar:multiplyScalar,number:number,pow:pow$1,round:round$1,subtract:subtract$1}),vacuumImpedance=createVacuumImpedance({BigNumber:BigNumber,Unit:Unit,config:config$2}),wienDisplacement=createWienDisplacement({BigNumber:BigNumber,Unit:Unit,config:config$2}),atomicMass=createAtomicMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),bohrMagneton=createBohrMagneton({BigNumber:BigNumber,Unit:Unit,config:config$2}),boltzmann=createBoltzmann({BigNumber:BigNumber,Unit:Unit,config:config$2}),conductanceQuantum=createConductanceQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),createUnit=createCreateUnit({Unit:Unit,typed:typed}),deuteronMass=createDeuteronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),dotPow=createDotPow({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,pow:pow$1,typed:typed}),electricConstant=createElectricConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),elementaryCharge=createElementaryCharge({BigNumber:BigNumber,Unit:Unit,config:config$2}),expm=createExpm({abs:abs$1,add:add$1,identity:identity$1,inv:inv,multiply:multiply$1,typed:typed}),faraday=createFaraday({BigNumber:BigNumber,Unit:Unit,config:config$2}),firstRadiation=createFirstRadiation({BigNumber:BigNumber,Unit:Unit,config:config$2}),gamma$1=createGamma({BigNumber:BigNumber,Complex:Complex,config:config$2,multiplyScalar:multiplyScalar,pow:pow$1,typed:typed}),gravitationConstant=createGravitationConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),hartreeEnergy=createHartreeEnergy({BigNumber:BigNumber,Unit:Unit,config:config$2}),klitzing=createKlitzing({BigNumber:BigNumber,Unit:Unit,config:config$2}),loschmidt=createLoschmidt({BigNumber:BigNumber,Unit:Unit,config:config$2}),magneticConstant=createMagneticConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarMass=createMolarMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarPlanckConstant=createMolarPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),neutronMass=createNeutronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),nuclearMagneton=createNuclearMagneton({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckCharge=createPlanckCharge({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckLength=createPlanckLength({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckTemperature=createPlanckTemperature({BigNumber:BigNumber,Unit:Unit,config:config$2}),protonMass=createProtonMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),reducedPlanckConstant=createReducedPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),rydberg=createRydberg({BigNumber:BigNumber,Unit:Unit,config:config$2}),setIntersect=createSetIntersect({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),speedOfLight=createSpeedOfLight({BigNumber:BigNumber,Unit:Unit,config:config$2}),stefanBoltzmann=createStefanBoltzmann({BigNumber:BigNumber,Unit:Unit,config:config$2}),thomsonCrossSection=createThomsonCrossSection({BigNumber:BigNumber,Unit:Unit,config:config$2}),avogadro=createAvogadro({BigNumber:BigNumber,Unit:Unit,config:config$2}),bohrRadius=createBohrRadius({BigNumber:BigNumber,Unit:Unit,config:config$2}),coulomb=createCoulomb({BigNumber:BigNumber,Unit:Unit,config:config$2}),divide$1=createDivide({divideScalar:divideScalar,equalScalar:equalScalar,inv:inv,matrix:matrix$2,multiply:multiply$1,typed:typed}),electronMass=createElectronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),factorial$1=createFactorial({gamma:gamma$1,typed:typed}),gravity=createGravity({BigNumber:BigNumber,Unit:Unit,config:config$2}),inverseConductanceQuantum=createInverseConductanceQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),lup=createLup({DenseMatrix:DenseMatrix,Spa:Spa,SparseMatrix:SparseMatrix,abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,equalScalar:equalScalar,larger:larger,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),magneticFluxQuantum=createMagneticFluxQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarMassC12=createMolarMassC12({BigNumber:BigNumber,Unit:Unit,config:config$2}),multinomial=createMultinomial({add:add$1,divide:divide$1,factorial:factorial$1,isInteger:isInteger,isPositive:isPositive,multiply:multiply$1,typed:typed}),permutations=createPermutations({factorial:factorial$1,typed:typed}),planckMass=createPlanckMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),quantumOfCirculation=createQuantumOfCirculation({BigNumber:BigNumber,Unit:Unit,config:config$2}),secondRadiation=createSecondRadiation({BigNumber:BigNumber,Unit:Unit,config:config$2}),stirlingS2=createStirlingS2({bignumber:bignumber,addScalar:addScalar,combinations:combinations,divideScalar:divideScalar,factorial:factorial$1,isInteger:isInteger,isNegative:isNegative,larger:larger,multiplyScalar:multiplyScalar,number:number,pow:pow$1,subtract:subtract$1,typed:typed}),unit=createUnitFunction({Unit:Unit,typed:typed}),bellNumbers=createBellNumbers({addScalar:addScalar,isInteger:isInteger,isNegative:isNegative,stirlingS2:stirlingS2,typed:typed}),eigs=createEigs({abs:abs$1,add:add$1,addScalar:addScalar,atan:atan$1,bignumber:bignumber,column:column,complex:complex,config:config$2,cos:cos$1,diag:diag,divideScalar:divideScalar,dot:dot,equal:equal$1,flatten:flatten$3,im:im$1,inv:inv,larger:larger,matrix:matrix$2,matrixFromColumns:matrixFromColumns,multiply:multiply$1,multiplyScalar:multiplyScalar,number:number,qr:qr,re:re$1,sin:sin$1,smaller:smaller,sqrt:sqrt$1,subtract:subtract$1,typed:typed,usolve:usolve,usolveAll:usolveAll}),fermiCoupling=createFermiCoupling({BigNumber:BigNumber,Unit:Unit,config:config$2}),mean=createMean({add:add$1,divide:divide$1,typed:typed}),molarVolume=createMolarVolume({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckConstant=createPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),setSymDifference=createSetSymDifference({Index:Index,concat:concat,setDifference:setDifference,size:size$1,subset:subset,typed:typed}),classicalElectronRadius=createClassicalElectronRadius({BigNumber:BigNumber,Unit:Unit,config:config$2}),lusolve=createLusolve({DenseMatrix:DenseMatrix,lsolve:lsolve,lup:lup,matrix:matrix$2,slu:slu,typed:typed,usolve:usolve}),median=createMedian({add:add$1,compare:compare,divide:divide$1,partitionSelect:partitionSelect,typed:typed}),setUnion=createSetUnion({Index:Index,concat:concat,setIntersect:setIntersect,setSymDifference:setSymDifference,size:size$1,subset:subset,typed:typed}),variance=createVariance({add:add$1,apply:apply,divide:divide$1,isNaN:isNaN$2,multiply:multiply$1,subtract:subtract$1,typed:typed}),kldivergence=createKldivergence({divide:divide$1,dotDivide:dotDivide,isNumeric:isNumeric,log:log$1,matrix:matrix$2,multiply:multiply$1,sum:sum,typed:typed}),norm=createNorm({abs:abs$1,add:add$1,conj:conj$1,ctranspose:ctranspose,eigs:eigs,equalScalar:equalScalar,larger:larger,matrix:matrix$2,multiply:multiply$1,pow:pow$1,smaller:smaller,sqrt:sqrt$1,typed:typed}),planckTime=createPlanckTime({BigNumber:BigNumber,Unit:Unit,config:config$2}),rotationMatrix=createRotationMatrix({BigNumber:BigNumber,DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,addScalar:addScalar,config:config$2,cos:cos$1,matrix:matrix$2,multiplyScalar:multiplyScalar,norm:norm,sin:sin$1,typed:typed,unaryMinus:unaryMinus}),gasConstant=createGasConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),std=createStd({sqrt:sqrt$1,typed:typed,variance:variance}),mad=createMad({abs:abs$1,map:map$1,median:median,subtract:subtract$1,typed:typed}),rotate=createRotate({multiply:multiply$1,rotationMatrix:rotationMatrix,typed:typed}),math$2={},mathWithTransform={},classes={},Chain=createChainClass({math:math$2}),Node=createNode({mathWithTransform:mathWithTransform}),ObjectNode=createObjectNode({Node:Node}),OperatorNode=createOperatorNode({Node:Node}),ParenthesisNode=createParenthesisNode({Node:Node}),RelationalNode=createRelationalNode({Node:Node}),ArrayNode=createArrayNode({Node:Node}),BlockNode=createBlockNode({Node:Node,ResultSet:ResultSet}),ConditionalNode=createConditionalNode({Node:Node}),ConstantNode=createConstantNode({Node:Node}),RangeNode=createRangeNode({Node:Node}),reviver=createReviver({classes:classes}),chain$1=createChain({Chain:Chain,typed:typed}),FunctionAssignmentNode=createFunctionAssignmentNode({Node:Node,typed:typed}),AccessorNode=createAccessorNode({Node:Node,subset:subset}),AssignmentNode=createAssignmentNode({matrix:matrix$2,Node:Node,subset:subset}),IndexNode=createIndexNode({Node:Node,size:size$1}),SymbolNode=createSymbolNode({Unit:Unit,Node:Node,math:math$2}),FunctionNode=createFunctionNode({Node:Node,SymbolNode:SymbolNode,math:math$2}),parse$2=createParse({AccessorNode:AccessorNode,ArrayNode:ArrayNode,AssignmentNode:AssignmentNode,BlockNode:BlockNode,ConditionalNode:ConditionalNode,ConstantNode:ConstantNode,FunctionAssignmentNode:FunctionAssignmentNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,RangeNode:RangeNode,RelationalNode:RelationalNode,SymbolNode:SymbolNode,config:config$2,numeric:numeric,typed:typed}),resolve=createResolve({ConstantNode:ConstantNode,FunctionNode:FunctionNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,parse:parse$2}),simplifyCore=createSimplifyCore({AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,divide:divide$1,equal:equal$1,isZero:isZero,multiply:multiply$1,pow:pow$1,subtract:subtract$1}),compile=createCompile({parse:parse$2,typed:typed}),Help=createHelpClass({parse:parse$2}),leafCount=createLeafCount({parse:parse$2,typed:typed}),simplify$2=createSimplify({bignumber:bignumber,fraction:fraction,AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,config:config$2,divide:divide$1,equal:equal$1,isZero:isZero,mathWithTransform:mathWithTransform,matrix:matrix$2,multiply:multiply$1,parse:parse$2,pow:pow$1,resolve:resolve,simplifyCore:simplifyCore,subtract:subtract$1,typed:typed}),symbolicEqual=createSymbolicEqual({OperatorNode:OperatorNode,parse:parse$2,simplify:simplify$2,typed:typed}),evaluate$1=createEvaluate({parse:parse$2,typed:typed}),help=createHelp({Help:Help,mathWithTransform:mathWithTransform,typed:typed}),Parser=createParserClass({evaluate:evaluate$1}),rationalize=createRationalize({bignumber:bignumber,fraction:fraction,AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,config:config$2,divide:divide$1,equal:equal$1,isZero:isZero,mathWithTransform:mathWithTransform,matrix:matrix$2,multiply:multiply$1,parse:parse$2,pow:pow$1,simplify:simplify$2,simplifyCore:simplifyCore,subtract:subtract$1,typed:typed}),derivative$1=createDerivative({ConstantNode:ConstantNode,FunctionNode:FunctionNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,config:config$2,equal:equal$1,isZero:isZero,numeric:numeric,parse:parse$2,simplify:simplify$2,typed:typed}),parser=createParser({Parser:Parser,typed:typed});_extends$1(math$2,{e:e,false:_false,fineStructure:fineStructure,i:i,Infinity:_Infinity,LN10:LN10,LOG10E:LOG10E,NaN:_NaN,null:_null,phi:phi,SQRT1_2:SQRT1_2,sackurTetrode:sackurTetrode,tau:tau,true:_true,E:e,version:version$1,efimovFactor:efimovFactor,LN2:LN2,pi:pi,replacer:replacer,reviver:reviver,SQRT2:SQRT2,typed:typed,unaryPlus:unaryPlus,PI:pi,weakMixingAngle:weakMixingAngle,abs:abs$1,acos:acos$1,acot:acot$1,acsc:acsc$1,addScalar:addScalar,arg:arg,asech:asech$1,asinh:asinh$1,atan: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o=a.length,s=Array(o+1);for(s[0]=0,r=0;r=u){if(i[l]=m[c],0===c)return;++l,s=f[--c],u=p[c]}else 0===n[o=a[r[s]]]?(n[o]=1,f[c]=s,m[++c]=o,s=t[o],p[c]=u=t[o+1]):++s},numeric.ccsLPSolve=function(e,t,r,n,i,a,o){var s=e[0],u=e[1],c=e[2];s.length;var l,f,p,m,d,h,y,g,v,x=t[0],b=t[1],_=t[2];for(f=x[i],p=x[i+1],n.length=0,l=f;la&&(o=i,a=s);for(_(v[r])=c){if(i[f]=a[d[l]],0===l)return;++f,u=p[--l],c=m[l]}else 0===n[s=r[u]]?(n[s]=1,p[l]=u,d[++l]=s,u=t[s=a[s]],m[l]=c=t[s+1]):++u}},numeric.ccsLPSolve0=function(e,t,r,n,i,a,o,s){var u=e[0],c=e[1],l=e[2];u.length;var f,p,m,d,h,y,g,v,x,b=t[0],_=t[1],w=t[2];for(p=b[i],m=b[i+1],n.length=0,f=p;fa&&(o=i,a=s);for(_(v[w[r]])r[n]&&(r[n]=t.length),t)t.hasOwnProperty(i)&&e(t[i],r,n+1);return r},numeric.sclone=function e(t,r,n){void 0===r&&(r=0),void 0===n&&(n=numeric.sdim(t).length);var i,a=Array(t.length);if(r===n-1){for(i in t)t.hasOwnProperty(i)&&(a[i]=t[i]);return a}for(i in t)t.hasOwnProperty(i)&&(a[i]=e(t[i],r+1,n));return a},numeric.sdiag=function(e){var t,r,n=e.length,i=Array(n);for(t=n-1;t>=1;t-=2)r=t-1,i[t]=[],i[t][t]=e[t],i[r]=[],i[r][r]=e[r];return 0===t&&(i[0]=[],i[0][0]=e[t]),i},numeric.sidentity=function(e){return numeric.sdiag(numeric.rep([e],1))},numeric.stranspose=function(e){var t,r,n,i=[];for(t in e.length,e)if(e.hasOwnProperty(t))for(r in n=e[t])n.hasOwnProperty(r)&&("object"!=typeof i[r]&&(i[r]=[]),i[r][t]=n[r]);return i},numeric.sLUP=function(e,t){throw new Error("The function numeric.sLUP had a bug in it and has been removed. 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numeric.sdotMM(e,t);default:throw new Error("numeric.sdot not implemented for tensors of order "+r+" and "+n)}},numeric.sscatter=function(e){var t,r,n,i,a=e[0].length,o=e.length,s=[];for(r=a-1;r>=0;--r)if(e[o-1][r]){for(i=s,n=0;n=0;--a)r[a]=[];for(a=i;a>=0;--a)r[a].push(n[a]);r[i+1].push(o)}}else e(o,r,n);return n.length>i&&n.pop(),r},numeric.cLU=function(e){var t,r,n,i,a,o,s=e[0],u=e[1],c=e[2],l=s.length,f=0;for(t=0;tf&&(f=s[t]);f++;var p,m=Array(f),d=Array(f),h=numeric.rep([f],1/0),y=numeric.rep([f],-1/0);for(n=0;ny[t]&&(y[t]=r);for(t=0;ty[t+1]&&(y[t+1]=y[t]);for(t=f-1;t>=1;t--)h[t]=0;p--){for(;c[m]>p;)i[p]-=l[m]*i[c[m]],m--;i[p]/=l[m],m--}return i},numeric.cgrid=function(e,t){"number"==typeof e&&(e=[e,e]);var r,n,i,a=numeric.rep(e,-1);if("function"!=typeof t)if("L"===t)t=function(t,r){return t>=e[0]/2||ri&&(i=a[n]);for(i++,r=numeric.rep([i],0),n=0;n1;)i[n=o((t+r)/2)]<=e?t=n:r=n;return this._at(e,t)}a=e.length;var s,u=Array(a);for(s=a-1;-1!==s;--s)u[s]=this.at(e[s]);return u},numeric.Spline.prototype.diff=function(){var e,t,r,n=this.x,i=this.yl,a=this.yr,o=this.kl,s=this.kr,u=i.length,c=o,l=s,f=Array(u),p=Array(u),m=numeric.add,d=numeric.mul,h=numeric.div,y=numeric.sub;for(e=u-1;-1!==e;--e)t=n[e+1]-n[e],r=y(a[e+1],i[e]),f[e]=h(m(d(r,6),d(o[e],-4*t),d(s[e+1],-2*t)),t*t),p[e+1]=h(m(d(r,-6),d(o[e],2*t),d(s[e+1],4*t)),t*t);return new numeric.Spline(n,c,l,f,p)},numeric.Spline.prototype.roots=function(){function e(e){return e*e}var t=[],r=this.x,n=this.yl,i=this.yr,a=this.kl,o=this.kr;"number"==typeof n[0]&&(n=[n],i=[i],a=[a],o=[o]);var s,u,c,l,f,p,m,d,h,y,g,v,x,b,_,w,N,$,A,M,S,E,T,O=n.length,C=r.length-1,k=(t=Array(O),Math.sqrt);for(s=0;s!==O;++s){for(l=n[s],f=i[s],p=a[s],m=o[s],d=[],u=0;u!==C;u++){for(u>0&&f[u]*l[u]<0&&d.push(r[u]),w=r[u+1]-r[u],r[u],g=l[u],v=f[u+1],h=p[u]/w,x=(y=m[u+1]/w)+3*g+2*h-3*v,b=3*(y+h+2*(g-v)),(_=e(h-y+3*(g-v))+12*y*g)<=0?N=($=x/b)>r[u]&&$r[u]&&$r[u]&&A0)S=E,$=A;else{for(var D=0;!((T=($*E-A*S)/($-A))<=S||T>=E);)if((M=this._at(T,u))*A>0)E=T,A=M,-1===D&&($*=.5),D=-1;else{if(!(M*$>0))break;S=T,$=M,1===D&&(A*=.5),D=1}d.push(T),S=N[c+1],$=this._at(S,u)}else d.push(S),S=E,$=A;0===A&&d.push(E)}t[s]=d}return"number"==typeof this.yl[0]?t[0]:t},numeric.spline=function(e,t,r,n){var i,a=e.length,o=[],s=[],u=[],c=numeric.sub,l=numeric.mul,f=numeric.add;for(i=a-2;i>=0;i--)s[i]=e[i+1]-e[i],u[i]=c(t[i+1],t[i]);"string"!=typeof r&&"string"!=typeof n||(r=n="periodic");var p=[[],[],[]];switch(typeof r){case"undefined":o[0]=l(3/(s[0]*s[0]),u[0]),p[0].push(0,0),p[1].push(0,1),p[2].push(2/s[0],1/s[0]);break;case"string":o[0]=f(l(3/(s[a-2]*s[a-2]),u[a-2]),l(3/(s[0]*s[0]),u[0])),p[0].push(0,0,0),p[1].push(a-2,0,1),p[2].push(1/s[a-2],2/s[a-2]+2/s[0],1/s[0]);break;default:o[0]=r,p[0].push(0),p[1].push(0),p[2].push(1)}for(i=1;i20)throw new Error("Numerical gradient 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s,u,c,l,f,p,m,d,h,y,g,v,x,b=[e],_=[r],w=[n(e,r)],N=[],$=[3/40,9/40],A=[44/45,-56/15,32/9],M=[19372/6561,-25360/2187,64448/6561,-212/729],S=[9017/3168,-355/33,46732/5247,49/176,-5103/18656],E=[35/384,0,500/1113,125/192,-2187/6784,11/84],T=[.10013431883002395,0,.3918321794184259,-.02982460176594817,.05893268337240795,-.04497888809104361,5618549.5/235043384],O=[.2,.3,.8,8/9,1,1],C=[-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,1/40],k=0,D=(t-e)/10,I=0,B=numeric.add,z=numeric.mul,R=Math.min,P=Math.abs,q=numeric.norminf,L=Math.pow,F=numeric.any,j=numeric.lt,U=numeric.and;numeric.sub;var G=new numeric.Dopri(b,_,w,N,-1,"");for("function"==typeof o&&(g=o(e,r));et&&(D=t-e),s=n(e+O[0]*D,B(r,z(.2*D,w[k]))),u=n(e+O[1]*D,B(B(r,z($[0]*D,w[k])),z($[1]*D,s))),c=n(e+O[2]*D,B(B(B(r,z(A[0]*D,w[k])),z(A[1]*D,s)),z(A[2]*D,u))),l=n(e+O[3]*D,B(B(B(B(r,z(M[0]*D,w[k])),z(M[1]*D,s)),z(M[2]*D,u)),z(M[3]*D,c))),f=n(e+O[4]*D,B(B(B(B(B(r,z(S[0]*D,w[k])),z(S[1]*D,s)),z(S[2]*D,u)),z(S[3]*D,c)),z(S[4]*D,l))),p=n(e+D,h=B(B(B(B(B(r,z(w[k],D*E[0])),z(u,D*E[2])),z(c,D*E[3])),z(l,D*E[4])),z(f,D*E[5]))),(y="number"==typeof(m=B(B(B(B(B(z(w[k],D*C[0]),z(u,D*C[2])),z(c,D*C[3])),z(l,D*C[4])),z(f,D*C[5])),z(p,D*C[6])))?P(m):q(m))>i){if(e+(D=.2*D*L(i/y,.25))===e){G.msg="Step size became too small";break}}else{if(N[k]=B(B(B(B(B(B(r,z(w[k],D*T[0])),z(u,D*T[2])),z(c,D*T[3])),z(l,D*T[4])),z(f,D*T[5])),z(p,D*T[6])),b[++k]=e+D,_[k]=h,w[k]=p,"function"==typeof o){var V,Z,H=e,X=e+.5*D;if(v=o(X,N[k-1]),F(x=U(j(g,0),j(0,v)))||(H=X,g=v,v=o(X=e+D,h),x=U(j(g,0),j(0,v))),F(x)){for(var W,Q,Y=0,J=1,K=1;;){if("number"==typeof g)Z=(K*v*H-J*g*X)/(K*v-J*g);else 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t=e[0],r=e.slice(1);if("apply"===t){if("string"!=typeof r[0])throw Error("Non string functions not implemented for conversion to mathjs");if("factorial"===r[0])return new math.OperatorNode("!","factorial",[this.convert(r[1])]);let e=functionConverstions[r[0]];e||(e=r[0]);const t=new math.SymbolNode(e),n=r[1];let i;return i="tuple"===n[0]?n.slice(1).map(function(e,t){return this.convert(e)}.bind(this)):[this.convert(n)],new math.FunctionNode(t,i)}if("lts"===t||"gts"===t){const e=r[0],n=r[1];if("tuple"!==e[0]||"tuple"!==n[0])throw new Error("Badly formed ast");const i=e.slice(1).map(function(e,t){return this.convert(e)}.bind(this));let a=[];for(let r=1;r","larger",i.slice(r-1,r+1))):"lts"===t?a.push(new math.OperatorNode("<=","smallerEq",i.slice(r-1,r+1))):a.push(new math.OperatorNode(">=","largerEq",i.slice(r-1,r+1)));let o=new math.OperatorNode("and","and",a.slice(0,2));for(let e=2;e=","largerEq",[e,o])):u.push(new math.OperatorNode(">","larger",[e,o])),a[2]?u.push(new 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math.OperatorNode("and","and",p);return"notsubset"!==t&&"notsuperset"!==t||(m=new math.OperatorNode("not","not",[m])),m}if("matrix"===t){let e=r[0],t=e[1],n=e[2],i=r[1];if(!Number.isInteger(t)||!Number.isInteger(n))throw Error("Matrix must have integer dimensions");let a=[];for(let e=1;e<=t;e++){let t=[];for(let r=1;r<=n;r++)t.push(this.convert(i[e][r]));a.push(new math.ArrayNode(t))}return new math.ArrayNode(a)}if(t in operators$2)return operators$2[t](r.map(function(e,t){return this.convert(e)}.bind(this)));throw Error("Operator "+t+" not implemented for conversion to mathjs")}}var function_normalizations={ln:"log",arccos:"acos",arccosh:"acosh",arcsin:"asin",arcsinh:"asinh",arctan:"atan",arctanh:"atanh",arcsec:"asec",arcsech:"asech",arccsc:"acsc",arccsch:"acsch",arccot:"acot",arccoth:"acoth",cosec:"csc"},create_trig_inverses_for=["cos","cosh","sin","sinh","tan","tanh","sec","sech","csc","csch","cot","coth"],move_exponents_outside_for=["cos","cosh","sin","sinh","tan","tanh","sec","sech","csc","csch","cot","coth"];function normalize_function_names(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("apply"===r){if("sqrt"===n[0])return["^",normalize_function_names(n[1]),.5];var i=normalize_function_names_sub(n[0]);i=["apply",i];var a=n.slice(1).map((function(e){return normalize_function_names(e)}));return a=a.length>1?["tuple"].concat(a):a[0],i.push(a),i}return"^"===r&&"e"===n[0]&&math$1.define_e?["apply","exp",normalize_function_names(n[1])]:"binom"===r?["apply","nCr",["tuple",normalize_function_names(n[0]),normalize_function_names(n[1])]]:[r].concat(n.map((function(e){return normalize_function_names(e)})))}function normalize_function_names_sub(e){if("string"==typeof e)return e in function_normalizations?function_normalizations[e]:e;if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if("^"===t&&2===r.length&&-1===r[1]){let e=normalize_function_names_sub(r[0]);if(create_trig_inverses_for.includes(e))return"a"+e}return[t].concat(r.map((function(e){return normalize_function_names_sub(e)})))}function normalize_applied_functions(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("apply"===r){let e=n[0];if("^"===e[0]){let t=e[1],r=e[2];return-1!==r&&move_exponents_outside_for.includes(t)?["^",["apply",t,normalize_applied_functions(n[1])],r]:["apply",e,normalize_applied_functions(n[1])]}let t=0;for(;"prime"===e[0];)t+=1,e=e[1];let r=["apply",e,normalize_applied_functions(n[1])];for(let e=0;e2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_integer_ast(e,o[0],r),is_integer_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_integer_ast(a[0],n,r);if("*"===i){return!!a.every((function(e){return is_integer_ast(e,n,r)}))||void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!is_positive_ast(a[1],n,!0,r))return;if(!1===e)return!0}let t=is_integer_ast(a[0],n,r),i=is_integer_ast(a[1],n,r);if(!t)return t;if(!i)return;return!!is_positive_ast(a[1],n,!1,r)||void 0}if("+"===i){let e=0;for(let t=0;t0)return;e+=1}if(void 0===i)return}return 0===e}if("apply"===i)return!!(functions.C.Z&&functions.C.Z.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.Z&&functions.R.Z.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.Z&&functions.nonzeroC.Z.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.Z&&functions.nonneg.Z.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.Z&&functions.pos.Z.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("/"===i||"prime"===i)return;return!1}return!1}function is_real_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e)return Number.isFinite(e);var n=evaluate_to_constant(e,!1);if(null!==n)return"number"==typeof n&&Number.isFinite(n);if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}if("in"===a&&o[0]===e&&"R"===o[1])return negate_adjust(!0,s);if("notin"===a&&o[0]===e&&"R"===o[1])return negate_adjust(!1,s);if(!1===s){if("in"===a&&o[0]===e&&"Z"===o[1])return!0}else if("notin"===a&&o[0]===e&&"Z"===o[1])return!0;if("<"===a||"le"===a){let t=variables(n),r=functions$2(n);if(-1!==t.indexOf(e)&&0===r.length)return!0}if("="===a&&!s||"ne"===a&&s){let t=narrow_assumptions(i,r);if(o[0]===e)return is_real_ast(o[1],t);if(o[1]===e)return is_real_ast(o[0],t)}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_real_ast(e,o[0],r),is_real_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_real_ast(a[0],n,r);if("*"===i||"+"===i){if(a.length>2&&(a=(e=unflattenRight(e)).slice(1)),"*"===i&&(!1===is_nonzero_ast(a[0],n,r)||!1===is_nonzero_ast(a[1],n,r)))return!0;let t=is_real_ast(a[0],n,r),o=is_real_ast(a[1],n,r);return!(!t||!o)||!(t&&!1===o||o&&!1===t)&&void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r),t=is_positive_ast(a[1],n,!0,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!t)return;if(!1===e)return!0}let i=is_real_ast(a[0],n,r),o=is_real_ast(a[1],n,r);if(!i||!o)return;if(!is_positive_ast(a[0],n,!1,r)){return!!is_integer_ast(a[1],n,r)||void 0}return!!is_positive_ast(a[0],n,!0,r)||(!!t||void 0)}if("/"===i){if(!is_nonzero_ast(a[1],n,r))return;if(!1===is_nonzero_ast(a[0],n,r))return!0;if(!is_real_ast(a[0],n,r)||!is_real_ast(a[1],n,r))return;return!0}if("apply"===i)return!!(functions.C.R&&functions.C.R.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.R&&functions.R.R.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.R&&functions.nonzeroC.R.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.R&&functions.nonneg.R.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.R&&functions.pos.R.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("prime"===i)return;return!1}return!1}function is_complex_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e)return Number.isFinite(e);var n=evaluate_to_constant(e,!1);if(null!==n)return"number"==typeof n?Number.isFinite(n):!(void 0===n.re||!Number.isFinite(n.re)||void 0===n.im||!Number.isFinite(n.im));if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}if("in"===a&&o[0]===e&&"C"===o[1])return negate_adjust(!0,s);if("notin"===a&&o[0]===e&&"C"===o[1])return negate_adjust(!1,s);if(!1===s){if("in"===a){if(o[0]===e&&"Z"===o[1])return!0;if(o[0]===e&&"R"===o[1])return!0}}else if("notin"===a){if(o[0]===e&&"Z"===o[1])return!0;if(o[0]===e&&"R"===o[1])return!0}if("<"===a||"le"===a){let t=variables(n),r=functions$2(n);if(-1!==t.indexOf(e)&&0===r.length)return!0}if("="===a&&!s||"ne"===a&&s){let t=narrow_assumptions(i,r);if(o[0]===e)return is_complex_ast(o[1],t);if(o[1]===e)return is_complex_ast(o[0],t)}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_complex_ast(e,o[0],r),is_complex_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_complex_ast(a[0],n,r);if("*"===i||"+"===i){if("*"===i&&!a.every((e=>!1!==is_nonzero_ast(e,n,r))))return!0;return!!a.every((e=>is_complex_ast(e,n,r)))||void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r),t=is_positive_ast(a[1],n,!0,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!t)return;if(!1===e)return!0}let i=is_complex_ast(a[0],n,r),o=is_complex_ast(a[1],n,r);return!(!i||!o)||void 0}if("/"===i){if(!is_nonzero_ast(a[1],n,r))return;if(!1===is_nonzero_ast(a[0],n,r))return!0;if(!is_complex_ast(a[0],n,r)||!is_complex_ast(a[1],n,r))return;return!0}if("apply"===i)return!!(functions.C.C&&functions.C.C.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.C&&functions.R.C.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.C&&functions.nonzeroC.C.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.C&&functions.nonneg.C.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.C&&functions.pos.C.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("prime"===i)return;return!1}return!1}function is_nonzero_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e){if(Number.isFinite(e))return 0!==e;if(Number.isNaN(e))return;return!0}var n=evaluate_to_constant(e,!1);if(null!==n){if("number"==typeof n){if(Number.isFinite(n))return 0!==n;if(Number.isNaN(n))return;return!0}return void 0!==n.re&&void 0!==n.im&&(0!==n.re||0!==n.im)||void 0}if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}let u=narrow_assumptions(i,r);if("="===a&&!s||"ne"===a&&s){if(o[0]===e)return is_nonzero_ast(o[1],u);if(o[1]===e)return is_nonzero_ast(o[0],u)}if("ne"===a&&!s||"="===a&&s){if(o[0]===e&&!1===is_nonzero_ast(o[1],u))return!0;if(o[1]===e&&!1===is_nonzero_ast(o[0],u))return!0}if("<"===a)if(s){if(o[0]===e&&is_positive_ast(o[1],u,!0))return!0;if(o[1]===e&&is_negative_ast(o[0],u,!0))return!0}else{if(o[0]===e&&is_negative_ast(o[1],u,!1))return!0;if(o[1]===e&&is_positive_ast(o[0],u,!1))return!0}if("le"===a)if(s){if(o[0]===e&&is_positive_ast(o[1],u,!1))return!0;if(o[1]===e&&is_negative_ast(o[0],u,!1))return!0}else{if(o[0]===e&&is_negative_ast(o[1],u,!0))return!0;if(o[1]===e&&is_positive_ast(o[0],u,!0))return!0}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_nonzero_ast(e,o[0],r),is_nonzero_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_nonzero_ast(a[0],n,r);if("+"===i){if(a.length>2&&(a=(e=unflattenRight(e)).slice(1)),equal(a[0],simplify(["-",a[1]],r)))return!1;let t=is_nonzero_ast(a[0],n,r),i=is_nonzero_ast(a[1],n,r);if(!1===t)return i;if(!1===i)return t;let o=is_real_ast(a[0],n,r),s=is_real_ast(a[1],n,r);if(!o||!s)return!0===o?!1===s||void 0:!0===s&&!1===o||void 0;let u=is_positive_ast(a[0],n,!1,r),c=is_positive_ast(a[1],n,!1,r),l=is_positive_ast(a[0],n,!0,r),f=is_positive_ast(a[1],n,!0,r);return!!(u&&f||l&&c)||(!1===u&&!1===f||!1===l&&!1===c||void 0)}if("*"===i){let e=!0;for(let t=0;t0:e>=0);var i=is_real_ast(e,t,n);if(!i)return i;var a=evaluate_to_constant(e,!1);if(null!==a)return"number"==typeof a&&(!!Number.isFinite(a)&&(r?a>0:a>=0));if("string"==typeof e){let i;if(i=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(i))return;let a=i,o=i[0],s=i.slice(1),u=!1;for(;"not"===o;){if(u=!u,i=s[0],!Array.isArray(i))return;o=i[0],s=i.slice(1)}let c=narrow_assumptions(a,n);if("="===o&&!u||"ne"===o&&u){if(s[0]===e)return is_positive_ast(s[1],c,r);if(s[1]===e)return is_positive_ast(s[0],c,r)}if("<"===o)if(u){if(s[0]===e&&is_positive_ast(s[1],c,r))return!0;if(s[1]===e&&is_negative_ast(s[0],c,!r))return!1}else{if(s[0]===e&&is_negative_ast(s[1],c,!1))return!1;if(s[1]===e&&is_positive_ast(s[0],c,!1))return!0}if("le"===o)if(u){if(s[0]===e&&is_positive_ast(s[1],c,!1))return!0;if(s[1]===e&&is_negative_ast(s[0],c,!1))return!1}else{if(s[0]===e&&is_negative_ast(s[1],c,!r))return!1;if(s[1]===e&&is_positive_ast(s[0],c,r))return!0}if("and"!==o&&"or"!==o)return;if(u)return;return s.length>2&&(i=unflattenRight(i),s=i.slice(1)),simple_assumption_combination(o,is_positive_ast(e,s[0],r,n),is_positive_ast(e,s[1],r,n))}if(Array.isArray(e)){let i;i=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let a=e[0],o=e.slice(1);if("-"===a)return is_negative_ast(o[0],i,r,n);if("+"===a){o.length>2&&(o=(e=unflattenRight(e)).slice(1));let t=is_positive_ast(o[0],i,!1,n),a=is_positive_ast(o[1],i,!1,n),s=is_positive_ast(o[0],i,!0,n),u=is_positive_ast(o[1],i,!0,n);if(r){if(t&&u||s&&a)return!0}else if(t&&a)return!0;if(r){if(!1===s&&!1===u)return!1}else if(!1===t&&!1===u||!1===s&&!1===a)return!1;return}if("*"===a){if(!o.every((e=>!1!==is_nonzero_ast(e,i,n))))return!r;o.length>2&&(o=(e=unflattenRight(e)).slice(1));let t=is_real_ast(o[0],i,n),a=is_real_ast(o[1],i,n);if(void 0===t||void 0===a)return;if(!1===t)return!1===a&&void 0;if(!1===a)return!1;let s=is_positive_ast(o[0],i,!1,n),u=is_positive_ast(o[1],i,!1,n),c=is_positive_ast(o[0],i,!0,n),l=is_positive_ast(o[1],i,!0,n);if(r){if(c&&l||!1===s&&!1===u)return!0;if(!1===c&&u||s&&!1===l)return!1}else{if(s&&u||!1===c&&!1===l)return!0;if(c&&!1===u||!1===s&&l)return!1}return}if("/"===a){if(!is_nonzero_ast(o[1],i,n))return;if(!1===is_nonzero_ast(o[0],i,n))return!r;let e=is_positive_ast(o[1],i,!0,n);if(void 0===e)return;let t=e?r:!r,a=is_positive_ast(o[0],i,t,n);if(void 0===a)return;return!0===a?!0===e:!0!==e}if("^"===a){let e=is_nonzero_ast(o[0],i,n);if(e){if(!1===is_nonzero_ast(o[1],i,n)){if(o[0]===1/0||o[0]===-1/0)return;return!0}}else{if(!is_positive_ast(o[1],i,!0,n))return;if(!1===e)return!r;if(r)return}if(!0!==is_real_ast(o[0],i,n))return;if(!is_positive_ast(o[0],i,r,n)){return!!is_integer_ast(simplify(["/",o[1],2],n),i,n)||void 0}return!!is_real_ast(o[1],i,n)||void 0}if("apply"===a&&!r)return!!(functions.C.nonneg&&functions.C.nonneg.includes(o[0])&&is_complex_ast(o[1],i,n))||(!!(functions.R.nonneg&&functions.R.nonneg.includes(o[0])&&is_real_ast(o[1],i,n))||(!!(functions.nonzeroC.nonneg&&functions.nonzeroC.nonneg.includes(o[0])&&is_nonzero_ast(o[1],i,n)&&is_complex_ast(o[1],i,n))||(!!(functions.nonneg.nonneg&&functions.nonneg.nonneg.includes(o[0])&&is_positive_ast(o[1],i,!1,n))||(!!(functions.pos.nonneg&&functions.pos.nonneg.includes(o[0])&&is_positive_ast(o[1],i,!0,n))||void 0))));if("apply"===a&&r)return!!(functions.C.pos&&functions.C.pos.includes(o[0])&&is_complex_ast(o[1],i,n))||(!!(functions.R.pos&&functions.R.pos.includes(o[0])&&is_real_ast(o[1],i,n))||(!!(functions.nonzeroC.pos&&functions.nonzeroC.pos.includes(o[0])&&is_nonzero_ast(o[1],i,n)&&is_complex_ast(o[1],i,n))||(!!(functions.nonneg.pos&&functions.nonneg.pos.includes(o[0])&&is_positive_ast(o[1],i,!1,n))||(!!(functions.pos.pos&&functions.pos.pos.includes(o[0])&&is_positive_ast(o[1],i,!0,n))||void 0))));if("prime"===a)return;return!1}return!1}function is_negative_ast(e,t,r,n){void 0===r&&(r=!0);var i=is_real_ast(e,t,n);if(!0===i){let i=is_positive_ast(e,t,!r,n);return!1===i||!0!==i&&void 0}return i}function tuples_to_vectors(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("tuple"===r){return["vector"].concat(n.map((function(e,t){return tuples_to_vectors(e)})))}if("apply"===r){if("tuple"===n[1][0]){let e=tuples_to_vectors(n[0]),t=n[1].slice(1);return["apply",e,["tuple"].concat(t.map((function(e,t){return tuples_to_vectors(e)})))]}}else if("gts"===r||"lts"===r||"interval"===r){let e=n[0],t=n[1];if("tuple"!==e[0]||"tuple"!==t[0])throw new Error("Badly formed ast");return[r,["tuple"].concat(e.slice(1).map((function(e,t){return tuples_to_vectors(e)}))),t]}return[r].concat(n.map((function(e,t){return tuples_to_vectors(e)})))}function to_intervals(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("tuple"===r&&2===n.length){let e=["tuple"].concat(n.map((function(e,t){return to_intervals(e)})));return e=["interval",e,["tuple",!1,!1]],e}if("array"===r&&2===n.length){let e=["tuple"].concat(n.map((function(e,t){return to_intervals(e)})));return e=["interval",e,["tuple",!0,!0]],e}if("apply"===r){if("tuple"===n[1][0]){let e=to_intervals(n[0]),t=n[1].slice(1);return["apply",e,["tuple"].concat(t.map((function(e,t){return to_intervals(e)})))]}}else if("gts"===r||"lts"===r||"interval"===r){let e=n[0],t=n[1];if("tuple"!==e[0]||"tuple"!==t[0])throw new Error("Badly formed ast");return[r,["tuple"].concat(e.slice(1).map((function(e,t){return to_intervals(e)}))),t]}return[r].concat(n.map((function(e,t){return to_intervals(e)})))}function altvectors_to_vectors(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("altvector"===r){return["vector"].concat(n.map((function(e,t){return altvectors_to_vectors(e)})))}return[r].concat(n.map((function(e,t){return altvectors_to_vectors(e)})))}function ParseError(e,t){this.name="ParseError",this.message=e||"Error parsing input",this.stack=(new Error).stack,this.location=t}functions.C.nonneg=["abs"],functions.C.nonzero=["exp"],functions.C.R=["abs","arg"],functions.C.C=["abs","arg","exp","sign","cos","cosh","sin","sinh","erf","sqrt","log","ln","log10"],functions.R.pos=["exp"],functions.R.nonneg=["abs","exp","arg"],functions.R.R=["abs","arg","exp","sign","cos","cosh","sin","sinh","erf"],functions.R.Z=["sign"],functions.nonzeroC.pos=["abs"],functions.nonneg.nonneg=["abs","exp","arg","sqrt","erf"],functions.nonzeroC.nonzero=["abs"],functions.nonneg.R=[...new Set(functions.R.R.concat(functions.nonneg.nonneg))],functions.pos.pos=["abs","exp","sqrt","erf"],functions.pos.nonneg=functions.pos.pos,functions.pos.nonzero=["abs","exp","sqrt","erf"],functions.pos.R=functions.nonneg.R.concat(["log","ln","log10"]),ParseError.prototype=Object.create(Error.prototype),ParseError.prototype.constructor=ParseError;class lexer{constructor(e,t="\\s"){this.input="",this.location=0,this.token_rules=[],this.initial_whitespace=new RegExp("^("+t+")+");for(let t of e)this.token_rules.push([new RegExp("^"+t[0])].concat(t.slice(1)))}set_input(e){if("string"!=typeof e)throw new Error("Input must be a string");this.input=e,this.location=0}return_state(){return{input:this.input,location:this.location}}set_state({input:e=null,location:t=0}={}){null!==e&&(this.input=e,this.location=t)}advance({remove_initial_space:e=!0}={}){let t=this.initial_whitespace.exec(this.input);if(t){let r=t[0].length;if(this.input=this.input.slice(r),this.location+=r,!e)return{token_type:"SPACE",token_text:t[0],original_text:t[0]}}if(0===this.input.length)return{token_type:"EOF",token_text:"",original_text:""};for(var r of(t=null,this.token_rules))if(t=r[0].exec(this.input),t){let e=t[0].length;this.input=this.input.slice(e),this.location+=e;break}return null===t?{token_type:"INVALID",token_text:this.input[0],original_text:this.input[0]}:r.length>2?{token_type:r[1],token_text:r[2],original_text:t[0]}:{token_type:r[1],token_text:t[0],original_text:t[0]}}unput(e){if("string"!=typeof e)throw new Error("Input must be a string");this.location-=e.length,this.input=e+this.input}}var is_associative={"+":!0,"*":!0,and:!0,or:!0,union:!0,intersect:!0};function flatten(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if(r=r.map((function(e,t){return flatten(e)})),is_associative[t]){for(var n=[],i=0;i2?n=n.concat(r[i].slice(1)):n.push(r[i]);r=n}return[t].concat(r)}const sci_notat_exp_regex$1="(E[+\\-]?[0-9]+\\s*($|(?=\\,|\\||\\)|\\}|\\])))?",number_rules_sci$1=[["[0-9]+(\\.[0-9]*)?"+sci_notat_exp_regex$1,"NUMBER"],["\\.[0-9]+"+sci_notat_exp_regex$1,"NUMBER"]],number_rules_non_sci$1=[["[0-9]+(\\.[0-9]*)?","NUMBER"],["\\.[0-9]+","NUMBER"]],base_text_rules=[["\\*\\*","^"],["\\*","*"],["\\xB7","*"],["·","*"],["•","*"],["⋅","*"],["×","*"],["/","/"],["-","-"],["֊","-"],["־","-"],["᠆","-"],["‐","-"],["‑","-"],["‒","-"],["–","-"],["—","-"],["―","-"],["⁻","-"],["₋","-"],["−","-"],["⸺","-"],["⸻","-"],["﹘","-"],["﹣","-"],["－","-"],["\\+","+"],["\\^","^"],["‸","^"],["ʌ","^"],["\\|","|"],["\\(","("],["\\)",")"],["\\[","["],["\\]","]"],["\\{","{"],["\\}","}"],["⟨","LANGLE"],["⟩","RANGLE"],["〈","LANGLE"],["〉","RANGLE"],[",",","],[":",":"],["α","VARMULTICHAR","alpha"],["β","VARMULTICHAR","beta"],["ϐ","VARMULTICHAR","beta"],["Γ","VARMULTICHAR","Gamma"],["γ","VARMULTICHAR","gamma"],["Δ","VARMULTICHAR","Delta"],["δ","VARMULTICHAR","delta"],["ε","VARMULTICHAR","epsilon"],["ϵ","VARMULTICHAR","epsilon"],["ζ","VARMULTICHAR","zeta"],["η","VARMULTICHAR","eta"],["Θ","VARMULTICHAR","Theta"],["ϴ","VARMULTICHAR","Theta"],["θ","VARMULTICHAR","theta"],["ᶿ","VARMULTICHAR","theta"],["ϑ","VARMULTICHAR","theta"],["ι","VARMULTICHAR","iota"],["κ","VARMULTICHAR","kappa"],["Λ","VARMULTICHAR","Lambda"],["λ","VARMULTICHAR","lambda"],["μ","VARMULTICHAR","mu"],["µ","VARMULTICHAR","mu"],["ν","VARMULTICHAR","nu"],["Ξ","VARMULTICHAR","Xi"],["ξ","VARMULTICHAR","xi"],["Π","VARMULTICHAR","Pi"],["π","VARMULTICHAR","pi"],["ϖ","VARMULTICHAR","pi"],["ρ","VARMULTICHAR","rho"],["ϱ","VARMULTICHAR","rho"],["Σ","VARMULTICHAR","Sigma"],["σ","VARMULTICHAR","sigma"],["ς","VARMULTICHAR","sigma"],["τ","VARMULTICHAR","tau"],["Υ","VARMULTICHAR","Upsilon"],["υ","VARMULTICHAR","upsilon"],["Φ","VARMULTICHAR","Phi"],["φ","VARMULTICHAR","phi"],["ϕ","VARMULTICHAR","phi"],["Ψ","VARMULTICHAR","Psi"],["ψ","VARMULTICHAR","psi"],["Ω","VARMULTICHAR","Omega"],["ω","VARMULTICHAR","omega"],["oo(?![a-zA-Z0-9])","INFINITY"],["OO(?![a-zA-Z0-9])","INFINITY"],["infty(?![a-zA-Z0-9])","INFINITY"],["infinity(?![a-zA-Z0-9])","INFINITY"],["Infinity(?![a-zA-Z0-9])","INFINITY"],["∞","INFINITY"],["ℯ","VAR","e"],["♠","VARMULTICHAR","spade"],["♡","VARMULTICHAR","heart"],["♢","VARMULTICHAR","diamond"],["♣","VARMULTICHAR","club"],["★","VARMULTICHAR","bigstar"],["◯","VARMULTICHAR","bigcirc"],["◊","VARMULTICHAR","lozenge"],["△","VARMULTICHAR","bigtriangleup"],["▽","VARMULTICHAR","bigtriangledown"],["⧫","VARMULTICHAR","blacklozenge"],["■","VARMULTICHAR","blacksquare"],["▲","VARMULTICHAR","blacktriangle"],["▼","VARMULTICHAR","blacktriangledown"],["◀","VARMULTICHAR","blacktriangleleft"],["▶","VARMULTICHAR","blacktriangleright"],["□","VARMULTICHAR","Box"],["∘","VARMULTICHAR","circ"],["⋆","VARMULTICHAR","star"],["and(?![a-zA-Z0-9])","AND"],["\\&\\&?","AND"],["∧","AND"],["or(?![a-zA-Z0-9])","OR"],["∨","OR"],["not(?![a-zA-Z0-9])","NOT"],["¬","NOT"],["=","="],["᐀","="],["゠","="],["!=","NE"],["≠","NE"],["<=","LE"],["≤","LE"],[">=","GE"],["≥","GE"],["<","<"],[">",">"],["forall(?![a-zA-Z0-9])","FORALL"],["∀","FORALL"],["exists(?![a-zA-Z0-9])","EXISTS"],["∃","EXISTS"],["elementof(?![a-zA-Z0-9])","IN"],["∈","IN"],["notelementof(?![a-zA-Z0-9])","NOTIN"],["∉","NOTIN"],["containselement(?![a-zA-Z0-9])","NI"],["∋","NI"],["notcontainselement(?![a-zA-Z0-9])","NOTNI"],["∌","NOTNI"],["subset(?![a-zA-Z0-9])","SUBSET"],["⊂","SUBSET"],["subseteq(?![a-zA-Z0-9])","SUBSETEQ"],["⊆","SUBSETEQ"],["notsubset(?![a-zA-Z0-9])","NOTSUBSET"],["⊄","NOTSUBSET"],["notsubseteq(?![a-zA-Z0-9])","NOTSUBSETEQ"],["⊈","NOTSUBSETEQ"],["superset(?![a-zA-Z0-9])","SUPERSET"],["⊃","SUPERSET"],["superseteq(?![a-zA-Z0-9])","SUPERSETEQ"],["⊇","SUPERSETEQ"],["notsuperset(?![a-zA-Z0-9])","NOTSUPERSET"],["⊅","NOTSUPERSET"],["notsuperseteq(?![a-zA-Z0-9])","NOTSUPERSETEQ"],["⊉","NOTSUPERSETEQ"],["union(?![a-zA-Z0-9])","UNION"],["∪","UNION"],["intersect(?![a-zA-Z0-9])","INTERSECT"],["∩","INTERSECT"],["perp(?![a-zA-Z0-9])","PERP"],["⟂","PERP"],["parallel(?![a-zA-Z0-9])","PARALLEL"],["∥","PARALLEL"],["angle(?![a-zA-Z0-9])","ANGLE"],["∠","ANGLE"],["int(?![a-zA-Z0-9])","INT"],["∫","INT"],["!","!"],["'","'"],["_","_"],["\\.\\.\\.","LDOTS"],["[a-zA-Z∂][a-zA-Z∂0-9]*","VAR"],["[＿$%]","VAR"]],allowSimplifiedFunctionApplicationDefault$1=!0,splitSymbolsDefault=!0,unsplitSymbolsDefault=["alpha","beta","gamma","Gamma","delta","Delta","epsilon","zeta","eta","theta","Theta","iota","kappa","lambda","Lambda","mu","nu","xi","Xi","pi","Pi","rho","sigma","Sigma","tau","Tau","upsilon","Upsilon","phi","Phi","chi","psi","Psi","omega","Omega","angle","deg"],appliedFunctionSymbolsDefault$1=["abs","exp","log","ln","log10","sign","sqrt","erf","cos","cosh","acos","acosh","arccos","arccosh","cot","coth","acot","acoth","arccot","arccoth","csc","csch","acsc","acsch","arccsc","arccsch","sec","sech","asec","asech","arcsec","arcsech","sin","sinh","asin","asinh","arcsin","arcsinh","tan","tanh","atan","atan2","atanh","arctan","arctanh","arg","conj","re","im","det"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textToAst$4{constructor({allowSimplifiedFunctionApplication:e=allowSimplifiedFunctionApplicationDefault$1,splitSymbols:t=splitSymbolsDefault,unsplitSymbols:r=unsplitSymbolsDefault,appliedFunctionSymbols:n=appliedFunctionSymbolsDefault$1,functionSymbols:i=functionSymbolsDefault$1,operatorSymbols:a=operatorSymbolsDefault$1,units:o=unitsDefault$1,parseLeibnizNotation:s=parseLeibnizNotationDefault$1,parseScientificNotation:u=!0}={}){this.allowSimplifiedFunctionApplication=e,this.splitSymbols=t,this.unsplitSymbols=r,this.appliedFunctionSymbols=n,this.functionSymbols=i,this.operatorSymbols=a,this.units=o,this.parseLeibnizNotation=s;let c=base_text_rules;c=u?[...number_rules_sci$1,...c]:[...number_rules_non_sci$1,...c],this.lexer=new lexer(c)}advance(e){if(this.token=this.lexer.advance(e),"INVALID"===this.token.token_type)throw new ParseError("Invalid symbol '"+this.token.original_text+"'",this.lexer.location)}return_state(){return{lexer_state:this.lexer.return_state(),token:Object.assign({},this.token)}}set_state(e){this.lexer.set_state(e.lexer_state),this.token=Object.assign({},e.token)}convert(e){this.lexer.set_input(e),this.advance();var t=this.statement_list();if("EOF"!==this.token.token_type)throw new ParseError("Invalid location of '"+this.token.original_text+"'",this.lexer.location);return flatten(t)}statement_list(){for(var e=[this.statement()];","===this.token.token_type;)this.advance(),e.push(this.statement());return e=e.length>1?["list"].concat(e):e[0]}statement({inside_absolute_value:e=0}={}){if("LDOTS"===this.token.token_type)return this.advance(),["ldots"];var t;try{t=this.return_state();let r=this.statement_a({inside_absolute_value:e});return":"!==this.token.token_type?r:(this.advance(),[":",r,this.statement_a()])}catch(e){try{this.set_state(t);let r=this.statement_a({parse_absolute_value:!1});if("|"!==this.token.token_type)throw e;return this.advance(),["|",r,this.statement_a({parse_absolute_value:!1})]}catch(t){throw e}}}statement_a({inside_absolute_value:e=0,parse_absolute_value:t=!0}={}){for(var r=this.statement_b({inside_absolute_value:e,parse_absolute_value:t});"OR"===this.token.token_type;){let n=this.token.token_type.toLowerCase();this.advance(),r=[n,r,this.statement_b({inside_absolute_value:e,parse_absolute_value:t})]}return r}statement_b(e){for(var t=this.relation(e);"AND"===this.token.token_type;){let r=this.token.token_type.toLowerCase();this.advance(),t=[r,t,this.relation(e)]}return t}relation(e){if("NOT"===this.token.token_type||"!"===this.token.token_type)return this.advance(),["not",this.relation(e)];if("FORALL"===this.token.token_type||"EXISTS"===this.token.token_type){let t=this.token.token_type.toLowerCase();return this.advance(),[t,this.relation(e)]}for(var t=this.expression(e);"="===this.token.token_type||"NE"===this.token.token_type||"<"===this.token.token_type||">"===this.token.token_type||"LE"===this.token.token_type||"GE"===this.token.token_type||"IN"===this.token.token_type||"NOTIN"===this.token.token_type||"NI"===this.token.token_type||"NOTNI"===this.token.token_type||"SUBSET"===this.token.token_type||"NOTSUBSET"===this.token.token_type||"SUBSETEQ"===this.token.token_type||"NOTSUBSETEQ"===this.token.token_type||"SUPERSET"===this.token.token_type||"NOTSUPERSET"===this.token.token_type||"SUPERSETEQ"===this.token.token_type||"NOTSUPERSETEQ"===this.token.token_type;){let r=this.token.token_type.toLowerCase(),n=0;"<"===this.token.token_type||"LE"===this.token.token_type?n=-1:">"!==this.token.token_type&&"GE"!==this.token.token_type||(n=1),this.advance();let i=this.expression(e);if(-1===n)if("<"===this.token.token_type||"LE"===this.token.token_type){let n=["tuple"];"<"===r?n.push(!0):n.push(!1);let a=["tuple",t,i];for(;"<"===this.token.token_type||"LE"===this.token.token_type;)"<"===this.token.token_type?n.push(!0):n.push(!1),this.advance(),a.push(this.expression(e));t=["lts",a,n]}else t=[r,t,i];else if(1===n)if(">"===this.token.token_type||"GE"===this.token.token_type){let n=["tuple"];">"===r?n.push(!0):n.push(!1);let a=["tuple",t,i];for(;">"===this.token.token_type||"GE"===this.token.token_type;)">"===this.token.token_type?n.push(!0):n.push(!1),this.advance(),a.push(this.expression(e));t=["gts",a,n]}else t=[r,t,i];else if("="===r)for(t=["=",t,i];"="===this.token.token_type;)this.advance(),t.push(this.expression(e));else t=[r,t,i]}return t}expression(e){let t=!1;"+"===this.token.token_type&&(t=!0,this.advance());let r=!1;"-"===this.token.token_type&&(r=!0,this.advance());var n=this.term(e);if(r||t){if(!1===n)return(t?"+":"")+(r?"-":"");if("string"==typeof n&&[...n].every((e=>["+","-"].includes(e))))return(t?"+":"")+(r?"-":"")+n}for(!1===n&&(n="＿"),r&&(n=n>0?-n:["-",n]),t&&(n=["+",n]);["+","-","UNION","INTERSECT","PERP","PARALLEL"].includes(this.token.token_type);){let t=this.token.token_type.toLowerCase(),r=!1,i=!1;"-"===this.token.token_type?(t="+",r=!0,this.advance()):(this.advance(),"+"===t&&"-"===this.token.token_type&&(r=!0,i=!0,this.advance()));let a=this.term(e);if("+"===t){if(!1===a&&("number"==typeof n||"string"==typeof n))return i?n+"+-":r?n+"-":n+"+";if("string"==typeof a&&[...a].every((e=>["+","-"].includes(e)))&&("number"==typeof n||"string"==typeof n))return i?n+"+-"+a:r?n+"-"+a:n+"+"+a}!1===a&&(a="＿"),r&&(a=a>0?-a:["-",a]),n=[t,n,a]}return n}term(e){var t=this.factor(e),r=!1;do{if(r=!1,"*"===this.token.token_type){this.advance(),!1===t&&(t="＿");let n=this.factor(e);!1===n&&(n="＿"),t=["*",t,n],r=!0}else if("/"===this.token.token_type){this.advance(),!1===t&&(t="＿");let n=this.factor(e);!1===n&&(n="＿"),t=["/",t,n],r=!0}else{let n=Object.assign({},e);n.allow_absolute_value_closing=!0;let i=this.nonMinusFactor(n);!1!==i&&(!1===t&&(t="＿"),t=["*",t,i],r=!0)}}while(r);return this.convert_units_in_term(flatten(t))}convert_units_in_term(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("*"===t){let t=r.length;for(let[e,n]of r.entries()){let i=this.units[n];if(i){if(i.prefix&&e0){let a,o=n;return i.substitute&&(o=i.substitute),a=1===e?["unit",r[0],o]:["unit",["*",...r.slice(0,e)],o],e===t-1?a:this.convert_units_in_term(["*",a,...r.slice(e+1)])}}}return e}return"/"===t?["/",this.convert_units_in_term(r[0]),this.convert_units_in_term(r[1])]:e}factor(e){if("+"===this.token.token_text){this.advance();let t=this.factor(e);return!1===t?"+":"string"==typeof t&&[...t].every((e=>["+","-"].includes(e)))?"+"+t:["+",t]}if("-"===this.token.token_type){this.advance();let t=this.factor(e);return t>0?-t:!1===t?"-":"string"==typeof t&&[...t].every((e=>["+","-"].includes(e)))?"-"+t:["-",t]}let t=this.nonMinusFactor(e);return!1===t&&"PERP"===this.token.token_type&&(t="perp",this.advance()),t}nonMinusFactor(e){for(var t=this.baseFactor(e);"^"===this.token.token_type||"!"===this.token.token_type||"'"===this.token.token_type;)if(!1===t&&(t="＿"),"^"===this.token.token_type){this.advance(),t=["^",t,this.get_subsuperscript(e)]}else"!"===this.token.token_type?(t=["apply","factorial",t],this.advance()):(t=["prime",t],this.advance());return t}get_subsuperscript({parse_absolute_value:e}){if(["+","-","PERP"].includes(this.token.token_type)){let e=this.token.token_type.toLowerCase();return this.advance(),e}{let t=this.baseFactor({parse_absolute_value:e,in_subsuperscript_with_no_delimiters:!0});return!1===t&&(t="＿"),t}}baseFactor({inside_absolute_value:e=0,parse_absolute_value:t=!0,allow_absolute_value_closing:r=!1,in_subsuperscript_with_no_delimiters:n=!1}={}){var i=!1;if("NUMBER"===this.token.token_type)i=parseFloat(this.token.token_text),this.advance();else if("INFINITY"===this.token.token_type)i=1/0,this.advance();else if("VAR"===this.token.token_type||"VARMULTICHAR"===this.token.token_type){if(i=this.token.token_text,this.appliedFunctionSymbols.includes(i)||this.functionSymbols.includes(i)){let e=!1;if(this.appliedFunctionSymbols.includes(i)&&(e=!0),this.advance(),"_"===this.token.token_type){this.advance();let e=this.get_subsuperscript({parse_absolute_value:t});i="log"===i&&10===e?"log10":["_",i,e]}if(n)e&&(i=["apply",i,"＿"]);else{for(;"'"===this.token.token_type;)i=["prime",i],this.advance();for(;"^"===this.token.token_type;){this.advance(),i=["^",i,this.get_subsuperscript({parse_absolute_value:t})]}if("("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),"list"===e[0]&&(e[0]="tuple"),i=["apply",i,e]}else if(e){if(!this.allowSimplifiedFunctionApplication)throw new ParseError("Expecting ( after function",this.lexer.location);let e=this.factor({parse_absolute_value:t});!1===e&&(e="＿"),i=["apply",i,e]}}return i}if(this.operatorSymbols.includes(i))if(this.advance(),"("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),i="list"===e[0]?[i,...e.slice(1)]:[i,e]}else{let e=this.factor({parse_absolute_value:t});!1===e&&(e="＿"),i=[i,e]}else{if(this.parseLeibnizNotation){let e=this.return_state(),t=this.leibniz_notation();if(t)return t;this.set_state(e)}let n=this.splitSymbols;if(n&&("VARMULTICHAR"===this.token.token_type||this.unsplitSymbols.includes(i)||1===i.length||i.match(/[\d]/g))&&(n=!1),n){for(let e=i.length-1;e>=0;e--)this.lexer.unput(" "),this.lexer.unput(i[e]);return this.advance(),this.baseFactor({inside_absolute_value:e,parse_absolute_value:t,allow_absolute_value_closing:r})}this.advance()}}else if("("===this.token.token_type||"["===this.token.token_type||"{"===this.token.token_type||"LANGLE"===this.token.token_type){let e,t,r=this.token.token_type;"("===this.token.token_type?(e=")",t="]"):"["===this.token.token_type?(e="]",t=")"):"{"===this.token.token_type?(e="}",t=null):(e="RANGLE",t=null),this.advance();let n=1;if("list"===(i=this.statement_list())[0]&&(n=i.length-1),this.token.token_type!==e){if(2!==n||null===t)throw new ParseError("Expecting "+e,this.lexer.location);if(this.token.token_type!==t)throw new ParseError("Expecting ) or ]",this.lexer.location);let a;i[0]="tuple",a="("===r?["tuple",!1,!0]:["tuple",!0,!1],(i=["interval",i]).push(a)}else n>=2?i[0]="("===r?"tuple":"["===r?"array":"{"===r?"set":"altvector":"{"===r&&(i=("|"===i[0]||i[0],["set",i]));this.advance()}else if("|"!==this.token.token_type||!t||0!==e&&r){if("ANGLE"===this.token.token_type)if(this.advance(),"("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),"list"===e[0]?i=["angle",...e.slice(1)]:"*"===e[0]&&(i=["angle",e])}else{let e=[],r=this.nonMinusFactor({parse_absolute_value:t});for(;!1!==r;)e.push(r),r=this.nonMinusFactor({parse_absolute_value:t});i=0===e.length?"angle":["angle",...e]}else if("INT"===this.token.token_type){this.advance();let e="int";if("_"===this.token.token_type){this.advance(),e=["_",e,this.get_subsuperscript({parse_absolute_value:t})]}if("^"===this.token.token_type){this.advance(),e=["^",e,this.get_subsuperscript({parse_absolute_value:t})]}let r=flatten(this.term({parse_absolute_value:t}));if(Array.isArray(r)&&"*"===r[0]){let e=[];for(let t=0;t2&&(this.lexer.unput(this.token.token_text.slice(2)),this.token.token_text=this.token.token_text.slice(0,2));let s=this.token.token_text;if(2===s.length){if(!/[a-zA-Z]/.exec(s[1]))return!1;i.push(s[1])}else{if(this.advance(),("VAR"!==this.token.token_type||this.token.token_text.includes("∂"))&&"VARMULTICHAR"!==this.token.token_type)return!1;i.push(this.token.token_text)}let u=1,c=!1;if(this.advance({remove_initial_space:!1}),"SPACE"===this.token.token_type&&(c=!0,this.advance()),"^"===this.token.token_type){if(this.advance(),"NUMBER"!==this.token.token_type)return!1;if(u=parseFloat(this.token.token_text),!Number.isInteger(u))return!1;c=!1,this.advance({remove_initial_space:!1}),"SPACE"===this.token.token_type&&(c=!0,this.advance())}if(a.push(u),o+=u,o>r)return!1;if(o===r){if(!c&&("VAR"===this.token.token_type||"VARMULTICHAR"===this.token.token_type))return!1;"SPACE"===this.token.token_type&&this.advance();let o="derivative_leibniz";"∂"===t&&(o="partial_"+o),e=[o],1===r?e.push(n):e.push(["tuple",n,r]);let s=[];for(let e=0;et[e+1]));if(t.length!==n||i.length!==n)return subtree;let a=["+",...t.map(((e,t)=>["*",e,i[t]]))];r.push(a)}s.push(r)}return{success:!0,newMatrix:["matrix",["tuple",r,i],s]}}function a(e,t){let r=e[1][1],n=e[1][2],i=e[2],a=["tuple"];for(let e=0;e=0;t--){let n=r[t][0];if("matrix"===n){let n=i(r[t],e);if(!n.success)break;e=n.newMatrix,r.pop()}else{if(["tuple","list","vector","altvector","interval","set","array"].includes(n))break;1!==r[t]&&(e=a(e,r[t])),r.pop()}}for(;n.length>0;){let t=n[0][0];if("matrix"===t){let t=i(e,n[0]);if(!t.success)break;e=t.newMatrix,n.splice(0,1)}else{if(["tuple","list","vector","altvector","interval","set","array"].includes(t))break;1!==n[0]&&(e=a(e,n[0])),n.splice(0,1)}}return r.length>0||n.length>0?["*",...r,e,...n]:e}return e})),(t||r)&&(o=["*",["matrix",["tuple","m","n"],"matrixData"],"b"],s={variables:{n:Number.isInteger,m:Number.isInteger,matrixData:!0,b:!0}},n=transform(n,(function(e){let n=match$2(e,o,s);if(n){let i,a=n.m,o=n.n,s=n.b,u=n.matrixData,c=[];t&&(c.push("vector"),c.push("altvector")),r&&c.push("tuple");let l=[];if(c.includes(s[0]))i=s;else{if(!Array.isArray(s)||"*"!==s[0]||!c.includes(s[1][0]))return e;i=s[1],l=s.slice(2)}let f=i.slice(1);if(f.length!==o)return e;let p=[i[0]];for(let e=0;e["*",e,f[t]]))];p.push(t)}return l.length>0?["*",p,...l]:p}return e}))),n}function perform_vector_scalar_multiplications(e,t=!0){var r=get_tree(e);let n=function(e,t){let r=["*","a",[t,"vectorData"],"b"],n={allow_implicit_identities:["a","b"]};return e=transform(e,(function(e){let i=match$2(e,r,n);if(i){if(1===i.a&&1===i.b)return e;let r=i.vectorData;r=Array.isArray(r)&&r[0]===t?r.slice(1):[r];let n=[],a=[];Array.isArray(i.a)&&"*"===i.a[0]?n.push(...i.a.slice(1)):n.push(i.a),Array.isArray(i.b)&&"*"===i.b[0]?a.push(...i.b.slice(1)):a.push(i.b);for(let e=n.length-1;e>=0;e--){let t=n[e][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t))break;1!==n[e]&&(r=r.map((t=>["*",t,n[e]]))),n.pop()}for(;a.length>0;){let e=a[0][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(e))break;1!==a[0]&&(r=r.map((e=>["*",e,a[0]]))),a.splice(0,1)}let o=[t,...r];return n.length>0||a.length>0?["*",...n,o,...a]:o}return e})),e};return r=n(r,"vector"),r=n(r,"altvector"),t&&(r=n(r,"tuple")),r}function perform_matrix_scalar_multiplications(e){var t=get_tree(e);let r=["*","a",["matrix","size","matrixData"],"b"],n={allow_implicit_identities:["a","b"]};return t=transform(t,(function(e){let t=match$2(e,r,n);if(t){if(1===t.a&&1===t.b)return e;let r=t.matrixData,n=[],i=[];Array.isArray(t.a)&&"*"===t.a[0]?n.push(...t.a.slice(1)):n.push(t.a),Array.isArray(t.b)&&"*"===t.b[0]?i.push(...t.b.slice(1)):i.push(t.b);for(let e=n.length-1;e>=0;e--){let t=n[e][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t))break;1!==n[e]&&(r=r.map((t=>"tuple"===t?t:t.map((t=>"tuple"===t?t:["*",t,n[e]]))))),n.pop()}for(;i.length>0;){let e=i[0][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(e))break;1!==i[0]&&(r=r.map((e=>"tuple"===e?e:e.map((e=>"tuple"===e?e:["*",e,i[0]]))))),i.splice(0,1)}let a=["matrix",t.size,r];return n.length>0||i.length>0?["*",...n,a,...i]:a}return e})),t}function expand_relations(e){var t=get_tree(e);return transform(t,expand_relations_transform)}function expand_relations_transform(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if("="===t){if(r.length<=2)return e;let t=["and"];for(let e=0;e":"lts"===t?"le":"ge",i.push([a,e[r],e[r+1]])}let a=["and",i[0],i[1]];for(let e=2;e",n,c]),s[2]?a?f.push([">",n,l]):f.push(["le",n,l]):a?f.push(["ge",n,l]):f.push(["<",n,l]),u=a?["or"].concat(f):["and"].concat(f),u}if("subset"===t||"notsubset"===t||"superset"===t||"notsuperset"===t){let n,i,a=!1;if("notsubset"!==t&&"notsuperset"!==t||(a=!0),"subset"===t||"notsubset"===t?(n=r[0],i=r[1]):(n=r[1],i=r[0]),n=to_intervals(n),i=to_intervals(i),"interval"!==n[0]||"interval"!==i[0])return e;let o=n[1],s=n[2],u=i[1],c=i[2];if("tuple"!==o[0]||"tuple"!==s[0]||"tuple"!==u[0]||"tuple"!==c[0])throw new Error("Badly formed ast");let l,f=o[1],p=o[2],m=u[1],d=u[2],h=[];return s[1]&&!c[1]?a?h.push(["le",f,m]):h.push([">",f,m]):a?h.push(["<",f,m]):h.push(["ge",f,m]),s[2]&&!c[2]?a?h.push(["ge",p,d]):h.push(["<",p,d]):a?h.push([">",p,d]):h.push(["le",p,d]),l=a?["or"].concat(h):["and"].concat(h),l}return e}function substitute(e,t){var r=get_tree(e),n={};for(let e in t)n[e]=get_tree(t[e]);return substitute$1(r,n)}function substitute_component(e,t,r){let n=get_tree(e);if(get_tree(r),"number"==typeof t)t=[t];else if(!Array.isArray(t))throw Error("Invalid substitute_component: "+t);let i=["list","tuple","vector","altvector","array"];return function e(t,n,a){if(0===n.length)return r;if(!Array.isArray(t))throw Error("Invalid substitute_component: expected list, tuple, vector, or array");let o=t[0],s=t.slice(1);if(!i.includes(o))throw Error("Invalid substitute_component: expected list, tuple, vector, or array");let u=n[0];if(u<0||u>s.length-1)throw Error("Invalid substitute_component: component out of range");let c=n.slice(1),l=e(s[u],c);return[o,...s.slice(0,u),l,...s.slice(u+1)]}(n,t)}function get_component(e,t){let r=get_tree(e);if("number"==typeof t)t=[t];else if(!Array.isArray(t))throw Error("Invalid get_component: "+t);let n=["list","tuple","vector","altvector","array"];return function e(t,r){if(0===r.length)return t;if(!Array.isArray(t))throw Error("Invalid get_component: expected list, tuple, vector, or array");let i=t[0],a=t.slice(1);if(!n.includes(i))throw Error("Invalid get_component: expected list, tuple, vector, or array");let o=r[0];if(o<0||o>a.length-1)throw Error("Invalid get_component: component out of range");let s=r.slice(1);return e(a[o],s)}(r,t)}var transformation=Object.freeze({__proto__:null,expand:expand,expand_relations:expand_relations,substitute:substitute,substitute_component:substitute_component,get_component:get_component,perform_vector_scalar_multiplications:perform_vector_scalar_multiplications,perform_matrix_scalar_multiplications:perform_matrix_scalar_multiplications,perform_matrix_multiplications:perform_matrix_multiplications});function clean(e){return flatten$5(get_tree(e))}function evalf(e,t){return parseFloat(math$1.format(e,{notation:"exponential",precision:t}))}function collapse_unary_minus(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if(n=n.map((e=>collapse_unary_minus(e))),"-"===r){if("number"==typeof n[0])return-n[0];if(Array.isArray(n[0])&&"*"===n[0][0]&&"number"==typeof n[0][1])return["*",-n[0][1]].concat(n[0].slice(2));if(Array.isArray(n[0])&&"/"===n[0][0]){if("number"==typeof n[0][1])return["/",-n[0][1],n[0][2]];if(Array.isArray(n[0][1])&&"*"===n[0][1][0]&&"number"==typeof n[0][1][1])return["/",["*",-n[0][1][1]].concat(n[0][1].slice(2)),n[0][2]]}}return[r].concat(n)}function simplify(e,t,r){var n=get_tree(e);return contains_blank(n)?n:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),n=evaluate_numbers(n,{assumptions:t,max_digits:r,evaluate_functions:!0}),Array.isArray(n)?n=collect_like_terms_factors(n=perform_vector_matrix_additions_scalar_multiplications(n=simplify_logical(n,t)),t,r):n)}function simplify_logical(e,t){var r=get_tree(e);if(contains_blank(r))return r;void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),r=evaluate_numbers(r,{assumptions:t}),r=unflattenRight(r);var n=[];return n.push([["not",["not","a"]],"a"]),n.push([["not",["and","a","b"]],["or",["not","a"],["not","b"]]]),n.push([["not",["or","a","b"]],["and",["not","a"],["not","b"]]]),n.push([["not",["=","a","b"]],["ne","a","b"]]),n.push([["not",["ne","a","b"]],["=","a","b"]]),n.push([["not",["<","a","b"]],["le","b","a"]]),n.push([["not",["le","a","b"]],["not",["le","a","b"]]]),n.push([["not",["in","a","b"]],["notin","a","b"]]),n.push([["not",["subset","a","b"]],["notsubset","a","b"]]),r=flatten$5(r=applyAllTransformations(r,n,20))}function perform_vector_matrix_additions_scalar_multiplications(e,t=!0){var r=get_tree(e);r=perform_vector_scalar_multiplications(r=perform_matrix_scalar_multiplications(r),t);let n=["+","a","b"];return r=transform(r,(function(e){let r=match$2(e,n,{allow_permutations:!0});if(r){let n=["vector","altvector"];t&&n.push("tuple");let i={},a={},o=[];if(n.includes(r.a[0])){let e=r.a.length-1;i[e]||(i[e]=[]),i[e].push(r.a)}else if("matrix"===r.a[0]){let e=r.a[1].slice(1).toString();a[e]||(a[e]=[]),a[e].push(r.a)}else o.push(r.a);if(n.includes(r.b[0])){let e=r.b.length-1;i[e]||(i[e]=[]),i[e].push(r.b)}else if("matrix"===r.b[0]){let e=r.b[1].slice(1).toString();a[e]||(a[e]=[]),a[e].push(r.b)}else if("+"===r.b[0])for(let e of r.b.slice(1))if(n.includes(e[0])){let t=e.length-1;i[t]||(i[t]=[]),i[t].push(e)}else if("matrix"===e[0]){let t=e[1].slice(1).toString();a[t]||(a[t]=[]),a[t].push(e)}else o.push(e);else o.push(r.b);if(Object.values(i).every((e=>e.length<2))&&Object.values(a).every((e=>e.length<2)))return e;let s=o;for(let e in i)if(i[e].length<2)s.push(...i[e]);else{let t,r=i[e].some((e=>"vector"===e[0])),n=i[e].some((e=>"tuple"===e[0])),a=i[e].some((e=>"altvector"===e[0]));t=r||n&&a?["vector"]:a?["altvector"]:["tuple"];for(let r=0;re[r+1]))]);s.push(t)}for(let e in a)if(a[e].length<2)s.push(...a[e]);else{let[t,r]=e.split(",").map(Number),n=["tuple"];for(let i=0;ie[2][i+1][n+1]))]);n.push(t)}let i=["matrix",["tuple",t,r],n];s.push(i)}return 1===s.length?s[0]:["+",...s]}return e})),r}function contains_decimal_number(e){return"string"!=typeof e&&("number"==typeof e?!(!Number.isFinite(e)||Number.isInteger(e)):!!Array.isArray(e)&&e.slice(1).some((e=>contains_decimal_number(e))))}function contains_only_numbers(e,{include_number_symbols:t=!1,evaluate_functions:r=!1}={}){if("string"==typeof e){if(t){if("e"===e&&math$1.define_e)return!0;if("pi"===e&&math$1.define_pi)return!0}return!("i"!==e||!math$1.define_i)}return"number"==typeof e||!!Array.isArray(e)&&(r&&"apply"===e[0]?e.slice(2).every((e=>contains_only_numbers(e,{include_number_symbols:t}))):e.slice(1).every((e=>contains_only_numbers(e,{include_number_symbols:t}))))}function try_evaluate_sum_of_numbers(e,t,r){if("number"==typeof e){if(0===e)return t;if("number"==typeof t)return e+t;if(Array.isArray(t)&&"+"===t[0]&&"number"==typeof t[1])return["+",e+t[1],t[2]];if(!r&&Array.isArray(t)&&"+"===t[0]&&"number"==typeof t[2])return["+",e+t[2],t[1]]}return"number"==typeof t&&0===t?e:null}function try_evaluate_negate_number(e){if("number"==typeof e)return-e;if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1])return["*",-e[1]].concat(e.slice(2));if(Array.isArray(e)&&"/"===e[0]){if("number"==typeof e[1])return["/",-e[1],e[2]];if(Array.isArray(e[1])&&"*"===e[1][0]&&"number"==typeof e[1][1])return["/",["*",-e[1][1]].concat(e[1].slice(2)),e[2]]}return null}function try_evaluate_product_of_numbers(e,t){if("number"==typeof e){if(isNaN(e))return NaN;if("number"==typeof t)return e*t;if(!isFinite(e))return e===1/0&&is_negative_ast(t)||e===-1/0&&is_positive_ast(t)?-1/0:!1===is_nonzero_ast(t)?NaN:1/0;if(0===e)return 0;if(1===e)return t;if(-1===e)return["-",t];if(Array.isArray(t)&&"*"===t[0]&&"number"==typeof t[1])return e*=t[1],t=t[2],1===e?t:-1===e?["-",t]:["*",e,t]}if("number"==typeof t){if(isNaN(t))return NaN;if(!isFinite(t))return t===1/0&&is_negative_ast(e)||t===-1/0&&is_positive_ast(e)?-1/0:!1===is_nonzero_ast(e)?NaN:1/0;if(0===t)return 0;if(1===t)return e;if(-1===t)return["-",e];if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1])return t*=e[1],e=e[2],1===t?e:-1===t?["-",e]:["*",e,t]}if(math$1.define_i&&"i"===e){if("i"===t)return-1;if(Array.isArray(t)&&"*"===t[0]&&"i"===t[1])return["-",t[2]]}else if(math$1.define_i&&"i"===t&&Array.isArray(e)&&"*"===e[0]&&"i"===e[1])return["-",e[2]];return null}function try_evaluate_quotient_of_numbers(e,t,r,n){if("number"==typeof e){if(0===e){let e=is_nonzero_ast(t,r);if(e)return 0;if(!1===e)return NaN}if("number"==typeof t){let r=e/t;if(n===1/0||math$1.round(r,n)===r)return r;if(t<0)return["/",-e,-t]}if(Array.isArray(t)&&"*"===t[0]&&"number"==typeof t[1]){let r=e/t[1];if(n===1/0||math$1.round(r,n)===r)return["/",r,t[2]]}}else if("number"==typeof t){if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1]){let r=e[1]/t;if(n===1/0||math$1.round(r,n)===r)return 1===r?e[2]:["*",r,e[2]];if(t<0)return["/",["*",-e[1],e[2]],-t]}let r=1/t;if(n===1/0||math$1.round(r,n)===r)return["*",r,e];if(t<0)return Array.isArray(e)&&"-"===e[0]?["/",e[1],-t]:["-",["/",e,-t]]}return null}function evaluate_numbers_sub(e,t,r,n,i,a){if(void 0===e)return e;if("number"==typeof e)return a>0&&math$1.abs(e)0&&math$1.abs(t)evaluate_numbers_sub(e,t,r,n,i,a)));if("+"===s){let e=u[0],t=u[1];if(void 0===t)return e;let r=try_evaluate_sum_of_numbers(e,t,n);if(null!==r)return r;if("unit"===e[0]&&"unit"===t[0]){let r=get_unit_of_tree(e),i=get_unit_of_tree(t);if(r&&r===i){let i=try_evaluate_sum_of_numbers(remove_units(e,!1),remove_units(t,!1),n);if(null!==i)return add_unit(i,r)}}return[s].concat(u)}if("-"===s){let e=try_evaluate_negate_number(u[0]);if(null!==e)return e;if("unit"===u[0][0]){let e=get_unit_of_tree(u[0]);if(e){let t=try_evaluate_negate_number(remove_units(u[0],!1));if(null!==t)return add_unit(t,e)}}return[s].concat(u)}if("*"===s){let e=u[0],t=u[1];if(void 0===t)return e;let r=try_evaluate_product_of_numbers(e,t);if(null!==r)return r;if("unit"===e[0]&&"unit"!==t[0]){let r=get_unit_of_tree(e);if(r){let n=try_evaluate_product_of_numbers(remove_units(e,!1),t);if(null!==n)return add_unit(n,r)}}if("unit"!==e[0]&&"unit"===t[0]){let r=get_unit_of_tree(t);if(r){let n=try_evaluate_product_of_numbers(e,remove_units(t,!1));if(null!==n)return add_unit(n,r)}}return[s].concat(u)}if("/"===s){let e=u[0],n=u[1],i=try_evaluate_quotient_of_numbers(e,n,t,r);if(null!==i)return i;if("unit"===e[0]&&"unit"!==n[0]){let i=get_unit_of_tree(e);if(i){let a=try_evaluate_quotient_of_numbers(remove_units(e,!1),n,t,r);if(null!==a)return add_unit(a,i)}}return[s].concat(u)}if("^"===s){let e=u[0],n=u[1];if("number"==typeof n)if(0===n){if(!math$1.pow_strict)return 1;let r=is_nonzero_ast(e,t);if(r&&e!==1/0&&e!==-1/0)return 1;if(!1===r)return NaN}else{if(1===n)return e;if("number"==typeof e){let t=math$1.pow(e,n);if(r===1/0||math$1.round(t,r)===t)return t}}else if(1===e)return 1;return[s].concat(u)}return[s].concat(u)}function evaluate_numbers(e,{assumptions:t,max_digits:r,skip_ordering:n=!1,evaluate_functions:i=!1,set_small_zero:a=0}={}){(void 0===r||!Number.isInteger(r)&&r!==1/0)&&(r=0),!0===a&&(a=1e-14);var o,s=get_tree(e);return contains_blank(s)?s:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),n?o=evaluate_numbers_sub(s=unflattenRight(flatten$5(s)),t,r,n,i,a):(s=move_units_outside_products(s),s=unflattenRight(default_order(flatten$5(s))),o=default_order(evaluate_numbers_sub(s,t,r,n,i,a)),o=default_order(evaluate_numbers_sub(unflattenRight(o),t,r,n,i,a))),flatten$5(o=set_negative_zeros_to_zero(o)))}function set_negative_zeros_to_zero(e){return 0===e?0:Array.isArray(e)?[e[0],...e.slice(1).map(set_negative_zeros_to_zero)]:e}function collect_like_terms_factors(e,t,r){function n(e){return"number"==typeof e||!(!Array.isArray(e)||"-"!==e[0]||"number"!=typeof e[1])}function i(e){return"number"==typeof e&&e<0||!(!Array.isArray(e)||"-"!==e[0]||"number"!=typeof e[1])}function a(e){if("number"==typeof e)return!0;if(Array.isArray(e)&&"-"===e[0]&&"number"==typeof e[1])return!0;let t=evaluate_to_constant(e,!1);return!("number"!=typeof t||!Number.isFinite(t))}var o=get_tree(e);if(contains_blank(o))return o;void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),o=evaluate_numbers(o,{assumptions:t,max_digits:r,evaluate_functions:!0});var s=[];s.push([["/","x",["^","y","a"]],["*","x",["^","y",["-","a"]]],{evaluate_numbers:!0,max_digits:r}]),s.push([["/","x",["apply","exp","a"]],["*","x",["apply","exp",["-","a"]]],{evaluate_numbers:!0,max_digits:r,variables:{x:!0,a:!0}}]),s.push([["/","x","y"],["*","x",["^","y",["-",1]]],{evaluate_numbers:!0,max_digits:r}]),o=applyAllTransformations(o,s,40),s=[];for(let e in all_units){all_units[e].prefix?(s.push([["+",["unit",e,"x"],["unit",e,"y"]],["unit",e,["+","x","y"]],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["unit",e,"x"],["-",["unit",e,"y"]]],["unit",e,["+","x",["-","y"]]],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}])):(s.push([["+",["unit","x",e],["unit","y",e]],["unit",["+","x","y"],e],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["unit","x",e],["-",["unit","y",e]]],["unit",["+","x",["-","y"]],e],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]))}return s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:e=>is_nonzero_ast(e,t),n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:!0,n:e=>n(e)&&is_positive_ast(e,t),m:e=>n(e)&&is_positive_ast(e,t)},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:!0,n:e=>n(e)&&is_negative_ast(e,t),m:e=>n(e)&&is_negative_ast(e,t)},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["apply","exp","n"],["apply","exp","m"]],["apply","exp",["+","n","m"]],{variables:{n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n","x"],["*","m","x"]],["*",["+","n","m"],"x"],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n1","x"],["*",["/","n2","m2"],"x"]],["*",["+","n1",["/","n2","m2"]],"x"],{variables:{x:!0,n1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n1","x"],["*",["-",["/","n2","m2"]],"x"]],["*",["+","n1",["-",["/","n2","m2"]]],"x"],{variables:{x:!0,n1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*",["/","n1","m1"],"x"],["*",["/","n2","m2"],"x"]],["*",["+",["/","n1","m1"],["/","n2","m2"]],"x"],{variables:{x:!0,n1:n,m1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m1","m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*",["/","n1","m1"],"x"],["*",["-",["/","n2","m2"]],"x"]],["*",["+",["/","n1","m1"],["-",["/","n2","m2"]]],"x"],{variables:{x:!0,n1:n,m1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m1","m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n","x"],["-",["*","m","x"]]],["*",["+","n",["-","m"]],"x"],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["^",["*","x","y"],"a"],["*",["^","x","a"],["^","y","a"]],{allow_permutations:!0}]),s.push([["^",["^","x","n"],"m"],["^","x",["*","n","m"]],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_permutations:!0}]),s.push([["-",["+","a","b"]],["+",["-","a"],["-","b"]]]),s.push([["*","x","y"],["*","x","y"],{variables:{x:a,y:a},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),o=applyAllTransformations(o,s,40),(s=[]).push([["*","x",["^","y",["-","a"]]],["/","x",["^","y","a"]],{allow_extended_match:!0,allow_permutations:!0,evaluate_numbers:!0,max_digits:r,max_group:1}]),s.push([["*","x",["apply","exp",["-","a"]]],["/","x",["apply","exp","a"]],{allow_extended_match:!0,allow_permutations:!0,evaluate_numbers:!0,max_digits:r,max_group:1,variables:{x:!0,a:!0}}]),s.push([["*","x",["^","y","n"]],["/","x",["^","y",["-","n"]]],{variables:{x:!0,y:!0,n:i},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*","x",["apply","exp","n"]],["/","x",["apply","exp",["-","n"]]],{variables:{x:!0,n:i},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),o=applyAllTransformations(o,s,40),(s=[]).push([["^","y","n"],["/",1,["^","y",["-","n"]]],{variables:{y:!0,n:i},evaluate_numbers:!0,max_digits:r}]),s.push([["apply","exp","n"],["/",1,["apply","exp",["-","n"]]],{variables:{n:i},evaluate_numbers:!0,max_digits:r}]),o=applyAllTransformations(o,s,40),(s=[]).push([["*","x",["/","y","z"]],["/",["*","x","y"],"z"],{allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["/",["/","x","y"],"z"],["/","x",["*","y","z"]],{allow_extended_match:!0,allow_permutations:!0}]),s.push([["/","x",["/","y","z"]],["/",["*","x","z"],"y"],{allow_extended_match:!0,allow_permutations:!0}]),o=evaluate_numbers(o=applyAllTransformations(o,s,40),{assumptions:t,max_digits:r})}function simplify_ratios(e,t){function r(e){var t=1;return e=e.map((function(e){if("number"==typeof e)return e<0?(t*=-1,-e):e;if(!Array.isArray(e))return e;if("-"===e[0])return t*=-1,e[1];if("+"!==e[0])return e;var r=!1;if(("number"==typeof e[1]&&e[1]<0||Array.isArray(e[1])&&"-"===e[1][0]||Array.isArray(e[1])&&"*"===e[1][0]&&Number(e[1][1])<0)&&(r=!0),r){t*=-1;var n=e.slice(1).map((e=>["-",e]));return evaluate_numbers(["+"].concat(n))}return e})),{factors:e,sign_change:t}}var n=get_tree(e);return contains_blank(n)?n:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),function e(t,n){if(!Array.isArray(t))return n?["-",t]:t;var i=t[0];if("-"===i)return e(t[1],n=!0);var a=t.slice(1).map((t=>e(t)));if("/"!==i)return n?["-",[i,...a]]:[i,...a];var o,s=a[0],u=a[1];s=default_order(s,{ignore_negatives:!0});var c,l=r(o=Array.isArray(s)&&"*"===s[0]?s.slice(1):[s]);o=l.factors,n&&(l.sign_change*=-1),u=default_order(u,{ignore_negatives:!0});var f=r(c=Array.isArray(u)&&"*"===u[0]?u.slice(1):[u]);return c=f.factors,l.sign_change*f.sign_change<0&&(o[0]=["-",o[0]]),["/",s=1===o.length?o[0]:["*"].concat(o),u=1===c.length?c[0]:["*"].concat(c)]}(n))}function contains_blank(e){return"＿"===e||!!Array.isArray(e)&&e.some(contains_blank)}let all_units=get_all_units();function remove_units(e,t=!0){var r=get_tree(e);if(!Array.isArray(r))return r;let n=r[0],i=r.slice(1);if("unit"===n){let e=all_units[get_unit_of_tree(r)];if(!e)return r;let n=remove_units(e.prefix?i[1]:i[0],t);return t?e.scale(n):n}return[n,...i.map((e=>remove_units(e,t)))]}function remove_scaling_units(e){var t=get_tree(e);if(!Array.isArray(t))return t;let r=t[0],n=t.slice(1);if("unit"===r){let e=all_units[get_unit_of_tree(t)];if(!e||!e.only_scales)return t;let r=remove_scaling_units(e.prefix?n[1]:n[0]);return e.scale(r)}return[r,...n.map((e=>remove_scaling_units(e)))]}function add_unit(e,t){var r=get_tree(e);let n=all_units[t];return n?n.prefix?["unit",t,r]:["unit",r,t]:r}function move_units_outside_products(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("*"===t){let e=[],t=[];for(let n of r){let r=get_unit_value_of_tree(n);r?(e.push(r[0]),t.push(r[1])):t.push(n)}let n=["*",...t];for(let t of e)n=add_unit(n,t);return n}return[t,...r.map(move_units_outside_products)]}var simplify$1=Object.freeze({__proto__:null,clean:clean,simplify:simplify,simplify_logical:simplify_logical,evaluate_numbers:evaluate_numbers,collect_like_terms_factors:collect_like_terms_factors,collapse_unary_minus:collapse_unary_minus,simplify_ratios:simplify_ratios,default_order:default_order,perform_vector_matrix_additions_scalar_multiplications:perform_vector_matrix_additions_scalar_multiplications,remove_units:remove_units,add_unit:add_unit,remove_scaling_units:remove_scaling_units});function solve_linear(e,t,r){if("string"==typeof t){void 0===r&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(r=e.context.get_assumptions([e.variables()]));var n=simplify(get_tree(e),r);if(Array.isArray(n)){var i=n[0],a=n.slice(1);if("="===i||"ne"===i||"<"===i||"le"===i||">"===i||"ge"===i){var o=simplify(["+",a[0],["-",a[1]]],r),s=e=>!variables(e).includes(t);if(variables(o=simplify(applyAllTransformations(o,[[["+",["*","_a",t],["*","_b",t]],["*",["+","_a","_b"],t],{variables:{_a:s,_b:s},allow_permutations:!0,allow_extended_match:!0,allow_implicit_identities:["_a","_b"],evaluate_numbers:!0}]],20))).includes(t)){var u=match$2(o,["+",["*","_a",t],"_b"],{variables:{_a:s,_b:s},allow_permutations:!0,allow_implicit_identities:["_a","_b"]});if(u){var c=simplify(u._a),l=simplify(u._b);if(is_nonzero_ast(c,r)){if("="===i||"ne"===i||is_positive_ast(c,r)){let e=simplify(["/",["-",l],c]);return[i,t,e]}if(is_negative_ast(c,r)){var f=simplify(["/",["-",l],c]);return[i="<"===i?">":"le"===i?"ge":">"===i?"<":"le",t,f]}}}}}}}}var 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n=this.factor(e);this.simple_factor_or_function_or_parens(e)||"_"===e[0]&&"string"==typeof e[1]||(n="\\left("+n+"\\right)");for(let e=0;e1?s=s.trimRight()+"^{"+a+"}"+this.stringConvert(o):s+=this.stringConvert(o),s="\\frac{ "+s+" }{ ";let u=1;Array.isArray(i)&&(u=i.length-1);for(let t=1;t<=u;t++){let r=i[t],n=1,a="";Array.isArray(r)?(a=r[1],n=r[2]):a=r,s=s+e+this.stringConvert(a),n>1&&(s=s+"^{"+n+"}"),s+=" "}return s+="}",s}if("apply"===t){if("abs"===r[0])return"\\left|"+this.statement(r[1])+"\\right|";if("floor"===r[0])return"\\left\\lfloor "+this.statement(r[1])+" \\right\\rfloor";if("ceil"===r[0])return"\\left\\lceil "+this.statement(r[1])+" \\right\\rceil";if("factorial"===r[0]){let e=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||"_"===r[1][0]&&"string"==typeof r[1][1]?e+"!":"\\left("+e+"\\right)!"}if("sqrt"===r[0])return"\\sqrt{"+this.statement(r[1])+"}";let e,t=r[0];if("^"===t[0]&&(t=t[1]),"_"===t[0]&&(t=t[1]),"int"===t){let e,t=this.factor(r[0]),n=r[1];if(Array.isArray(n)&&"*"===n[0]){let t=[],r=["*"];for(let e=1;e0&&(e[e.length-1].match(/[a-zA-Z]/)&&(e+="\\,"),e+=t.map((e=>"d"+this.factor(e[1]))).join("\\,"))}return e||(e=this.term(r[1])),t+" "+e}e="log10"===r[0]?"\\log_{10}":"re"===r[0]?"\\Re":"im"===r[0]?"\\Im":this.factor(r[0]);let n=this.statement(r[1]);return"tuple"!==r[1][0]&&(n="\\left("+n+"\\right)"),e+n}if("angle"===t){let e=r.every((e=>{if("string"==typeof e&&1===e.length)return!0;if(!Array.isArray(e))return!1;let t=e[0];return"_"===t||"^"===t||"prime"===t}));return operators$1[t](r.map(function(e,t){return this.statement(e)}.bind(this)),e)}return"+"===t&&2===e.length?"+ "+this.factor(e[1]):"\\left("+this.statement(e)+"\\right)"}factorWithParenthesesIfNegatedOrExplicitPlus(e){var t=this.factor(e);return t.match(/^-/)||t.match(/^\+/)?"\\left("+t+"\\right)":t}termWithPlusIfNotNegated(e){var t=this.term(e);return t.match(/^-/)?t.match(/^-[^ ]/)?"- "+t.slice(1):t:"+ "+t}}const textToAst$2=new textToAst$4,astToLatex=new astToLatex$1;var derivatives={sin:textToAst$2.convert("cos x"),cos:textToAst$2.convert("-(sin x)"),tan:textToAst$2.convert("(sec x)^2"),cot:textToAst$2.convert("-((csc x)^2)"),sec:textToAst$2.convert("(sec x)*(tan x)"),csc:textToAst$2.convert("-(csc x)*(cot x)"),sqrt:textToAst$2.convert("1/(2*sqrt(x))"),log:textToAst$2.convert("1/x"),ln:textToAst$2.convert("1/x"),exp:textToAst$2.convert("exp(x)"),arcsin:textToAst$2.convert("1/sqrt(1 - x^2)"),arccos:textToAst$2.convert("-1/sqrt(1 - x^2)"),arctan:textToAst$2.convert("1/(1 + x^2)"),arccsc:textToAst$2.convert("-1/(sqrt(-1/x^2 + 1)*x^2)"),arcsec:textToAst$2.convert("1/(sqrt(-1/x^2 + 1)*x^2)"),arccot:textToAst$2.convert("-1/(1 + x^2)"),abs:textToAst$2.convert("abs(x)/x")};function derivative(e,t,r=[]){var n=get_tree(e),i="\\frac{d}{d"+t+"} ";if("number"==typeof n)return r.push("The derivative of a constant is zero, that is, \\("+i+astToLatex.convert(n)+" = 0\\)."),0;if(variables(n).indexOf(t)<0)return r.push("The derivative of a constant is zero, that is, \\("+i+astToLatex.convert(n)+" = 0\\)."),0;if("string"==typeof n)return t===n?(r.push("We know the derivative of the identity function is one, that is, \\("+i+astToLatex.convert(n)+" = 1\\)."),1):(r.push("As far as \\("+astToLatex.convert(t)+"\\) is concerned, \\("+astToLatex.convert(n)+"\\) is constant, so "+i+astToLatex.convert(n)+" = 0\\)."),0);if(!Array.isArray(n))return null;var a=n[0],o=n.slice(1);if("+"===a||"-"===a||"~"===a){r.push("Using the sum rule, \\("+i+astToLatex.convert(n)+" = "+o.map((function(e,t){return i+astToLatex.convert(e)})).join(" + ")+"\\).");let e=[a].concat(o.map((function(e,n){return derivative(e,t,r)})));return e=simplify(e),r.push("So using the sum rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("*"===a){let e=[],a=[];for(let r=0;r0){if(0===e.length){return r.push("Since the derivative of a constant is zero, \\("+i+astToLatex.convert(n)+" = 0.\\)"),0}let o=["*"].concat(e);if(1===e.length&&(o=e[0]),o===t){r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+a.map((function(e,t){return astToLatex.convert(e)})).join(" \\cdot ")+"\\).");let e=["*"].concat(a);return e=simplify(e),e}r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+a.map((function(e,t){return astToLatex.convert(e)})).join(" \\cdot ")+" \\cdot "+i+"\\left("+astToLatex.convert(o)+"\\right)\\).");let s=derivative(o,t,r),u=["*"].concat(a.concat([s]));return u=simplify(u),r.push("And so \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}r.push("Using the product rule, \\("+i+astToLatex.convert(n)+" = "+o.map((function(e,t){return o.map((function(r,n){return t===n?i+"\\left("+astToLatex.convert(e)+"\\right)":astToLatex.convert(r)})).join(" \\cdot ")})).join(" + ")+"\\).");let s=o.slice(),u=["+"].concat(o.map((function(e,n){return["*"].concat(s.map((function(e,i){if(n===i){let n=derivative(e,t,r);return 1===n?null:n}return e})).filter((function(e){return null!=e})))})));return u=simplify(u),r.push("So using the product rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if("/"===a){let e=o[0],a=o[1];if(variables(a).indexOf(t)<0){r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(["/",1,a])+" \\cdot "+i+"\\left("+astToLatex.convert(e)+"\\right)\\).");let o=derivative(e,t,r),s=textToAst$2.convert("(1/g)*d"),u=substitute$1(s,{d:o,g:a});return u=simplify(u),r.push("So \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if(variables(e).indexOf(t)<0){1!==e&&r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+" \\cdot "+i+"\\left("+astToLatex.convert(["/",1,a])+"\\right)\\)."),r.push("Since \\(\\frac{d}{du} \\frac{1}{u}\\) is \\(\\frac{-1}{u^2}\\), the chain rule gives \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\cdot \\frac{-1}{ "+astToLatex.convert(a)+"^2} \\cdot "+i+astToLatex.convert(a)+"\\).");let o=derivative(a,t,r),s=textToAst$2.convert("f * (-a/(g^2))"),u=substitute$1(s,{f:e,a:o,g:a});return u=simplify(u),r.push("So since \\(\\frac{d}{du} \\frac{1}{u}\\) is \\(\\frac{-1}{u^2}\\), the chain rule gives \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}r.push("Using the quotient rule, \\("+i+astToLatex.convert(n)+" = \\frac{"+i+"\\left("+astToLatex.convert(e)+"\\right) \\cdot "+astToLatex.convert(a)+" - "+astToLatex.convert(e)+"\\cdot "+i+"\\left("+astToLatex.convert(a)+"\\right)}{ \\left( "+astToLatex.convert(a)+" \\right)^2} \\).");let s=derivative(e,t,r),u=derivative(a,t,r),c=textToAst$2.convert("(a * g - f * b)/(g^2)"),l=substitute$1(c,{a:s,b:u,f:e,g:a});return l=simplify(l),r.push("So using the quotient rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(l)+"\\)."),l}if("^"===a){let e=o[0],a=o[1];if(variables(a).indexOf(t)<0){if("string"==typeof e&&"x"===e){if("number"==typeof a){let t=textToAst$2.convert("n * (f^m)"),o=substitute$1(t,{n:a,m:a-1,f:e});return o=simplify(o),r.push("By the power rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"}\\)."),o}let t=textToAst$2.convert("n * (f^(n-1))"),o=substitute$1(t,{n:a,f:e});return o=simplify(o),r.push("By the power rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"}\\)."),o}1!==a&&r.push("By the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"} \\cdot "+i+astToLatex.convert(e)+"\\).");let o=derivative(e,t,r);if(1===a)return o;if("number"==typeof a){let t=textToAst$2.convert("n * (f^m) * a"),s=substitute$1(t,{n:a,m:a-1,f:e,a:o});return s=simplify(s),r.push("So by the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}let s=textToAst$2.convert("n * (f^(n-1)) * a"),u=substitute$1(s,{n:a,f:e,a:o});return u=simplify(u),r.push("So by the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if("e"===e&&math$1.define_e){if("string"==typeof a&&a===t){let e=textToAst$2.convert("e^(f)"),o=substitute$1(e,{f:a});return o=simplify(o),r.push("The derivative of \\(e^"+astToLatex.convert(t)+"\\) is itself, that is, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(n)+"\\)."),o}r.push("Using the rule for \\(e^x\\) and the chain rule, we know \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(n)+" \\cdot "+i+astToLatex.convert(a)+"\\).");let e=textToAst$2.convert("e^(f)*d"),o=derivative(a,t,r),s=substitute$1(e,{f:a,d:o});return s=simplify(s),r.push("So using the rule for \\(e^x\\) and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}if("number"==typeof e){if("string"==typeof a&&a===t){let o=textToAst$2.convert("a^(f) * log(a)"),s=substitute$1(o,{a:e,f:a});return s=simplify(s),r.push("The derivative of \\(a^"+astToLatex.convert(t)+"\\) is \\(a^{"+astToLatex.convert(t)+"} \\, \\log a\\), that is, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}let o=textToAst$2.convert("a^(f) * log(a)"),s=substitute$1(o,{a:e,f:a});r.push("Using the rule for \\(a^x\\) and the chain rule, we know \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+" \\cdot "+i+astToLatex.convert(a)+"\\).");let u=textToAst$2.convert("a^(b)*log(a)*d"),c=derivative(a,t,r),l=substitute$1(u,{a:e,b:a,d:c});return l=simplify(l),r.push("So using the rule for \\(a^x\\) and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(l)+"\\)."),l}let s=e,u=a;r.push("Recall the general rule for exponents, namely that \\(\\frac{d}{dx} u(x)^{v(x)} = u(x)^{v(x)} \\cdot \\left( v'(x) \\cdot \\log u(x) + \\frac{v(x) \\cdot u'(x)}{u(x)} \\right)\\). In this case, \\(u(x) = "+astToLatex.convert(s)+"\\) and \\(v(x) = "+astToLatex.convert(u)+"\\).");let c=derivative(s,t,r),l=derivative(u,t,r),f=textToAst$2.convert("(f^g)*(b * log(f) + (g * a)/f)"),p=substitute$1(f,{a:c,b:l,f:s,g:u});return p=simplify(p),r.push("So by the general rule for exponents, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(p)+"\\)."),p}if("apply"===a&&!(o[0]in derivatives)){let e=o[1];r.push("By the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(substitute$1(["apply",o[0]+"'","x"],{x:e}))+" \\cdot "+i+astToLatex.convert(e)+"\\).");let a=["*",substitute$1(["apply",o[0]+"'","x"],{x:e}),derivative(e,t,r)];return a=simplify(a),r.push("So by the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+"\\)."),a}if("apply"===a&&o[0]in derivatives||a in derivatives){let e=!1;"apply"===a&&(a=o[0],o=o.slice(1),e=!0);let s=o[0];if("number"==typeof s){let e=0;return r.push("The derivative of a constant is zero so \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("string"==typeof s&&s===t){let e=["*",substitute$1(derivatives[a],{x:s})];return e=simplify(e),r.push("It is the case that \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("string"==typeof s&&s!==t){let e=0;return r.push("Since the derivative of a constant is zero, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}{let o=[a,"u"];e&&(o=["apply"].concat(o)),r.push("Recall \\(\\frac{d}{du}"+astToLatex.convert(o)+" = "+astToLatex.convert(derivative(o,"u",[]))+"\\)."),r.push("By the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(substitute$1(derivatives[a],{x:s}))+" \\cdot "+i+astToLatex.convert(s)+"\\).");let u=["*",substitute$1(derivatives[a],{x:s}),derivative(s,t,r)];return u=simplify(u),r.push("So by the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}}return 0}function lowercaseFirstLetter(e){return e.charAt(0).toLowerCase()+e.slice(1)}function simplify_story(e){for(let t=e.length-1;t>=1;t--)e[t]===e[t-1]&&e.splice(t,1);for(let t=0;t":function(e){return e.join(" > ")},lts:function(e){return e.join(" < ")},gts:function(e){return e.join(" > ")},le:function(e){return e.join(" ≤ ")},ge:function(e){return e.join(" ≥ ")},ne:function(e){return e.join(" ≠ ")},forall:function(e){return"∀ "+e[0]},exists:function(e){return"∃ "+e[0]},in:function(e){return e[0]+" ∈ "+e[1]},notin:function(e){return e[0]+" ∉ "+e[1]},ni:function(e){return e[0]+" ∋ "+e[1]},notni:function(e){return e[0]+" ∌ "+e[1]},subset:function(e){return e[0]+" ⊂ "+e[1]},subseteq:function(e){return e[0]+" ⊆ "+e[1]},notsubset:function(e){return e[0]+" ⊄ "+e[1]},notsubseteq:function(e){return e[0]+" ⊈ "+e[1]},superset:function(e){return e[0]+" ⊃ "+e[1]},superseteq:function(e){return e[0]+" ⊇ "+e[1]},notsuperset:function(e){return e[0]+" ⊅ "+e[1]},notsuperseteq:function(e){return e[0]+" ⊉ "+e[1]},union:function(e){return e.join(" ∪ ")},intersect:function(e){return e.join(" ∩ ")},perp:function(e){return e.join(" ⟂ ")},parallel:function(e){return e.join(" ∥ ")},derivative_leibniz:function(e){return"d"+e[0]+"/d"+e[1]},partial_derivative_leibniz:function(e){return"∂"+e[0]+"/∂"+e[1]},"|":function(e){return e[0]+" | "+e[1]},":":function(e){return e[0]+" : "+e[1]},binom:function(e){return"binom( "+e[0]+", "+e[1]+" )"},vec:function(e){return"vec("+e[0]+")"},linesegment:function(e){return"linesegment( "+e.join(", ")+" )"},angle:function(e,t){return t?"∠"+e.join(""):"∠( "+e.join(", ")+" )"},unit:function(e){return e[0]+" "+e[1]}},nonunicode_operators={"+":function(e){return e.join(" ")},"-":function(e){return"-"+e[0]},"*":function(e){return e.join(" ")},"/":function(e){return e[0]+"/"+e[1]},_:function(e){return e[0]+"_"+e[1]},"^":function(e){return e[0]+"^"+e[1]},prime:function(e){return e[0]+"'"},tuple:function(e){return"( "+e.join(", ")+" )"},array:function(e){return"[ "+e.join(", ")+" ]"},list:function(e){return e.join(", ")},set:function(e){return"{ "+e.join(", ")+" }"},vector:function(e){return"( "+e.join(", ")+" )"},altvector:function(e){return"( "+e.join(", ")+" )"},interval:function(e){return"( "+e.join(", ")+" )"},matrix:function(e){return"( "+e.join(", ")+" )"},and:function(e){return e.join(" and ")},or:function(e){return e.join(" or ")},not:function(e){return"not "+e[0]},"=":function(e){return e.join(" = ")},"<":function(e){return e.join(" < ")},">":function(e){return e.join(" > ")},lts:function(e){return e.join(" < ")},gts:function(e){return e.join(" > ")},le:function(e){return e.join(" <= ")},ge:function(e){return e.join(" >= ")},ne:function(e){return e.join(" ne ")},forall:function(e){return"forall "+e[0]},exists:function(e){return"exists "+e[0]},in:function(e){return e[0]+" elementof "+e[1]},notin:function(e){return e[0]+" notelementof "+e[1]},ni:function(e){return e[0]+" containselement "+e[1]},notni:function(e){return e[0]+" notcontainselement "+e[1]},subset:function(e){return e[0]+" subset "+e[1]},subseteq:function(e){return e[0]+" subseteq "+e[1]},notsubset:function(e){return e[0]+" notsubset "+e[1]},notsubseteq:function(e){return e[0]+" notsubseteq "+e[1]},superset:function(e){return e[0]+" superset "+e[1]},superseteq:function(e){return e[0]+" superseteq "+e[1]},notsuperset:function(e){return e[0]+" notsuperset "+e[1]},notsuperseteq:function(e){return e[0]+" notsuperseteq "+e[1]},union:function(e){return e.join(" union ")},intersect:function(e){return e.join(" intersect ")},perp:function(e){return e.join(" perp ")},parallel:function(e){return e.join(" parallel ")},derivative_leibniz:function(e){return"d"+e[0]+"/d"+e[1]},partial_derivative_leibniz:function(e){return"∂"+e[0]+"/∂"+e[1]},"|":function(e){return e[0]+" | "+e[1]},":":function(e){return e[0]+" : "+e[1]},binom:function(e){return"binom( "+e[0]+", "+e[1]+" )"},vec:function(e){return"vec("+e[0]+")"},linesegment:function(e){return"linesegment( "+e.join(", ")+" )"},angle:function(e,t){return t?"angle "+e.join(""):"angle( "+e.join(", ")+" )"},unit:function(e){return e[0]+" "+e[1]}},output_unicodeDefault=!0;class astToText$2{constructor({output_unicode:e=output_unicodeDefault,padToDigits:t=null,padToDecimals:r=null,showBlanks:n=!0}={}){this.output_unicode=e,this.operators=unicode_operators,e||(this.operators=nonunicode_operators),this.padToDigits=t,this.padToDecimals=r,this.showBlanks=n}convert(e){return this.statement(e)}statement(e){if(!Array.isArray(e))return this.single_statement(e);let t=e[0],r=e.slice(1);if("ldots"===t)return"...";if(!(t in this.operators)&&"apply"!==t)throw new Error("Badly formed ast: operator "+t+" not recognized.");return"and"===t||"or"===t?this.operators[t](r.map(function(e,t){let r=this.single_statement(e);return r.match(/ /)&&!r.match(/^\(.*\)$/)?"("+r+")":r}.bind(this))):this.single_statement(e)}single_statement(e){if(!Array.isArray(e))return this.expression(e);let t=e[0],r=e.slice(1);if("not"===t)return this.operators[t](r.map(function(e,t){let r=this.single_statement(e);return r.match(/ /)&&!r.match(/^\(.*\)$/)?"("+r+")":r}.bind(this)));if("exists"===t||"forall"===t)return this.operators[t]([this.single_statement(r[0])]);if("="===t||"ne"===t||"<"===t||">"===t||"le"===t||"ge"===t||"in"===t||"notin"===t||"ni"===t||"notni"===t||"subset"===t||"notsubset"===t||"subseteq"===t||"notsubseteq"===t||"superset"===t||"notsuperset"===t||"superseteq"===t||"notsuperseteq"===t)return this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this)));if("lts"===t||"gts"===t){let e=r[0],n=r[1];if("tuple"!==e[0]||"tuple"!==n[0])throw new Error("Badly formed ast");let i=this.expression(e[1]);for(let r=1;r ":"lts"===t?this.output_unicode?i+=" ≤ ":i+=" <= ":this.output_unicode?i+=" ≥ ":i+=" >= ",i+=this.expression(e[r+1]);return i}return this.expression(e)}expression(e){if(!Array.isArray(e))return this.term(e);let t=e[0],r=e.slice(1);return"+"===t?1===r.length?"+"+this.term(r[0]):this.operators[t](r.map(function(e,t){return t>0?this.termWithPlusIfNotNegated(e):this.term(e)}.bind(this))):["union","intersect","perp","parallel"].includes(t)?this.operators[t](r.map(function(e,t){return this.term(e)}.bind(this))):this.term(e)}term(e){if(!Array.isArray(e))return this.factor(e);let t=e[0],r=e.slice(1);if("-"===t)return this.operators[t](r.map(function(e,t){return this.term(e)}.bind(this)));if("*"===t)return this.operators[t](r.map(function(e,t){let n;return t>0?(n=this.factorWithParenthesesIfNegatedOrExplicitPlus(e),n.match(/^[0-9]/)?"* "+n:"angle"===e[0]&&r.length>1?"( "+n+" )":n):(n=this.factor(e),"angle"===e[0]&&r.length>1?"( "+n+" )":n)}.bind(this)));if("/"===t){let e=this.factor(r[0]),n=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[0])||(e="("+e+")"),this.simple_factor_or_function_or_parens(r[1])||(n="("+n+")"),this.operators[t]([e,n])}return"unit"===t?this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this))):this.factor(e)}symbolConvert(e){let t={alpha:"α",beta:"β",Gamma:"Γ",gamma:"γ",Delta:"Δ",delta:"δ",epsilon:"ε",zeta:"ζ",eta:"η",Theta:"ϴ",theta:"θ",iota:"ι",kappa:"κ",Lambda:"Λ",lambda:"λ",mu:"μ",nu:"ν",Xi:"Ξ",xi:"ξ",Pi:"Π",pi:"π",rho:"ρ",Sigma:"Σ",sigma:"σ",tau:"τ",Upsilon:"Υ",upsilon:"υ",Phi:"Φ",phi:"ϕ",Psi:"Ψ",psi:"ψ",Omega:"Ω",omega:"ω",perp:"⟂",int:"∫"};return this.output_unicode&&e in t?t[e]:this.showBlanks||"＿"!==e?e:""}simple_factor_or_function_or_parens(e){let t=this.factor(e);return!!(t.length<=1||"string"==typeof e&&e.match(/^\w+$/)||Array.isArray(e)&&"apply"===e[0]||t.match(/^\(.*\)$/)||t.match(/^⟨.*⟩$/))||"number"==typeof e&&(e>=0&&!e.toString().includes("e"))}factor(e){if("string"==typeof e)return this.symbolConvert(e);if("number"==typeof e){if(e===1/0)return this.output_unicode?"∞":"infinity";if(e===-1/0)return this.output_unicode?"-∞":"-infinity";if(Number.isNaN(e))return"NaN";{let t=e.toString(),r=t.indexOf("e");if(-1===r)return null!==this.padToDigits?t=padNumberStringToDigits(t,this.padToDigits):null!==this.padToDecimals&&(t=padNumberStringToDecimals(t,this.padToDecimals)),t;let n=t.substring(0,r),i=t.substring(r+1);if(null!==this.padToDigits)n=padNumberStringToDigits(n,this.padToDigits);else if(null!==this.padToDecimals){let r=Number(i);if(r>0)return t=e.toLocaleString("fullwide",{useGrouping:!1}),padNumberStringToDecimals(t,this.padToDecimals);n=padNumberStringToDecimals(n,this.padToDecimals+r)}return"+"===i[0]?n+" * 10^"+i.substring(1):n+" * 10^("+i+")"}}if(!Array.isArray(e))return"";let t=e[0],r=e.slice(1);if("^"===t){if(Number.isInteger(r[0])&&Number.isInteger(r[1])){let e;return e=r[0]<0?"("+r[0].toString()+")":r[0].toString(),r[1]<0?e+"^("+r[1].toString()+")":e+"^"+r[1].toString()}let e=this.factor(r[0]),t=r[0];for(;"prime"===t[0];)t=t[1];this.simple_factor_or_function_or_parens(t)||"_"===t[0]&&"string"==typeof t[1]||(e="("+e.toString()+")");let n=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||(n="("+n.toString()+")"),e+"^"+n}if("_"===t)return this.operators[t](r.map(function(e,t){let r=this.factor(e);return this.simple_factor_or_function_or_parens(e)?r:"("+r+")"}.bind(this)));if("prime"===t){let e=r[0],t=1;for(;"prime"===e[0];)t+=1,e=e[1];let n=this.factor(e);this.simple_factor_or_function_or_parens(e)||"_"===e[0]&&"string"==typeof e[1]||(n="("+n+")");for(let e=0;e1&&(s=s+"^"+a),s=s+this.symbolConvert(o)+"/";let u=1;Array.isArray(i)&&(u=i.length-1);for(let t=1;t<=u;t++){let r=i[t],n=1,a="";Array.isArray(r)?(a=r[1],n=r[2]):a=r,s=s+e+this.symbolConvert(a),n>1&&(s=s+"^"+n)}return s}if("apply"===t){if("abs"===r[0])return"|"+this.statement(r[1])+"|";if("factorial"===r[0]){let e=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||"_"===r[1][0]&&"string"==typeof r[1][1]?e+"!":"("+e+")!"}let e=r[0];if("^"===e[0]&&(e=e[1]),"_"===e[0]&&(e=e[1]),"int"===e){let e,t=this.factor(r[0]),n=r[1];if(Array.isArray(n)&&"*"===n[0]){let t=[],r=["*"];for(let e=1;e0&&(e+=" "+t.map((e=>"d"+this.factor(e[1]))).join(" "))}return e||(e=this.term(r[1])),t+" "+e}let t=this.factor(r[0]),n=this.statement(r[1]);return"tuple"!==r[1][0]&&(n="("+n+")"),t+n}if("angle"===t){let e=r.every((e=>{if("string"==typeof e&&1===e.length)return!0;if(!Array.isArray(e))return!1;let t=e[0];return"_"===t||"^"===t||"prime"===t}));return this.operators[t](r.map(function(e,t){return this.statement(e)}.bind(this)),e)}return"+"===t&&2===e.length?"+ "+this.factor(e[1]):"("+this.statement(e)+")"}factorWithParenthesesIfNegatedOrExplicitPlus(e){var t=this.factor(e);return t.match(/^-/)||t.match(/^\+/)?"("+t+")":t}termWithPlusIfNotNegated(e){let t=this.term(e);return t.match(/^-/)?t.match(/^-[^ ]/)?"- "+t.slice(1):t:"+ "+t}}var astToText$1=new astToText$2;function subscripts_to_strings(e,t=!1){var r=get_tree(e);if(!Array.isArray(r))return r;let n=r[0],i=r.slice(1);return"_"===n&&(t||i.every((e=>["number","string"].includes(typeof e))))?astToText$1.convert(r):[n].concat(i.map((e=>subscripts_to_strings(e,t))))}function strings_to_subscripts(e){var t=get_tree(e);if("string"==typeof t){let e=t.match(/^([0-9a-zA-Z]+)_([a-zA-Z]+|[0-9]+)$/);if(e){let t=Number(e[1]);isNaN(t)&&(t=e[1]);let r=Number(e[2]);return isNaN(r)&&(r=e[2]),["_",t,r]}return t}if(!Array.isArray(t))return t;let r=t[0],n=t.slice(1);return[r].concat(n.map(strings_to_subscripts))}var normalization=Object.freeze({__proto__:null,normalize_function_names:normalize_function_names,normalize_applied_functions:normalize_applied_functions,log_subscript_to_two_arg_log:log_subscript_to_two_arg_log,substitute_abs:substitute_abs,default_order:default_order,constants_to_floats:constants_to_floats,normalize_angle_linesegment_arg_order:normalize_angle_linesegment_arg_order,tuples_to_vectors:tuples_to_vectors,to_intervals:to_intervals,altvectors_to_vectors:altvectors_to_vectors,subscripts_to_strings:subscripts_to_strings,strings_to_subscripts:strings_to_subscripts}),astToText=new astToText$2;function generate_random_integer(e,t,r){return e=math$1.ceil(e),t=math$1.floor(t),math$1.floor(r()*(t-e+1))+e}const equals$5=function({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,relative_tolerance:a=1e-12,absolute_tolerance:o=0,tolerance_for_zero:s=1e-15,allowed_error_in_numbers:u=0,include_error_in_number_exponents:c=!1,allowed_error_is_absolute:l=!1,rng:f}){if(Array.isArray(e.tree)&&Array.isArray(t.tree)){let p=e.tree[0],m=e.tree.slice(1),d=t.tree[0],h=t.tree.slice(1);if("tuple"===p||"vector"===p||"altvector"===p||"list"===p||"array"===p||"matrix"===p||"interval"===p){if(d!==p)return!1;if(h.length!==m.length)return!1;for(let e=0;e","<","ge","le"].includes(p)){if(2!==h.length)return!1;if(">"===p?(p="<",m=[m[1],m[0]]):"ge"===p&&(p="le",m=[m[1],m[0]]),">"===d?(d="<",h=[h[1],h[0]]):"ge"===d&&(d="le",h=[h[1],h[0]]),p!==d)return!1;let e=["+",m[0],["-",m[1]]],t=["+",h[0],["-",h[1]]],y="="!==p;return component_equals({expr:n.fromAst(e),other:i.fromAst(t),randomBindings:r,expr_context:n,other_context:i,allow_proportional:!0,require_positive_proportion:y,relative_tolerance:a,absolute_tolerance:o,tolerance_for_zero:s,allowed_error_in_numbers:u,include_error_in_number_exponents:c,allowed_error_is_absolute:l,rng:f})}}return component_equals({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,relative_tolerance:a,absolute_tolerance:o,tolerance_for_zero:s,allowed_error_in_numbers:u,include_error_in_number_exponents:c,allowed_error_is_absolute:l,rng:f})},component_equals=function({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,allow_proportional:a=!1,require_positive_proportion:o=!1,relative_tolerance:s,absolute_tolerance:u,tolerance_for_zero:c,allowed_error_in_numbers:l,include_error_in_number_exponents:f,allowed_error_is_absolute:p,rng:m}){var d=1e-20*Number.MAX_VALUE,h=0,y=10;e=e.normalize_function_names(),t=t.normalize_function_names(),e=e.log_subscript_to_two_arg_log(),t=t.log_subscript_to_two_arg_log(),e=e.subscripts_to_strings(),t=t.subscripts_to_strings(),e=e.normalize_applied_functions(),t=t.normalize_applied_functions();let g=rename_functions_with_exponents(e.tree),v=rename_functions_with_exponents(t.tree);e=n.fromAst(rename_vecs(g)),t=i.fromAst(rename_vecs(v));var x=[...new Set([...e.variables(),...t.variables()])];math$1.define_pi&&(x=x.filter((function(e){return"pi"!==e}))),math$1.define_i&&(x=x.filter((function(e){return"i"!==e}))),math$1.define_e&&(x=x.filter((function(e){return"e"!==e})));var b=[];for(let e=0;e1===e.length||e.includes("_")||e.includes("^"))),w=_.filter((e=>x.includes(e)));if(_=_.filter((e=>!x.includes(e))),w.length>0){let r=e.tree,a=t.tree,o="x1";for(;[..._,...x].includes(o);)o+="x1";let s="x2";for(;[..._,...x].includes(s);)s+="x2";for(let e of w){let t=e+e;for(;[..._,...x].includes(t);)t+=e;let n=[[["apply",e,o],["apply",t,o],{variables:{[o]:!0}}]];r=applyAllTransformations(r,n),a=applyAllTransformations(a,n),_.push(t)}e=n.fromAst(r),t=i.fromAst(a)}try{var N=e.f(),$=t.f()}catch(r){return e.equalsViaSyntax(t,{allow_blanks:!0})}let A,M,S;if(l>0){let t=replace_numbers_with_parameters({expr:e,variables:x,include_exponents:f});A=n.fromAst(t.expr_with_params),M=t.parameters;let r=Object.keys(M);if(r.length>0){let e=A.derivative(r[0]);if(p||(e=e.multiply(M[r[0]])),r.length>1)for(let t of r.slice(1)){let r=A.derivative(t);p||(r=r.multiply(M[t])),e=e.add(r)}let t=e.multiply(l);try{S=t.f()}catch(e){}}}var E=1,T=[10,1,100,.1,1e3,.01],O=0;let C=0,k=!0,D=0;for(let e=0;e<1e3;e++){try{var I=B(T[O],m)}catch(e){continue}if(!1===I.always_zero&&(k=!1),!I.equal&&!I.out_of_bounds&&!I.always_zero&&!1!==I.sufficient_finite_values&&(D++,D>100))return!1;if(I.equal){if(I.always_zero){if(!k)continue;if(C+=1,C>5&&(O+=1,C=0),O>=T.length)return!0;continue}return!0}}return!1;function B(e,t){var n,i=r(t,x,e);for(let e=0;eh)||!(0===m||m>h))return{out_of_bounds:!0,always_zero:!1};var g=Math.min(p,m),v=Math.max(p,m),w=1;let A=0;if(S){try{A=math$1.abs(S(n))}catch(e){return{equal_at_start:!1,always_zero:!1}}if(!Number.isFinite(A))return{equal_at_start:!1,always_zero:!1}}if(A+=g*s,A=Math.min(A,.1*g),A+=0!==A||0!==l&&0!==f?u:c,!(0===v||math$1.abs(math$1.subtract(l,f))0))return{equal_at_start:!1,always_zero:!1}}var T=0===v,O=0;for(let e=0;e<100;e++){var C,k=r(t,x,E/100,i);for(let e=0;e=y)return{equal:!0,always_zero:T}}}return{sufficient_finite_values:!1,always_zero:T}}};function replace_numbers_with_parameters({expr:e,variables:t,include_exponents:r=!1}){let n={},i=0;function a(){i++;let e="par"+i;for(;t.includes(e);)i++,e="par"+i;return e}return{expr_with_params:function e(t){if("number"==typeof t){if(0===t)return t;{let e=a();return n[e]=t,e}}if("string"==typeof t){if("pi"===t){if(math$1.define_pi){let e=a();return n[e]=math$1.PI,e}}else if("e"===t&&math$1.define_e){let e=a();return n[e]=math$1.e,e}return t}if(!Array.isArray(t))return t;let i=t[0],o=t.slice(1);return"^"!==i||r?[i,...o.map(e)]:[i,e(o[0]),o[1]]}((e=e.evaluate_numbers({max_digits:1/0})).tree),parameters:n}}function rename_functions_with_exponents(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("apply"===t){let e=r[0];return Array.isArray(e)&&"^"===e[0]&&e.slice(1).every((e=>["number","string"].includes(typeof e)))&&(e=astToText.convert(e)),["apply",e,r[1]]}return[t,...r.map(rename_functions_with_exponents)]}function rename_vecs(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);return"vec"===t&&1===r.length?"__vec_"+astToText.convert(r[0]):[t,...r.map(rename_vecs)]}function randomComplexBindings(e,t,r,n){var i={};return void 0===n?t.forEach((function(t){i[t]=math$1.complex(2*e()*r-r,2*e()*r-r)})):t.forEach((function(t){i[t]=math$1.complex(n[t].re+2*e()*r-r,n[t].im+2*e()*r-r)})),i}const equals$4=function(e,t,{relative_tolerance:r=1e-12,absolute_tolerance:n=0,tolerance_for_zero:i=1e-15,allowed_error_in_numbers:a=0,include_error_in_number_exponents:o=!1,allowed_error_is_absolute:s=!1,allow_blanks:u=!1}={}){if(!u&&(e.variables().includes("＿")||t.variables().includes("＿")))return!1;let c=seedrandom$1("complex_seed");return e=e.remove_scaling_units(),t=t.remove_scaling_units(),!(!e.isAnalytic({allow_abs:!0,allow_arg:!0,allow_relation:!0})||!t.isAnalytic({allow_abs:!0,allow_arg:!0,allow_relation:!0}))&&equals$5({expr:e,other:t,randomBindings:randomComplexBindings,expr_context:e.context,other_context:t.context,relative_tolerance:r,absolute_tolerance:n,tolerance_for_zero:i,allowed_error_in_numbers:a,include_error_in_number_exponents:o,allowed_error_is_absolute:s,rng:c})};function randomRealBindings(e,t,r,n){var i={};return void 0===n?t.forEach((function(t){i[t]=2*e()*r-r})):t.forEach((function(t){i[t]=n[t]+2*e()*r-r})),i}const equals$3=function(e,t,{relative_tolerance:r=1e-12,absolute_tolerance:n=0,tolerance_for_zero:i=1e-15,allowed_error_in_numbers:a=0,include_error_in_number_exponents:o=!1,allowed_error_is_absolute:s=!1}={}){if(!e.isAnalytic()||!t.isAnalytic())return!1;let u=seedrandom("real_seed");return equals$5({expr:e,other:t,randomBindings:randomRealBindings,expr_context:e.context,other_content:t.context,relative_tolerance:r,absolute_tolerance:n,tolerance_for_zero:i,allowed_error_in_numbers:a,include_error_in_number_exponents:o,allowed_error_is_absolute:s,rng:u})},equals$2=function(e,t,{allowed_error_in_numbers:r=0,include_error_in_number_exponents:n=!1,allowed_error_is_absolute:i=!1,allow_blanks:a=!1}={}){if(!a&&(e.variables().includes("＿")||t.variables().includes("＿")))return!1;let o=e.normalize_function_names().normalize_applied_functions().normalize_angle_linesegment_arg_order(),s=t.normalize_function_names().normalize_applied_functions().normalize_angle_linesegment_arg_order();return equal(o.tree,s.tree,{allowed_error_in_numbers:r,include_error_in_number_exponents:n,allowed_error_is_absolute:i})},equals$1=function(e,t,{min_elements_match:r=3,match_partial:n=!1}={}){if(!is_discrete_infinite_set(e))return!1;if(is_discrete_infinite_set(t)){var i=[];let r=e.context.get_assumptions(e);if(void 0!==r&&i.push(r),r=t.context.get_assumptions(t),void 0!==r&&i.push(r),i=0===i.length?void 0:1===i.length?i[0]:clean_assumptions(["and"].concat(i)),n){let r=contained_in(e.tree,t.tree,i,n);if(!1===r)return 0;let a=contained_in(t.tree,e.tree,i,n);return!1===a?0:!0===r?!0===a?1:a:!0===a?r:Math.min(r,a)}return contained_in(e.tree,t.tree,i,n)&&contained_in(t.tree,e.tree,i,n)}{let n=t.tree;if("list"!==n[0])return!1;let i=n.length-2;if("ldots"!==n[i+1][0])return!1;if(icontained_in(e,t,r)))}var i=e[1],a=e[2],o=e[3],s=e[4];if(!Array.isArray(o)||"-"!==o[0]||o[1]!==1/0||s!==1/0)return!1;i=simplify(["/",i,a],r,1/0);var u=t.slice(1),c=[];for(let e=0;ee[0])))];let f=0;for(let e of l){let t=c.map((function(t,r){let n=e/t[0];return Number.isInteger(n)?[t[0],n,r]:void 0})).filter((e=>e)),a=[];for(let n of t){let t=n[0],o=n[1],s=n[2],u=c[s][2],l=c[s][3];for(let n=0;nf&&(f=t)}}return!!(n&&f>0)&&f}function sequence_from_discrete_infinite(e,t){var r=e.tree.slice(1);if(r.length>1)return;let n=r[0][1],i=r[0][2],a=evaluate_numbers(r[0][3]),o=r[0][4];if(!Number.isInteger(a)||o!==1/0)return;let s=[];for(let e=0;e0))throw Error(`Have not implemented equality check with ${n} sign errors.`);if(n>1){let e=r;r=function(t,r){return equalSpecifiedSignErrors(t,r,{equalityFunction:e,n_sign_errors:n-1})}}var i,a,o=e.tree,s=[[o]],u=0;e.tree=["-",o];var c=r(e,t);if(e.tree=o,c)return!0;for(;i=s[u++];)if(i=i[0],Array.isArray(i))for(a=1;a"];function isAnalytic(e,{allow_abs:t=!1,allow_arg:r=!1,allow_relation:n=!1}={}){var i=normalize_applied_functions(normalize_function_names(e)),a=operators$3(i=subscripts_to_strings(i));for(let e=0;e+")},"-":function(e){return"-"+e.join("-")+""},"*":function(e){return e.join('\\cdot*')},"/":function(e){return astToGuppy$1.dfrac(e[0],e[1])},"^":function(e){return astToGuppy$1.power(e[0],e[1])},sin:function(e){return astToGuppy$1.trig("sin",e[0])},cos:function(e){return astToGuppy$1.trig("cos",e[0])},tan:function(e){return astToGuppy$1.trig("tan",e[0])},arcsin:function(e){return astToGuppy$1.trig("arcsin",e[0])},arccos:function(e){return astToGuppy$1.trig("arccos",e[0])},arctan:function(e){return astToGuppy$1.trig("arctan",e[0])},arccsc:function(e){return astToGuppy$1.trig("arccsc",e[0])},arcsec:function(e){return astToGuppy$1.trig("arcsec",e[0])},arccot:function(e){return astToGuppy$1.trig("arccot",e[0])},csc:function(e){return astToGuppy$1.trig("csc",e[0])},sec:function(e){return astToGuppy$1.trig("sec",e[0])},cot:function(e){return astToGuppy$1.trig("cot",e[0])},log:function(e){return astToGuppy$1.trig("log",e[0])},exp:function(e){return astToGuppy$1.trig("exp",e[0])},ln:function(e){return astToGuppy$1.trig("ln",e[0])},sqrt:function(e){return astToGuppy$1.sqrt(e[0])},abs:function(e){return astToGuppy$1.abs(e[0])}}}static dfrac(e,t){return'\\dfrac{}{}\\frac{}{}()/()'+e+''+t+""}static trig(e,t){return'\\'+e+'\\left(\\right) '+e+'()'+t+""}static sqrt(e){return'\\sqrt{}sqrt()'+e+""}static power(e,t){return'{}^{}()^()'+e+''+t+""}static abs(e){return'\\left|\\right|abs()'+e+""}static paren(e){return'\\left(\\right)()'+e+""}static isFunctionSymbol(e){return-1!==["sin","cos","tan","csc","sec","cot","arcsin","arccos","arctan","arccsc","arcsec","arccot","log","ln","exp","sqrt","abs","this.factorial"].indexOf(e)}static isGreekLetterSymbol(e){return-1!==["pi","theta","theta","Theta","alpha","nu","beta","xi","Xi","gamma","Gamma","delta","Delta","pi","Pi","epsilon","epsilon","rho","rho","zeta","sigma","Sigma","eta","tau","upsilon","Upsilon","iota","phi","phi","Phi","kappa","chi","lambda","Lambda","psi","Psi","omega","Omega"].indexOf(e)}factorWithParenthesesIfNegated(e){var t=this.factor(e);return t.toString().match(/^-/)?astToGuppy$1.paren(t.toString()):t}factor(e){if("string"==typeof e)return astToGuppy$1.isGreekLetterSymbol(e)?'\\'+e+' $'+e+"":""+e+"";if("number"==typeof e)return""+e+"";if(!Array.isArray(e))return"";var t=e[0],r=e.slice(1);return"apply"===t&&(t=e[1],r=e.slice(2)),"abs"===t?this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this))):astToGuppy$1.isFunctionSymbol(t)?"this.factorial"!==t||1!==r[0].toString().length&&!r[0].toString().match(/^[0-9]*$/)?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):this.operators[t](r):"^"===t||"~"===t?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):astToGuppy$1.paren(this.expression(e))}term(e){if(!Array.isArray(e))return this.factor(e);var t=e[0],r=e.slice(1);return"*"===t?this.operators[t](r.map(function(e,t){var r=this.factorWithParenthesesIfNegated(e);return r.toString().match(/^[0-9]/)&&t>0?" * "+r:r}.bind(this))):"/"===t?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):this.factor(e)}expression(e){if(!Array.isArray(e))return this.term(e);var t=e[0],r=e.slice(1);return"+"===t||"-"===t?this.operators[t](r.map(function(e,t){return this.factorWithParenthesesIfNegated(e)}.bind(this))):this.term(e)}convert(e){return(""+this.expression(e)+"").replace(/<\/e>/g,"")}}const glslOperators={"+":function(e){var t=e[0];return e.slice(1).forEach((function(e){t=t+"+"+e})),t},"-":function(e){var t="-"+e[0];return e.slice(1).forEach((function(e){t=t+"-"+e})),t},"~":function(e){var t="vec2(0.0,0.0)";return e.forEach((function(e){t=t+"-"+e})),t},"*":function(e){var t=e[0];return e.slice(1).forEach((function(e){t="cmul("+t+","+e+")"})),t},"/":function(e){var t=e[0];return e.slice(1).forEach((function(e){t="cdiv("+t+","+e+")"})),t},sin:function(e){return"csin("+e[0]+")"},cos:function(e){return"ccos("+e[0]+")"},tan:function(e){return"ctan("+e[0]+")"},sinh:function(e){return"csinh("+e[0]+")"},cosh:function(e){return"ccosh("+e[0]+")"},arcsin:function(e){return"carcsin("+e[0]+")"},arccos:function(e){return"carccos("+e[0]+")"},arctan:function(e){return"carctan("+e[0]+")"},arccsc:function(e){return"carcsin(cdiv(vec2(1.0,0),"+e[0]+"))"},arcsec:function(e){return"carccos(cdiv(vec2(1.0,0),"+e[0]+"))"},arccot:function(e){return"carctan(cdiv(vec2(1.0,0),"+e[0]+"))"},csc:function(e){return"ccsc("+e[0]+")"},sec:function(e){return"csec("+e[0]+")"},cot:function(e){return"ccot("+e[0]+")"},exp:function(e){return"cexp("+e[0]+")"},conj:function(e){return"conjugate("+e[0]+")"},sqrt:function(e){return"cpower("+e[0]+",vec2(0.5,0.0))"},log:function(e){return"clog("+e[0]+")"},ln:function(e){return"clog("+e[0]+")"},"^":function(e){return"cpower("+e[0]+","+e[1]+")"},abs:function(e){return"cabs("+e[0]+")"},apply:function(e){return"vec2(NaN,NaN)"}};class astToGLSL$1{constructor(){}convert(e){if("boolean"==typeof e)throw Error("no support for boolean");if("string"==typeof e)return"e"===e?"vec2(2.71828182845905,0.0)":"pi"===e?"vec2(3.14159265358979,0.0)":"i"===e?"vec2(0.0,1.0)":String(e);if("number"==typeof e)return"vec2("+String(e)+",0.0)";if("real"in e&&"imaginary"in e)return e;if(!Array.isArray(e))throw Error("Invalid ast");var t=e[0],r=e.slice(1);if("apply"===t){if("string"!=typeof r[0])throw Error("Non string functions not implemented for conversion to GLSL");t=r[0],r=r.slice(1);return glslOperators[t](r.map(function(e,t){return this.convert(e)}.bind(this)))}if(t in glslOperators)return glslOperators[t](r.map(function(e,t){return this.convert(e)}.bind(this)));throw Error("Operator "+t+" not implemented for conversion to mathjs")}}var astToGuppy=new astToGuppy$1,astToGLSL=new astToGLSL$1;const tex=function(e,t){return new astToLatex$1(t).convert(e.tree)},toLatex=tex,toString=function(e,t){return new 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e(t.start,t.end,t.step)},e}),{isClass:!0}),name$4x="Matrix",dependencies$4x=[],createMatrixClass=factory(name$4x,dependencies$4x,(()=>{function e(){if(!(this instanceof e))throw new SyntaxError("Constructor must be called with the new operator")}return e.prototype.type="Matrix",e.prototype.isMatrix=!0,e.prototype.storage=function(){throw new Error("Cannot invoke storage on a Matrix interface")},e.prototype.datatype=function(){throw new Error("Cannot invoke datatype on a Matrix interface")},e.prototype.create=function(e,t){throw new Error("Cannot invoke create on a Matrix interface")},e.prototype.subset=function(e,t,r){throw new Error("Cannot invoke subset on a Matrix interface")},e.prototype.get=function(e){throw new Error("Cannot invoke get on a Matrix interface")},e.prototype.set=function(e,t,r){throw new Error("Cannot invoke set on a Matrix interface")},e.prototype.resize=function(e,t){throw new Error("Cannot invoke resize on a Matrix interface")},e.prototype.reshape=function(e,t){throw new Error("Cannot invoke reshape on a Matrix interface")},e.prototype.clone=function(){throw new Error("Cannot invoke clone on a Matrix interface")},e.prototype.size=function(){throw new Error("Cannot invoke size on a Matrix interface")},e.prototype.map=function(e,t){throw new Error("Cannot invoke map on a Matrix interface")},e.prototype.forEach=function(e){throw new Error("Cannot invoke forEach on a Matrix interface")},e.prototype[Symbol.iterator]=function(){throw new Error("Cannot iterate a Matrix interface")},e.prototype.toArray=function(){throw new Error("Cannot invoke toArray on a Matrix interface")},e.prototype.valueOf=function(){throw new Error("Cannot invoke valueOf on a Matrix interface")},e.prototype.format=function(e){throw new Error("Cannot invoke format on a Matrix interface")},e.prototype.toString=function(){throw new Error("Cannot invoke toString on a Matrix 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a,o,s=n[0],u=n[1],c=[];for(a=0;a");if(1===a.length){t.dimension(0).forEach((function(t,i){validateIndex(t),e.set([t,0],r[i[0]],n)}))}else{var c=t.dimension(0),l=t.dimension(1);c.forEach((function(t,i){validateIndex(t),l.forEach((function(a,o){validateIndex(a),e.set([t,a],r[i[0]][o[0]],n)}))}))}}return e}(this,e,t,r);default:throw new SyntaxError("Wrong number of arguments")}},i.prototype.get=function(e){if(!isArray$1(e))throw new TypeError("Array expected");if(e.length!==this._size.length)throw new DimensionError(e.length,this._size.length);if(!this._values)throw new Error("Cannot invoke get on a Pattern only matrix");var t=e[0],r=e[1];validateIndex(t,this._size[0]),validateIndex(r,this._size[1]);var n=o(t,this._ptr[r],this._ptr[r+1],this._index);return nl-1||c>f-1)&&(u(this,Math.max(a+1,l),Math.max(c+1,f),i),l=this._size[0],f=this._size[1]),validateIndex(a,l),validateIndex(c,f);var d=o(a,this._ptr[c],this._ptr[c+1],this._index);return dArray.isArray(e)&&1===e.length?e[0]:e));if(2!==n.length)throw new Error("Only two dimensions matrix are supported");return n.forEach((function(e){if(!isNumber$1(e)||!isInteger$1(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(n)+")")})),u(r?this.clone():this,n[0],n[1],t)},i.prototype.reshape=function(e,t){if(!isArray$1(e))throw new TypeError("Array expected");if(2!==e.length)throw new Error("Sparse matrices can only be reshaped in two dimensions");e.forEach((function(t){if(!isNumber$1(t)||!isInteger$1(t)||t<=-2||0===t)throw new TypeError("Invalid size, must contain positive integers or -1 (size: "+format$1(e)+")")}));var r=this._size[0]*this._size[1];if(r!==(e=processSizesWildcard(e,r))[0]*e[1])throw new Error("Reshaping sparse matrix will result in the wrong number of elements");var n=t?this.clone():this;if(this._size[0]===e[0]&&this._size[1]===e[1])return n;for(var i=[],a=0;a=n&&b<=a&&h(e._values[x],b-n,y-o)}else{for(var _={},w=g;w 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0;i.splice(f,0,t),n&&n.splice(f,0,m),i.splice(f<=l?l+1:l,1),n&&n.splice(f<=l?l+1:l,1)}else if(f=c||i[l]!==e)){var d=n?n[f]:void 0;i.splice(l,0,e),n&&n.splice(l,0,d),i.splice(l<=f?f+1:f,1),n&&n.splice(l<=f?f+1:f,1)}}},i}),{isClass:!0}),name$4k="number",dependencies$4k=["typed"];function getNonDecimalNumberParts(e){var t=e.match(/(0[box])([0-9a-fA-F]*)\.([0-9a-fA-F]*)/);return t?{input:e,radix:{"0b":2,"0o":8,"0x":16}[t[1]],integerPart:t[2],fractionalPart:t[3]}:null}function makeNumberFromNonDecimalParts(e){for(var t=parseInt(e.integerPart,e.radix),r=0,n=0;n{var{typed:t}=e,r=t("number",{"":function(){return 0},number:function(e){return e},string:function(e){if("NaN"===e)return NaN;var t=getNonDecimalNumberParts(e);if(t)return makeNumberFromNonDecimalParts(t);var r=0,n=e.match(/(0[box][0-9a-fA-F]*)i([0-9]*)/);n&&(r=Number(n[2]),e=n[1]);var i=Number(e);if(isNaN(i))throw new SyntaxError('String "'+e+'" is no valid number');if(n){if(i>2**r-1)throw new SyntaxError('String "'.concat(e,'" is out 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e},number:function(e){return!!e},null:function(e){return!1},BigNumber:function(e){return!e.isZero()},string:function(e){var t=e.toLowerCase();if("true"===t)return!0;if("false"===t)return!1;var r=Number(e);if(""!==e&&!isNaN(r))return!!r;throw new Error('Cannot convert "'+e+'" to a boolean')},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$4h="bignumber",dependencies$4h=["typed","BigNumber"],createBignumber=factory(name$4h,dependencies$4h,(e=>{var{typed:t,BigNumber:r}=e;return t("bignumber",{"":function(){return new r(0)},number:function(e){return new r(e+"")},string:function(e){var t=e.match(/(0[box][0-9a-fA-F]*)i([0-9]*)/);if(t){var n=t[2],i=r(t[1]),a=new r(2).pow(Number(n));if(i.gt(a.sub(1)))throw new SyntaxError('String "'.concat(e,'" is out of range'));var o=new r(2).pow(Number(n)-1);return i.gte(o)?i.sub(a):i}return new r(e)},BigNumber:function(e){return e},Fraction:function(e){return new r(e.n).div(e.d).times(e.s)},null:function(e){return new r(0)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$4g="complex",dependencies$4g=["typed","Complex"],createComplex=factory(name$4g,dependencies$4g,(e=>{var{typed:t,Complex:r}=e;return t("complex",{"":function(){return r.ZERO},number:function(e){return new r(e,0)},"number, number":function(e,t){return new r(e,t)},"BigNumber, BigNumber":function(e,t){return new r(e.toNumber(),t.toNumber())},Fraction:function(e){return new r(e.valueOf(),0)},Complex:function(e){return e.clone()},string:function(e){return r(e)},null:function(e){return r(0)},Object:function(e){if("re"in e&&"im"in e)return new r(e.re,e.im);if("r"in e&&"phi"in e||"abs"in e&&"arg"in e)return new r(e);throw new Error("Expected object with properties (re and im) or (r and phi) or (abs and arg)")},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$4f="fraction",dependencies$4f=["typed","Fraction"],createFraction=factory(name$4f,dependencies$4f,(e=>{var{typed:t,Fraction:r}=e;return t("fraction",{number:function(e){if(!isFinite(e)||isNaN(e))throw new Error(e+" cannot be represented as a fraction");return new r(e)},string:function(e){return new r(e)},"number, number":function(e,t){return new r(e,t)},null:function(e){return new r(0)},BigNumber:function(e){return new r(e.toString())},Fraction:function(e){return e},Object:function(e){return new r(e)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$4e="matrix",dependencies$4e=["typed","Matrix","DenseMatrix","SparseMatrix"],createMatrix=factory(name$4e,dependencies$4e,(e=>{var{typed:t,Matrix:r,DenseMatrix:n,SparseMatrix:i}=e;return t(name$4e,{"":function(){return a([])},string:function(e){return a([],e)},"string, string":function(e,t){return a([],e,t)},Array:function(e){return a(e)},Matrix:function(e){return a(e,e.storage())},"Array | Matrix, string":a,"Array | Matrix, string, string":a});function a(e,t,r){if("dense"===t||"default"===t||void 0===t)return new n(e,r);if("sparse"===t)return new i(e,r);throw new TypeError("Unknown matrix type "+JSON.stringify(t)+".")}})),name$4d="matrixFromFunction",dependencies$4d=["typed","matrix","isZero"],createMatrixFromFunction=factory(name$4d,dependencies$4d,(e=>{var{typed:t,matrix:r,isZero:n}=e;return t(name$4d,{"Array | Matrix, function, string, string":function(e,t,r,n){return i(e,t,r,n)},"Array | Matrix, function, string":function(e,t,r){return i(e,t,r)},"Matrix, function":function(e,t){return i(e,t,"dense")},"Array, function":function(e,t){return i(e,t,"dense").toArray()},"Array | Matrix, string, function":function(e,t,r){return i(e,r,t)},"Array | Matrix, string, string, function":function(e,t,r,n){return i(e,n,t,r)}});function i(e,t,i,a){var o;return(o=void 0!==a?r(i,a):r(i)).resize(e),o.forEach((function(e,r){var i=t(r);n(i)||o.set(r,i)})),o}})),name$4c="matrixFromRows",dependencies$4c=["typed","matrix","flatten","size"],createMatrixFromRows=factory(name$4c,dependencies$4c,(e=>{var{typed:t,matrix:r,flatten:n,size:i}=e;return t(name$4c,{"...Array":function(e){return a(e)},"...Matrix":function(e){return r(a(e.map((e=>e.toArray()))))}});function a(e){if(0===e.length)throw new TypeError("At least one row is needed to construct a matrix.");var t=o(e[0]),r=[];for(var i of e){var a=o(i);if(a!==t)throw new TypeError("The vectors had different length: "+(0|t)+" ≠ "+(0|a));r.push(n(i))}return r}function o(e){var t=i(e);if(1===t.length)return t[0];if(2===t.length){if(1===t[0])return t[1];if(1===t[1])return t[0];throw new TypeError("At least one of the arguments is not a vector.")}throw new TypeError("Only one- or two-dimensional vectors are supported.")}})),name$4b="matrixFromColumns",dependencies$4b=["typed","matrix","flatten","size"],createMatrixFromColumns=factory(name$4b,dependencies$4b,(e=>{var{typed:t,matrix:r,flatten:n,size:i}=e;return t(name$4b,{"...Array":function(e){return a(e)},"...Matrix":function(e){return r(a(e.map((e=>e.toArray()))))}});function a(e){if(0===e.length)throw new TypeError("At least one column is needed to construct a matrix.");for(var t=o(e[0]),r=[],i=0;i{var{typed:t}=e;return t(name$4a,{"Unit, Array":function(e,t){return e.splitUnit(t)}})})),name$49="unaryMinus",dependencies$49=["typed"],createUnaryMinus=factory(name$49,dependencies$49,(e=>{var{typed:t}=e;return t(name$49,{number:unaryMinusNumber,Complex:function(e){return e.neg()},BigNumber:function(e){return e.neg()},Fraction:function(e){return e.neg()},Unit:function(e){var t=e.clone();return t.value=this(e.value),t},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$48="unaryPlus",dependencies$48=["typed","config","BigNumber"],createUnaryPlus=factory(name$48,dependencies$48,(e=>{var{typed:t,config:r,BigNumber:n}=e;return t(name$48,{number:unaryPlusNumber,Complex:function(e){return e},BigNumber:function(e){return e},Fraction:function(e){return e},Unit:function(e){return e.clone()},"Array | Matrix":function(e){return deepMap(e,this)},"boolean | string":function(e){return"BigNumber"===r.number?new n(+e):+e}})})),name$47="abs",dependencies$47=["typed"],createAbs=factory(name$47,dependencies$47,(e=>{var{typed:t}=e;return t(name$47,{number:absNumber,Complex:function(e){return e.abs()},BigNumber:function(e){return e.abs()},Fraction:function(e){return e.abs()},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.abs()}})})),name$46="apply",dependencies$46=["typed","isInteger"],createApply=factory(name$46,dependencies$46,(e=>{var{typed:t,isInteger:r}=e;return t(name$46,{"Array | Matrix, number | BigNumber, function":function(e,t,n){if(!r(t))throw new TypeError("Integer number expected for dimension");var i=Array.isArray(e)?arraySize(e):e.size();if(t<0||t>=i.length)throw new IndexError(t,i.length);return isMatrix(e)?e.create(_apply(e.valueOf(),t,n)):_apply(e,t,n)}})}));function _apply(e,t,r){var n,i,a;if(t<=0){if(Array.isArray(e[0])){for(a=_switch(e),i=[],n=0;n{var{typed:t}=e;return t(name$45,{"number, number":addNumber,"Complex, Complex":function(e,t){return e.add(t)},"BigNumber, BigNumber":function(e,t){return e.plus(t)},"Fraction, Fraction":function(e,t){return e.add(t)},"Unit, Unit":function(e,t){if(null===e.value||void 0===e.value)throw new Error("Parameter x contains a unit with undefined value");if(null===t.value||void 0===t.value)throw new Error("Parameter y contains a unit with undefined value");if(!e.equalBase(t))throw new Error("Units do not match");var r=e.clone();return r.value=this(r.value,t.value),r.fixPrefix=!1,r}})})),name$44="cbrt",dependencies$44=["config","typed","isNegative","unaryMinus","matrix","Complex","BigNumber","Fraction"],createCbrt=factory(name$44,dependencies$44,(e=>{var{config:t,typed:r,isNegative:n,unaryMinus:i,matrix:a,Complex:o,BigNumber:s,Fraction:u}=e;return r(name$44,{number:cbrtNumber,Complex:c,"Complex, boolean":c,BigNumber:function(e){return e.cbrt()},Unit:function(e){if(e.value&&isComplex(e.value)){var t=e.clone();return t.value=1,(t=t.pow(1/3)).value=c(e.value),t}var r,a=n(e.value);a&&(e.value=i(e.value)),r=isBigNumber(e.value)?new s(1).div(3):isFraction(e.value)?new u(1,3):1/3;var o=e.pow(r);return a&&(o.value=i(o.value)),o},"Array | Matrix":function(e){return deepMap(e,this)}});function c(e,r){var n=e.arg()/3,i=e.abs(),s=new o(cbrtNumber(i),0).mul(new o(0,n).exp());if(r){var u=[s,new o(cbrtNumber(i),0).mul(new o(0,n+2*Math.PI/3).exp()),new o(cbrtNumber(i),0).mul(new o(0,n-2*Math.PI/3).exp())];return"Array"===t.matrix?u:a(u)}return s}})),name$43="algorithm11",dependencies$43=["typed","equalScalar"],createAlgorithm11=factory(name$43,dependencies$43,(e=>{var{typed:t,equalScalar:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=r,h=0,y=i;"string"==typeof l&&(f=l,d=t.find(r,[f,f]),h=t.convert(0,f),n=t.convert(n,f),y=t.find(i,[f,f]));for(var g=[],v=[],x=[],b=0;b{var{typed:t,DenseMatrix:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=i;"string"==typeof l&&(f=l,n=t.convert(n,f),d=t.find(i,[f,f]));for(var h=[],y=[],g=[],v=0;v{var{typed:t}=e;return function(e,n,i,a){var o,s=e._data,u=e._size,c=e._datatype,l=i;"string"==typeof c&&(o=c,n=t.convert(n,o),l=t.find(i,[o,o]));var f=u.length>0?r(l,0,u,u[0],s,n,a):[];return e.createDenseMatrix({data:f,size:clone$3(u),datatype:o})};function r(e,t,n,i,a,o,s){var u=[];if(t===n.length-1)for(var c=0;c{var{typed:t,config:r,round:n}=e;return t(name$40,{number:function(e){return nearlyEqual$1(e,n(e),r.epsilon)?n(e):Math.ceil(e)},"number, number":function(e,t){if(nearlyEqual$1(e,n(e,t),r.epsilon))return n(e,t);var[i,a]="".concat(e,"e").split("e"),o=Math.ceil(Number("".concat(i,"e").concat(Number(a)+t)));return[i,a]="".concat(o,"e").split("e"),Number("".concat(i,"e").concat(Number(a)-t))}})})),createCeil=factory(name$40,dependencies$40,(e=>{var{typed:t,config:r,round:n,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}=e,u=createAlgorithm11({typed:t,equalScalar:a}),c=createAlgorithm12({typed:t,DenseMatrix:s}),l=createAlgorithm14({typed:t}),f=createCeilNumber({typed:t,config:r,round:n});return t("ceil",{number:f.signatures.number,"number,number":f.signatures["number,number"],Complex:function(e){return e.ceil()},"Complex, number":function(e,t){return e.ceil(t)},"Complex, BigNumber":function(e,t){return e.ceil(t.toNumber())},BigNumber:function(e){return nearlyEqual(e,n(e),r.epsilon)?n(e):e.ceil()},"BigNumber, BigNumber":function(e,t){return nearlyEqual(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),Decimal.ROUND_CEIL)},Fraction:function(e){return e.ceil()},"Fraction, number":function(e,t){return e.ceil(t)},"Fraction, BigNumber":function(e,t){return e.ceil(t.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},"Array, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(i(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return a(e,0)?o(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3$="cube",dependencies$3$=["typed"],createCube=factory(name$3$,dependencies$3$,(e=>{var{typed:t}=e;return t(name$3$,{number:cubeNumber,Complex:function(e){return e.mul(e).mul(e)},BigNumber:function(e){return e.times(e).times(e)},Fraction:function(e){return e.pow(3)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(3)}})})),name$3_="exp",dependencies$3_=["typed"],createExp=factory(name$3_,dependencies$3_,(e=>{var{typed:t}=e;return t(name$3_,{number:expNumber,Complex:function(e){return e.exp()},BigNumber:function(e){return e.exp()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3Z="expm1",dependencies$3Z=["typed","Complex"],createExpm1=factory(name$3Z,dependencies$3Z,(e=>{var{typed:t,Complex:r}=e;return t(name$3Z,{number:expm1Number,Complex:function(e){var t=Math.exp(e.re);return new r(t*Math.cos(e.im)-1,t*Math.sin(e.im))},BigNumber:function(e){return e.exp().minus(1)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3Y="fix",dependencies$3Y=["typed","Complex","matrix","ceil","floor","equalScalar","zeros","DenseMatrix"],createFixNumber=factory(name$3Y,["typed","ceil","floor"],(e=>{var{typed:t,ceil:r,floor:n}=e;return t(name$3Y,{number:function(e){return e>0?n(e):r(e)},"number, number":function(e,t){return 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Matrix":function(e){return deepMap(e,this)},"Array | Matrix, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(n(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return o(e,0)?s(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3X="floor",dependencies$3X=["typed","config","round","matrix","equalScalar","zeros","DenseMatrix"],createFloorNumber=factory(name$3X,["typed","config","round"],(e=>{var{typed:t,config:r,round:n}=e;return t(name$3X,{number:function(e){return nearlyEqual$1(e,n(e),r.epsilon)?n(e):Math.floor(e)},"number, number":function(e,t){if(nearlyEqual$1(e,n(e,t),r.epsilon))return n(e,t);var[i,a]="".concat(e,"e").split("e"),o=Math.floor(Number("".concat(i,"e").concat(Number(a)+t)));return[i,a]="".concat(o,"e").split("e"),Number("".concat(i,"e").concat(Number(a)-t))}})})),createFloor=factory(name$3X,dependencies$3X,(e=>{var{typed:t,config:r,round:n,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}=e,u=createAlgorithm11({typed:t,equalScalar:a}),c=createAlgorithm12({typed:t,DenseMatrix:s}),l=createAlgorithm14({typed:t}),f=createFloorNumber({typed:t,config:r,round:n});return t("floor",{number:f.signatures.number,"number,number":f.signatures["number,number"],Complex:function(e){return e.floor()},"Complex, number":function(e,t){return e.floor(t)},"Complex, BigNumber":function(e,t){return e.floor(t.toNumber())},BigNumber:function(e){return nearlyEqual(e,n(e),r.epsilon)?n(e):e.floor()},"BigNumber, BigNumber":function(e,t){return nearlyEqual(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),Decimal.ROUND_FLOOR)},Fraction:function(e){return e.floor()},"Fraction, number":function(e,t){return e.floor(t)},"Fraction, BigNumber":function(e,t){return e.floor(t.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},"Array, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(i(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return a(e,0)?o(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3W="algorithm01",dependencies$3W=["typed"],createAlgorithm01=factory(name$3W,dependencies$3W,(e=>{var{typed:t}=e;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,l=r._ptr,f=r._size,p=r._datatype;if(o.length!==f.length)throw new DimensionError(o.length,f.length);if(o[0]!==f[0]||o[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+f+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,d,h=o[0],y=o[1],g="string"==typeof s&&s===p?s:void 0,v=g?t.find(n,[g,g]):n,x=[];for(m=0;m{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A,M=a&&l?[]:void 0,S=[],E=[],T=a&&l?[]:void 0,O=a&&l?[]:void 0,C=[],k=[];for(w=0;w{var{typed:t,DenseMatrix:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=i;"string"==typeof l&&(f=l,n=t.convert(n,f),d=t.find(i,[f,f]));for(var h=[],y=[],g=[],v=0;v{var{typed:t}=e;return function(e,n,i){var a,o=e._data,s=e._size,u=e._datatype,c=n._data,l=n._size,f=n._datatype,p=[];if(s.length!==l.length)throw new DimensionError(s.length,l.length);for(var m=0;m0?r(d,0,p,p[0],o,c):[];return e.createDenseMatrix({data:h,size:p,datatype:a})};function r(e,t,n,i,a,o){var s=[];if(t===n.length-1)for(var u=0;u{var{typed:t,matrix:r,equalScalar:n,BigNumber:i,DenseMatrix:a}=e,o=createAlgorithm01({typed:t}),s=createAlgorithm04({typed:t,equalScalar:n}),u=createAlgorithm10({typed:t,DenseMatrix:a}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t});return t(name$3S,{"number, number":gcdNumber,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function gcd must be integer numbers");var r=new i(0);for(;!t.isZero();){var n=e.mod(t);e=t,t=n}return e.lt(r)?e.neg():e},"Fraction, Fraction":function(e,t){return e.gcd(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return u(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return l(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return l(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i{var{typed:t,equalScalar:r}=e;return function(e,n,i,a){var o=e._data,s=e._size,u=e._datatype,c=n._values,l=n._index,f=n._ptr,p=n._size,m=n._datatype;if(s.length!==p.length)throw new DimensionError(s.length,p.length);if(s[0]!==p[0]||s[1]!==p[1])throw new RangeError("Dimension mismatch. Matrix A ("+s+") must match Matrix B ("+p+")");if(!c)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var d,h=s[0],y=s[1],g=r,v=0,x=i;"string"==typeof u&&u===m&&(d=u,g=t.find(r,[d,d]),v=t.convert(0,d),x=t.find(i,[d,d]));for(var b=[],_=[],w=[],N=0;N{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._size,s=e._datatype,u=n._values,c=n._size,l=n._datatype;if(o.length!==c.length)throw new DimensionError(o.length,c.length);if(o[0]!==c[0]||o[1]!==c[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+c+")");var f,p=o[0],m=o[1],d=r,h=0,y=i;"string"==typeof s&&s===l&&(f=s,d=t.find(r,[f,f]),h=t.convert(0,f),y=t.find(i,[f,f]));for(var g=a&&u?[]:void 0,v=[],x=[],b=g?[]:void 0,_=[],w=[],N=0;N{var{typed:t,matrix:r,equalScalar:n}=e,i=createAlgorithm02({typed:t,equalScalar:n}),a=createAlgorithm06({typed:t,equalScalar:n}),o=createAlgorithm11({typed:t,equalScalar:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3P,{"number, number":lcmNumber,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function lcm must be integer numbers");if(e.isZero())return e;if(t.isZero())return t;var r=e.times(t);for(;!t.isZero();){var n=t;t=e.mod(n),e=n}return r.div(e).abs()},"Fraction, Fraction":function(e,t){return e.lcm(t)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return o(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return o(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return u(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return u(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i{var{typed:t,config:r,Complex:n}=e;return t(name$3O,{number:function(e){return e>=0||r.predictable?log10Number(e):new n(e,0).log().div(Math.LN10)},Complex:function(e){return new n(e).log().div(Math.LN10)},BigNumber:function(e){return!e.isNegative()||r.predictable?e.log():new n(e.toNumber(),0).log().div(Math.LN10)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3N="log2",dependencies$3N=["typed","config","Complex"],createLog2=factory(name$3N,dependencies$3N,(e=>{var{typed:t,config:r,Complex:n}=e;return t(name$3N,{number:function(e){return e>=0||r.predictable?log2Number(e):i(new n(e,0))},Complex:i,BigNumber:function(e){return!e.isNegative()||r.predictable?e.log(2):i(new n(e.toNumber(),0))},"Array | Matrix":function(e){return deepMap(e,this)}});function i(e){var t=Math.sqrt(e.re*e.re+e.im*e.im);return new n(Math.log2?Math.log2(t):Math.log(t)/Math.LN2,Math.atan2(e.im,e.re)/Math.LN2)}})),name$3M="algorithm03",dependencies$3M=["typed"],createAlgorithm03=factory(name$3M,dependencies$3M,(e=>{var{typed:t}=e;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,l=r._ptr,f=r._size,p=r._datatype;if(o.length!==f.length)throw new DimensionError(o.length,f.length);if(o[0]!==f[0]||o[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+f+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,d=o[0],h=o[1],y=0,g=n;"string"==typeof s&&s===p&&(m=s,y=t.convert(0,m),g=t.find(n,[m,m]));for(var v=[],x=0;x{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A=a&&l?[]:void 0,M=[],S=[],E=A?[]:void 0,T=A?[]:void 0,O=[],C=[];for(w=0;w{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm02({typed:t,equalScalar:n}),o=createAlgorithm03({typed:t}),s=createAlgorithm05({typed:t,equalScalar:n}),u=createAlgorithm11({typed:t,equalScalar:n}),c=createAlgorithm12({typed:t,DenseMatrix:i}),l=createAlgorithm13({typed:t}),f=createAlgorithm14({typed:t});return t(name$3K,{"number, number":modNumber,"BigNumber, BigNumber":function(e,t){if(t.isNeg())throw new Error("Cannot calculate mod for a negative divisor");return t.isZero()?e:e.mod(t)},"Fraction, Fraction":function(e,t){if(t.compare(0)<0)throw new Error("Cannot calculate mod for a negative divisor");return e.compare(0)>=0?e.mod(t):e.mod(t).add(t).mod(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return l(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return u(e,t,this,!1)},"DenseMatrix, any":function(e,t){return f(e,t,this,!1)},"any, SparseMatrix":function(e,t){return c(t,e,this,!0)},"any, DenseMatrix":function(e,t){return f(t,e,this,!0)},"Array, any":function(e,t){return f(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return f(r(t),e,this,!0).valueOf()}})})),name$3J="multiplyScalar",dependencies$3J=["typed"],createMultiplyScalar=factory(name$3J,dependencies$3J,(e=>{var{typed:t}=e;return t("multiplyScalar",{"number, number":multiplyNumber,"Complex, Complex":function(e,t){return e.mul(t)},"BigNumber, BigNumber":function(e,t){return e.times(t)},"Fraction, Fraction":function(e,t){return e.mul(t)},"number | Fraction | BigNumber | Complex, Unit":function(e,t){var r=t.clone();return r.value=null===r.value?r._normalize(e):this(r.value,e),r},"Unit, number | Fraction | BigNumber | Complex":function(e,t){var r=e.clone();return r.value=null===r.value?r._normalize(t):this(r.value,t),r},"Unit, Unit":function(e,t){return e.multiply(t)}})})),name$3I="multiply",dependencies$3I=["typed","matrix","addScalar","multiplyScalar","equalScalar","dot"],createMultiply=factory(name$3I,dependencies$3I,(e=>{var{typed:t,matrix:r,addScalar:n,multiplyScalar:i,equalScalar:a,dot:o}=e,s=createAlgorithm11({typed:t,equalScalar:a}),u=createAlgorithm14({typed:t});function c(e,t){switch(e.length){case 1:switch(t.length){case 1:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vectors must have the same length");break;case 2:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vector length ("+e[0]+") must match Matrix rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;case 2:switch(t.length){case 1:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix columns ("+e[1]+") must match Vector length ("+t[0]+")");break;case 2:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix A columns ("+e[1]+") must match Matrix B rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix A has "+e.length+" dimensions)")}}function l(e,r){if("dense"!==r.storage())throw new Error("Support for SparseMatrix not implemented");return function(e,r){var a,o=e._data,s=e._size,u=e._datatype,c=r._data,l=r._size,f=r._datatype,p=s[0],m=l[1],d=n,h=i;u&&f&&u===f&&"string"==typeof u&&(a=u,d=t.find(n,[a,a]),h=t.find(i,[a,a]));for(var y=[],g=0;gM)for(var E=0,T=0;T{var{typed:t,matrix:r,equalScalar:n,BigNumber:i}=e,a=createAlgorithm01({typed:t}),o=createAlgorithm02({typed:t,equalScalar:n}),s=createAlgorithm06({typed:t,equalScalar:n}),u=createAlgorithm11({typed:t,equalScalar:n}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t}),f="Complex number not supported in function nthRoot. Use nthRoots instead.";return t(name$3H,{number:nthRootNumber,"number, number":nthRootNumber,BigNumber:function(e){return p(e,new i(2))},Complex:function(e){throw new Error(f)},"Complex, number":function(e,t){throw new Error(f)},"BigNumber, BigNumber":p,"Array | Matrix":function(e){return this(e,2)},"SparseMatrix, SparseMatrix":function(e,t){if(1===t.density())return s(e,t,this);throw new Error("Root must be non-zero")},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){if(1===t.density())return a(e,t,this,!1);throw new Error("Root must be non-zero")},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){if(1===t.density())return u(t,e,this,!0);throw new Error("Root must be non-zero")},"number | BigNumber, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return this(r(e),t).valueOf()},"number | BigNumber, Array":function(e,t){return this(e,r(t)).valueOf()}});function p(e,t){var r=i.precision,n=i.clone({precision:r+2}),a=new i(0),o=new n(1),s=t.isNegative();if(s&&(t=t.neg()),t.isZero())throw new Error("Root must be non-zero");if(e.isNegative()&&!t.abs().mod(2).equals(1))throw new Error("Root must be odd when a is negative.");if(e.isZero())return s?new n(1/0):0;if(!e.isFinite())return s?a:e;var u=e.abs().pow(o.div(t));return u=e.isNeg()?u.neg():u,new i((s?o.div(u):u).toPrecision(r))}})),name$3G="sign",dependencies$3G=["typed","BigNumber","Fraction","complex"],createSign=factory(name$3G,dependencies$3G,(e=>{var{typed:t,BigNumber:r,complex:n,Fraction:i}=e;return t(name$3G,{number:signNumber,Complex:function(e){return 0===e.im?n(signNumber(e.re)):e.sign()},BigNumber:function(e){return new r(e.cmp(0))},Fraction:function(e){return new i(e.s,1)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){if(!e._isDerived()&&0!==e.units[0].unit.offset)throw new TypeError("sign is ambiguous for units with offset");return this(e.value)}})})),name$3F="sqrt",dependencies$3F=["config","typed","Complex"],createSqrt=factory(name$3F,dependencies$3F,(e=>{var{config:t,typed:r,Complex:n}=e;return r("sqrt",{number:i,Complex:function(e){return e.sqrt()},BigNumber:function(e){return!e.isNegative()||t.predictable?e.sqrt():i(e.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(.5)}});function i(e){return isNaN(e)?NaN:e>=0||t.predictable?Math.sqrt(e):new n(e,0).sqrt()}})),name$3E="square",dependencies$3E=["typed"],createSquare=factory(name$3E,dependencies$3E,(e=>{var{typed:t}=e;return t(name$3E,{number:squareNumber,Complex:function(e){return e.mul(e)},BigNumber:function(e){return e.times(e)},Fraction:function(e){return e.mul(e)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(2)}})})),name$3D="subtract",dependencies$3D=["typed","matrix","equalScalar","addScalar","unaryMinus","DenseMatrix"],createSubtract=factory(name$3D,dependencies$3D,(e=>{var{typed:t,matrix:r,equalScalar:n,addScalar:i,unaryMinus:a,DenseMatrix:o}=e,s=createAlgorithm01({typed:t}),u=createAlgorithm03({typed:t}),c=createAlgorithm05({typed:t,equalScalar:n}),l=createAlgorithm10({typed:t,DenseMatrix:o}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$3D,{"number, number":function(e,t){return e-t},"Complex, Complex":function(e,t){return e.sub(t)},"BigNumber, BigNumber":function(e,t){return e.minus(t)},"Fraction, Fraction":function(e,t){return e.sub(t)},"Unit, Unit":function(e,t){if(null===e.value)throw new Error("Parameter x contains a unit with undefined value");if(null===t.value)throw new Error("Parameter y contains a unit with undefined value");if(!e.equalBase(t))throw new Error("Units do not match");var r=e.clone();return r.value=this(r.value,t.value),r.fixPrefix=!1,r},"SparseMatrix, SparseMatrix":function(e,t){return checkEqualDimensions(e,t),c(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return checkEqualDimensions(e,t),u(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return checkEqualDimensions(e,t),s(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return checkEqualDimensions(e,t),f(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return l(e,a(t),i)},"DenseMatrix, any":function(e,t){return p(e,t,this)},"any, SparseMatrix":function(e,t){return l(t,e,this,!0)},"any, DenseMatrix":function(e,t){return p(t,e,this,!0)},"Array, any":function(e,t){return p(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return p(r(t),e,this,!0).valueOf()}})}));function checkEqualDimensions(e,t){var r=e.size(),n=t.size();if(r.length!==n.length)throw new DimensionError(r.length,n.length)}var name$3C="xgcd",dependencies$3C=["typed","config","matrix","BigNumber"],createXgcd=factory(name$3C,dependencies$3C,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t(name$3C,{"number, number":function(e,t){var i=xgcdNumber(e,t);return"Array"===r.matrix?i:n(i)},"BigNumber, BigNumber":function(e,t){var a,o,s,u,c=new i(0),l=new i(1),f=c,p=l,m=l,d=c;if(!e.isInt()||!t.isInt())throw new Error("Parameters in function xgcd must be integer numbers");for(;!t.isZero();)o=e.div(t).floor(),s=e.mod(t),a=f,f=p.minus(o.times(f)),p=a,a=m,m=d.minus(o.times(m)),d=a,e=t,t=s;u=e.lt(c)?[e.neg(),p.neg(),d.neg()]:[e,e.isZero()?0:p,d];return"Array"===r.matrix?u:n(u)}})})),name$3B="invmod",dependencies$3B=["typed","config","BigNumber","xgcd","equal","smaller","mod","add","isInteger"],createInvmod=factory(name$3B,dependencies$3B,(e=>{var{typed:t,config:r,BigNumber:n,xgcd:i,equal:a,smaller:o,mod:s,add:u,isInteger:c}=e;return t(name$3B,{"number, number":l,"BigNumber, BigNumber":l});function l(e,t){if(!c(e)||!c(t))throw new Error("Parameters in function invmod must be integer numbers");if(e=s(e,t),a(t,0))throw new Error("Divisor must be non zero");var r=i(e,t);r=r.valueOf();var[l,f]=r;return a(l,n(1))?(f=s(f,t),o(f,n(0))&&(f=u(f,t)),f):NaN}})),name$3A="algorithm09",dependencies$3A=["typed","equalScalar"],createAlgorithm09=factory(name$3A,dependencies$3A,(e=>{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A,M=a&&l?[]:void 0,S=[],E=[],T=M?[]:void 0,O=[];for(w=0;w{var{typed:t,matrix:r,equalScalar:n,multiplyScalar:i}=e,a=createAlgorithm02({typed:t,equalScalar:n}),o=createAlgorithm09({typed:t,equalScalar:n}),s=createAlgorithm11({typed:t,equalScalar:n}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3z,{"any, any":i,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,i,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,i,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,i,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,i)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,i,!1)},"DenseMatrix, any":function(e,t){return c(e,t,i,!1)},"any, SparseMatrix":function(e,t){return s(t,e,i,!0)},"any, DenseMatrix":function(e,t){return c(t,e,i,!0)},"Array, any":function(e,t){return c(r(e),t,i,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,i,!0).valueOf()}})}));function bitAndBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitAnd");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero()||t.eq(-1)||e.eq(t))return e;if(t.isZero()||e.eq(-1))return t;if(!e.isFinite()||!t.isFinite()){if(!e.isFinite()&&!t.isFinite())return e.isNegative()===t.isNegative()?e:new r(0);if(!e.isFinite())return t.isNegative()?e:e.isNegative()?new r(0):t;if(!t.isFinite())return e.isNegative()?t:t.isNegative()?new r(0):e}return bitwise(e,t,(function(e,t){return e&t}))}function bitNotBigNumber(e){if(e.isFinite()&&!e.isInteger())throw new Error("Integer expected in function bitNot");var t=e.constructor,r=t.precision;t.config({precision:1e9});var n=e.plus(new t(1));return n.s=-n.s||null,t.config({precision:r}),n}function bitOrBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitOr");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);var n=new r(-1);return e.isZero()||t.eq(n)||e.eq(t)?t:t.isZero()||e.eq(n)?e:e.isFinite()&&t.isFinite()?bitwise(e,t,(function(e,t){return e|t})):!e.isFinite()&&!e.isNegative()&&t.isNegative()||e.isNegative()&&!t.isNegative()&&!t.isFinite()?n:e.isNegative()&&t.isNegative()?e.isFinite()?e:t:e.isFinite()?t:e}function bitwise(e,t,r){var n,i,a,o,s,u=e.constructor,c=+(e.s<0),l=+(t.s<0);if(c){n=decCoefficientToBinaryString(bitNotBigNumber(e));for(var f=0;f0;)r(a[--m],o[--d])===h&&(y=y.plus(g)),g=g.times(v);for(;d>0;)r(s,o[--d])===h&&(y=y.plus(g)),g=g.times(v);return u.config({precision:x}),0===h&&(y.s=-y.s),y}function decCoefficientToBinaryString(e){for(var t=e.d,r=t[0]+"",n=1;n0)if(++s>c)for(s-=c;s--;)u+="0";else s1&&(null!==l[m+1]&&void 0!==l[m+1]||(l[m+1]=0),l[m+1]+=l[m]>>1,l[m]&=1)}return l.reverse()}function bitXor$1(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitXor");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero())return t;if(t.isZero())return e;if(e.eq(t))return new r(0);var n=new r(-1);return e.eq(n)?bitNotBigNumber(t):t.eq(n)?bitNotBigNumber(e):e.isFinite()&&t.isFinite()?bitwise(e,t,(function(e,t){return e^t})):e.isFinite()||t.isFinite()?new r(e.isNegative()===t.isNegative()?1/0:-1/0):n}function leftShiftBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function leftShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:e.isFinite()||t.isFinite()?t.lt(55)?e.times(Math.pow(2,t.toNumber())+""):e.times(new r(2).pow(t)):new r(NaN)}function rightArithShiftBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function rightArithShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:t.isFinite()?t.lt(55)?e.div(Math.pow(2,t.toNumber())+"").floor():e.div(new r(2).pow(t)).floor():e.isNegative()?new r(-1):e.isFinite()?new r(0):new r(NaN)}var name$3y="bitAnd",dependencies$3y=["typed","matrix","equalScalar"],createBitAnd=factory(name$3y,dependencies$3y,(e=>{var{typed:t,matrix:r,equalScalar:n}=e,i=createAlgorithm02({typed:t,equalScalar:n}),a=createAlgorithm06({typed:t,equalScalar:n}),o=createAlgorithm11({typed:t,equalScalar:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3y,{"number, number":bitAndNumber,"BigNumber, BigNumber":bitAndBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3x="bitNot",dependencies$3x=["typed"],createBitNot=factory(name$3x,dependencies$3x,(e=>{var{typed:t}=e;return t(name$3x,{number:bitNotNumber,BigNumber:bitNotBigNumber,"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3w="bitOr",dependencies$3w=["typed","matrix","equalScalar","DenseMatrix"],createBitOr=factory(name$3w,dependencies$3w,(e=>{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm01({typed:t}),o=createAlgorithm04({typed:t,equalScalar:n}),s=createAlgorithm10({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3w,{"number, number":bitOrNumber,"BigNumber, BigNumber":bitOrBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$3v="algorithm07",dependencies$3v=["typed","DenseMatrix"],createAlgorithm07=factory(name$3v,dependencies$3v,(e=>{var{typed:t,DenseMatrix:r}=e;return function(e,i,a){var o=e._size,s=e._datatype,u=i._size,c=i._datatype;if(o.length!==u.length)throw new DimensionError(o.length,u.length);if(o[0]!==u[0]||o[1]!==u[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+u+")");var l,f,p,m=o[0],d=o[1],h=0,y=a;"string"==typeof s&&s===c&&(l=s,h=t.convert(0,l),y=t.find(a,[l,l]));var g=[];for(f=0;f{var{typed:t,matrix:r,DenseMatrix:n}=e,i=createAlgorithm03({typed:t}),a=createAlgorithm07({typed:t,DenseMatrix:n}),o=createAlgorithm12({typed:t,DenseMatrix:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3u,{"number, number":bitXorNumber,"BigNumber, BigNumber":bitXor$1,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3t="arg",dependencies$3t=["typed"],createArg=factory(name$3t,dependencies$3t,(e=>{var{typed:t}=e;return t(name$3t,{number:function(e){return Math.atan2(0,e)},BigNumber:function(e){return e.constructor.atan2(0,e)},Complex:function(e){return e.arg()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3s="conj",dependencies$3s=["typed"],createConj=factory(name$3s,dependencies$3s,(e=>{var{typed:t}=e;return t(name$3s,{number:function(e){return e},BigNumber:function(e){return e},Complex:function(e){return e.conjugate()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3r="im",dependencies$3r=["typed"],createIm=factory(name$3r,dependencies$3r,(e=>{var{typed:t}=e;return t(name$3r,{number:function(e){return 0},BigNumber:function(e){return e.mul(0)},Fraction:function(e){return e.mul(0)},Complex:function(e){return e.im},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3q="re",dependencies$3q=["typed"],createRe=factory(name$3q,dependencies$3q,(e=>{var{typed:t}=e;return t(name$3q,{number:function(e){return e},BigNumber:function(e){return e},Fraction:function(e){return e},Complex:function(e){return e.re},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3p="not",dependencies$3p=["typed"],createNot=factory(name$3p,dependencies$3p,(e=>{var{typed:t}=e;return t(name$3p,{number:notNumber,Complex:function(e){return 0===e.re&&0===e.im},BigNumber:function(e){return e.isZero()||e.isNaN()},Unit:function(e){return null===e.value||this(e.value)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3o="or",dependencies$3o=["typed","matrix","equalScalar","DenseMatrix"],createOr=factory(name$3o,dependencies$3o,(e=>{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm05({typed:t,equalScalar:n}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3o,{"number, number":orNumber,"Complex, Complex":function(e,t){return 0!==e.re||0!==e.im||0!==t.re||0!==t.im},"BigNumber, BigNumber":function(e,t){return!e.isZero()&&!e.isNaN()||!t.isZero()&&!t.isNaN()},"Unit, Unit":function(e,t){return this(e.value||0,t.value||0)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$3n="xor",dependencies$3n=["typed","matrix","DenseMatrix"],createXor=factory(name$3n,dependencies$3n,(e=>{var{typed:t,matrix:r,DenseMatrix:n}=e,i=createAlgorithm03({typed:t}),a=createAlgorithm07({typed:t,DenseMatrix:n}),o=createAlgorithm12({typed:t,DenseMatrix:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3n,{"number, number":xorNumber,"Complex, Complex":function(e,t){return(0!==e.re||0!==e.im)!=(0!==t.re||0!==t.im)},"BigNumber, BigNumber":function(e,t){return(!e.isZero()&&!e.isNaN())!=(!t.isZero()&&!t.isNaN())},"Unit, Unit":function(e,t){return this(e.value||0,t.value||0)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3m="concat",dependencies$3m=["typed","matrix","isInteger"],createConcat=factory(name$3m,dependencies$3m,(e=>{var{typed:t,matrix:r,isInteger:n}=e;return t(name$3m,{"...Array | Matrix | number | BigNumber":function(e){var t,i,a=e.length,o=-1,s=!1,u=[];for(t=0;t0&&o>i)throw new IndexError(o,i+1)}else{var l=clone$3(c).valueOf(),f=arraySize(l);if(u[t]=l,i=o,o=f.length-1,t>0&&o!==i)throw new DimensionError(i+1,o+1)}}if(0===u.length)throw new SyntaxError("At least one matrix expected");for(var p=u.shift();u.length;)p=_concat(p,u.shift(),o,0);return s?r(p):p},"...string":function(e){return e.join("")}})}));function _concat(e,t,r,n){if(n{var{typed:t,Index:r,matrix:n,range:i}=e;return t(name$3l,{"Matrix, number":a,"Array, number":function(e,t){return a(n(clone$3(e)),t).valueOf()}});function a(e,t){if(2!==e.size().length)throw new Error("Only two dimensional matrix is supported");validateIndex(t,e.size()[1]);var n=i(0,e.size()[0]),a=new r(n,t);return e.subset(a)}})),name$3k="count",dependencies$3k=["typed","size","prod"],createCount=factory(name$3k,dependencies$3k,(e=>{var{typed:t,size:r,prod:n}=e;return t(name$3k,{string:function(e){return e.length},"Matrix | Array":function(e){return n(r(e))}})})),name$3j="cross",dependencies$3j=["typed","matrix","subtract","multiply"],createCross=factory(name$3j,dependencies$3j,(e=>{var{typed:t,matrix:r,subtract:n,multiply:i}=e;return t(name$3j,{"Matrix, Matrix":function(e,t){return r(a(e.toArray(),t.toArray()))},"Matrix, Array":function(e,t){return r(a(e.toArray(),t))},"Array, Matrix":function(e,t){return r(a(e,t.toArray()))},"Array, Array":a});function a(e,t){var r=Math.max(arraySize(e).length,arraySize(t).length);e=squeeze$1(e),t=squeeze$1(t);var a=arraySize(e),o=arraySize(t);if(1!==a.length||1!==o.length||3!==a[0]||3!==o[0])throw new RangeError("Vectors with length 3 expected (Size A = ["+a.join(", ")+"], B = ["+o.join(", ")+"])");var s=[n(i(e[1],t[2]),i(e[2],t[1])),n(i(e[2],t[0]),i(e[0],t[2])),n(i(e[0],t[1]),i(e[1],t[0]))];return r>1?[s]:s}})),name$3i="diag",dependencies$3i=["typed","matrix","DenseMatrix","SparseMatrix"],createDiag=factory(name$3i,dependencies$3i,(e=>{var{typed:t,matrix:r,DenseMatrix:n,SparseMatrix:i}=e;return t(name$3i,{Array:function(e){return a(e,0,arraySize(e),null)},"Array, number":function(e,t){return a(e,t,arraySize(e),null)},"Array, BigNumber":function(e,t){return a(e,t.toNumber(),arraySize(e),null)},"Array, string":function(e,t){return a(e,0,arraySize(e),t)},"Array, number, string":function(e,t,r){return a(e,t,arraySize(e),r)},"Array, BigNumber, string":function(e,t,r){return a(e,t.toNumber(),arraySize(e),r)},Matrix:function(e){return a(e,0,e.size(),e.storage())},"Matrix, number":function(e,t){return a(e,t,e.size(),e.storage())},"Matrix, BigNumber":function(e,t){return a(e,t.toNumber(),e.size(),e.storage())},"Matrix, string":function(e,t){return a(e,0,e.size(),t)},"Matrix, number, string":function(e,t,r){return a(e,t,e.size(),r)},"Matrix, BigNumber, string":function(e,t,r){return a(e,t.toNumber(),e.size(),r)}});function a(e,t,a,o){if(!isInteger$1(t))throw new TypeError("Second parameter in function diag must be an integer");var s=t>0?t:0,u=t<0?-t:0;switch(a.length){case 1:return function(e,t,r,a,o,s){var u=[a+o,a+s];if(r&&"sparse"!==r&&"dense"!==r)throw new TypeError("Unknown matrix type ".concat(r,'"'));var c="sparse"===r?i.diagonal(u,e,t):n.diagonal(u,e,t);return null!==r?c:c.valueOf()}(e,t,o,a[0],u,s);case 2:return function(e,t,n,i,a,o){if(isMatrix(e)){var s=e.diagonal(t);return null!==n?n!==s.storage()?r(s,n):s:s.valueOf()}for(var u=Math.min(i[0]-a,i[1]-o),c=[],l=0;l1&&void 0!==arguments[1]?arguments[1]:{};return r=null==r?Number.POSITIVE_INFINITY:r,t=null==t?JSON.stringify:t,function n(){"object"!=typeof n.cache&&(n.cache={values:new Map,lru:lruQueue(r||Number.POSITIVE_INFINITY)});for(var i=[],a=0;a{var{typed:t}=e;return t("filter",{"Array, function":_filterCallback,"Matrix, function":function(e,t){return e.create(_filterCallback(e.toArray(),t))},"Array, RegExp":filterRegExp,"Matrix, RegExp":function(e,t){return e.create(filterRegExp(e.toArray(),t))}})}));function _filterCallback(e,t){var r=maxArgumentCount(t);return filter$2(e,(function(e,n,i){return 1===r?t(e):2===r?t(e,[n]):t(e,[n],i)}))}var name$3g="flatten",dependencies$3g=["typed","matrix"],createFlatten=factory(name$3g,dependencies$3g,(e=>{var{typed:t,matrix:r}=e;return t(name$3g,{Array:function(e){return flatten$4(clone$3(e))},Matrix:function(e){var t=flatten$4(clone$3(e.toArray()));return r(t)}})})),name$3f="forEach",dependencies$3f=["typed"],createForEach=factory(name$3f,dependencies$3f,(e=>{var{typed:t}=e;return t(name$3f,{"Array, function":_forEach,"Matrix, function":function(e,t){return e.forEach(t)}})}));function _forEach(e,t){var r=maxArgumentCount(t);!function n(i,a){Array.isArray(i)?forEach$1(i,(function(e,t){n(e,a.concat(t))})):1===r?t(i):2===r?t(i,a):t(i,a,e)}(e,[])}var name$3e="getMatrixDataType",dependencies$3e=["typed"],createGetMatrixDataType=factory(name$3e,dependencies$3e,(e=>{var{typed:t}=e;return t(name$3e,{Array:function(e){return getArrayDataType(e,typeOf$1)},Matrix:function(e){return e.getDataType()}})})),name$3d="identity",dependencies$3d=["typed","config","matrix","BigNumber","DenseMatrix","SparseMatrix"],createIdentity=factory(name$3d,dependencies$3d,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i,DenseMatrix:a,SparseMatrix:o}=e;return t(name$3d,{"":function(){return"Matrix"===r.matrix?n([]):[]},string:function(e){return n(e)},"number | BigNumber":function(e){return u(e,e,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber, string":function(e,t){return u(e,e,t)},"number | BigNumber, number | BigNumber":function(e,t){return u(e,t,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber, number | BigNumber, string":function(e,t,r){return u(e,t,r)},Array:function(e){return s(e)},"Array, string":function(e,t){return s(e,t)},Matrix:function(e){return s(e.valueOf(),e.storage())},"Matrix, string":function(e,t){return s(e.valueOf(),t)}});function s(e,t){switch(e.length){case 0:return t?n(t):[];case 1:return u(e[0],e[0],t);case 2:return u(e[0],e[1],t);default:throw new Error("Vector containing two values expected")}}function u(e,t,r){var n=isBigNumber(e)||isBigNumber(t)?i:null;if(isBigNumber(e)&&(e=e.toNumber()),isBigNumber(t)&&(t=t.toNumber()),!isInteger$1(e)||e<1)throw new Error("Parameters in function identity must be positive integers");if(!isInteger$1(t)||t<1)throw new Error("Parameters in function identity must be positive integers");var s=n?new i(1):1,u=n?new n(0):0,c=[e,t];if(r){if("sparse"===r)return o.diagonal(c,s,0,u);if("dense"===r)return a.diagonal(c,s,0,u);throw new TypeError('Unknown matrix type "'.concat(r,'"'))}for(var l=resize$1([],c,u),f=e{var{typed:t,matrix:r,multiplyScalar:n}=e;return t(name$3c,{"Matrix, Matrix":function(e,t){return r(i(e.toArray(),t.toArray()))},"Matrix, Array":function(e,t){return r(i(e.toArray(),t))},"Array, Matrix":function(e,t){return r(i(e,t.toArray()))},"Array, Array":i});function i(e,t){if(1===arraySize(e).length&&(e=[e]),1===arraySize(t).length&&(t=[t]),arraySize(e).length>2||arraySize(t).length>2)throw new RangeError("Vectors with dimensions greater then 2 are not supported expected (Size x = "+JSON.stringify(e.length)+", y = "+JSON.stringify(t.length)+")");var r=[],i=[];return e.map((function(e){return t.map((function(t){return i=[],r.push(i),e.map((function(e){return t.map((function(t){return i.push(n(e,t))}))}))}))}))&&r}})),name$3b="map",dependencies$3b=["typed"],createMap=factory(name$3b,dependencies$3b,(e=>{var{typed:t}=e;return t(name$3b,{"Array, function":_map$1,"Matrix, function":function(e,t){return e.map(t)}})}));function _map$1(e,t){var r=maxArgumentCount(t);return function n(i,a){if(Array.isArray(i))return i.map((function(e,t){return n(e,a.concat(t))}));try{return 1===r?t(i):2===r?t(i,a):t(i,a,e)}catch(t){if(t instanceof TypeError&&"data"in t&&"wrongType"===t.data.category){var o="map attempted to call '".concat(t.data.fn,"(").concat(i),s=JSON.stringify(a);throw 2===r?o+=","+s:1!==r&&(o+=",".concat(s,",").concat(e)),o+=")' but argument ".concat(t.data.index+1," of type "),o+="".concat(t.data.actual," does not match expected type "),o+=t.data.expected.join(" or "),new TypeError(o)}throw t}}(e,[])}var name$3a="diff",dependencies$3a=["typed","matrix","subtract","number"],createDiff=factory(name$3a,dependencies$3a,(e=>{var{typed:t,matrix:r,subtract:n,number:i}=e;return t(name$3a,{"Array | Matrix":function(e){return isMatrix(e)?r(o(e.toArray())):o(e)},"Array | Matrix, number":function(e,t){if(!isInteger$1(t))throw new RangeError("Dimension must be a whole number");return isMatrix(e)?r(a(e.toArray(),t)):a(e,t)},"Array | Matrix, BigNumber":function(e,t){return this(e,i(t))}});function a(e,t){if(isMatrix(e)&&(e=e.toArray()),!Array.isArray(e))throw RangeError("Array/Matrix does not have that many dimensions");if(t>0){var r=[];return e.forEach((e=>{r.push(a(e,t-1))})),r}if(0===t)return o(e);throw RangeError("Cannot have negative dimension")}function o(e){var t=[],r=e.length;if(r<2)return e;for(var n=1;n{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t("ones",{"":function(){return"Array"===r.matrix?a([]):a([],"default")},"...number | BigNumber | string":function(e){if("string"==typeof e[e.length-1]){var t=e.pop();return a(e,t)}return"Array"===r.matrix?a(e):a(e,"default")},Array:a,Matrix:function(e){var t=e.storage();return a(e.valueOf(),t)},"Array | Matrix, string":function(e,t){return a(e.valueOf(),t)}});function a(e,t){var r=function(e){var t=!1;return e.forEach((function(e,r,n){isBigNumber(e)&&(t=!0,n[r]=e.toNumber())})),t}(e),a=r?new i(1):1;if(function(e){e.forEach((function(e){if("number"!=typeof e||!isInteger$1(e)||e<0)throw new Error("Parameters in function ones must be positive integers")}))}(e),t){var o=n(t);return e.length>0?o.resize(e,a):o}var s=[];return e.length>0?resize$1(s,e,a):s}}));function noBignumber(){throw new Error('No "bignumber" implementation available')}function noFraction(){throw new Error('No "fraction" implementation available')}function noMatrix(){throw new Error('No "matrix" implementation available')}var name$38="range",dependencies$38=["typed","config","?matrix","?bignumber","smaller","smallerEq","larger","largerEq"],createRange=factory(name$38,dependencies$38,(e=>{var{typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u}=e;return t(name$38,{string:l,"string, boolean":l,"number, number":function(e,t){return c(f(e,t,1))},"number, number, number":function(e,t,r){return c(f(e,t,r))},"number, number, boolean":function(e,t,r){return c(r?p(e,t,1):f(e,t,1))},"number, number, number, boolean":function(e,t,r,n){return c(n?p(e,t,r):f(e,t,r))},"BigNumber, BigNumber":function(e,t){return c(m(e,t,new(0,e.constructor)(1)))},"BigNumber, BigNumber, BigNumber":function(e,t,r){return c(m(e,t,r))},"BigNumber, BigNumber, boolean":function(e,t,r){var n=e.constructor;return c(r?d(e,t,new n(1)):m(e,t,new n(1)))},"BigNumber, BigNumber, BigNumber, boolean":function(e,t,r,n){return c(n?d(e,t,r):m(e,t,r))}});function c(e){return"Matrix"===r.matrix?n?n(e):noMatrix():e}function l(e,t){var n=function(e){var t=e.split(":"),r=t.map((function(e){return Number(e)}));if(r.some((function(e){return isNaN(e)})))return null;switch(r.length){case 2:return{start:r[0],end:r[1],step:1};case 3:return{start:r[0],end:r[2],step:r[1]};default:return null}}(e);if(!n)throw new SyntaxError('String "'+e+'" is no valid range');return"BigNumber"===r.number?(void 0===i&&noBignumber(),c((t?d:m)(i(n.start),i(n.end),i(n.step)))):c((t?p:f)(n.start,n.end,n.step))}function f(e,t,r){var n=[],i=e;if(r>0)for(;a(i,t);)n.push(i),i+=r;else if(r<0)for(;s(i,t);)n.push(i),i+=r;return n}function p(e,t,r){var n=[],i=e;if(r>0)for(;o(i,t);)n.push(i),i+=r;else if(r<0)for(;u(i,t);)n.push(i),i+=r;return n}function m(e,t,r){var n=i(0),o=[],u=e;if(r.gt(n))for(;a(u,t);)o.push(u),u=u.plus(r);else if(r.lt(n))for(;s(u,t);)o.push(u),u=u.plus(r);return o}function d(e,t,r){var n=i(0),a=[],s=e;if(r.gt(n))for(;o(s,t);)a.push(s),s=s.plus(r);else if(r.lt(n))for(;u(s,t);)a.push(s),s=s.plus(r);return a}})),name$37="reshape",dependencies$37=["typed","isInteger","matrix"],createReshape=factory(name$37,dependencies$37,(e=>{var{typed:t,isInteger:r}=e;return t(name$37,{"Matrix, Array":function(e,t){return e.reshape(t)},"Array, Array":function(e,t){return t.forEach((function(e){if(!r(e))throw new TypeError("Invalid size for dimension: "+e)})),reshape$1(e,t)}})}));function ArgumentsError(e,t,r,n){if(!(this instanceof ArgumentsError))throw new SyntaxError("Constructor must be called with the new operator");this.fn=e,this.count=t,this.min=r,this.max=n,this.message="Wrong number of arguments in function "+e+" ("+t+" provided, "+r+(null!=n?"-"+n:"")+" expected)",this.stack=(new Error).stack}ArgumentsError.prototype=new Error,ArgumentsError.prototype.constructor=Error,ArgumentsError.prototype.name="ArgumentsError",ArgumentsError.prototype.isArgumentsError=!0;var name$36="resize",dependencies$36=["config","matrix"],createResize=factory(name$36,dependencies$36,(e=>{var{config:t,matrix:r}=e;return function(e,n,i){if(2!==arguments.length&&3!==arguments.length)throw new ArgumentsError("resize",arguments.length,2,3);if(isMatrix(n)&&(n=n.valueOf()),isBigNumber(n[0])&&(n=n.map((function(e){return isBigNumber(e)?e.toNumber():e}))),isMatrix(e))return e.resize(n,i,!0);if("string"==typeof e)return function(e,t,r){if(void 0!==r){if("string"!=typeof r||1!==r.length)throw new TypeError("Single character expected as defaultValue")}else r=" ";if(1!==t.length)throw new DimensionError(t.length,1);var n=t[0];if("number"!=typeof n||!isInteger$1(n))throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(t)+")");if(e.length>n)return e.substring(0,n);if(e.length{var{typed:t,multiply:r,rotationMatrix:n}=e;return t(name$35,{"Array , number | BigNumber | Complex | Unit":function(e,t){return i(e,2),r(n(t),e).toArray()},"Matrix , number | BigNumber | Complex | Unit":function(e,t){return i(e,2),r(n(t),e)},"Array, number | BigNumber | Complex | Unit, Array | Matrix":function(e,t,a){return i(e,3),r(n(t,a),e)},"Matrix, number | BigNumber | Complex | Unit, Array | Matrix":function(e,t,a){return i(e,3),r(n(t,a),e)}});function i(e,t){var r=Array.isArray(e)?arraySize(e):e.size();if(r.length>2)throw new RangeError("Vector must be of dimensions 1x".concat(t));if(2===r.length&&1!==r[1])throw new RangeError("Vector must be of dimensions 1x".concat(t));if(r[0]!==t)throw new RangeError("Vector must be of dimensions 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Matrix A ("+u+") must match Matrix B ("+m+")");if(!a||!l)throw new Error("Cannot perform operation on Pattern Sparse Matrices");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));for(var _,w,N,$,A=[],M=[],S=[],E=[],T=[],O=0;O{var{typed:t,matrix:r,equalScalar:n,zeros:i,DenseMatrix:a}=e,o=createAlgorithm01({typed:t}),s=createAlgorithm02({typed:t,equalScalar:n}),u=createAlgorithm08({typed:t,equalScalar:n}),c=createAlgorithm10({typed:t,DenseMatrix:a}),l=createAlgorithm11({typed:t,equalScalar:n}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$2y,{"number, number":leftShiftNumber,"BigNumber, BigNumber":leftShiftBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return u(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return s(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return f(e,t,this)},"Array, 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name$2q="equalText",dependencies$2q=["typed","compareText","isZero"],createEqualText=factory(name$2q,dependencies$2q,(e=>{var{typed:t,compareText:r,isZero:n}=e;return t(name$2q,{"any, any":function(e,t){return n(r(e,t))}})})),name$2p="smaller",dependencies$2p=["typed","config","matrix","DenseMatrix"],createSmaller=factory(name$2p,dependencies$2p,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2p,{"boolean, boolean":function(e,t){return e{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2o,{"boolean, boolean":function(e,t){return e<=t},"number, number":function(e,t){return e<=t||nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.lte(t)||nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return 1!==e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2n="larger",dependencies$2n=["typed","config","matrix","DenseMatrix"],createLarger=factory(name$2n,dependencies$2n,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2n,{"boolean, boolean":function(e,t){return e>t},"number, number":function(e,t){return e>t&&!nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.gt(t)&&!nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return 1===e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2m="largerEq",dependencies$2m=["typed","config","matrix","DenseMatrix"],createLargerEq=factory(name$2m,dependencies$2m,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2m,{"boolean, boolean":function(e,t){return e>=t},"number, number":function(e,t){return e>=t||nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.gte(t)||nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return-1!==e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, 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i=e.length;if(i!==t.length)return!1;for(var a=0;a{var{typed:t,config:r,equalScalar:n,matrix:i,DenseMatrix:a}=e,o=createAlgorithm03({typed:t}),s=createAlgorithm07({typed:t,DenseMatrix:a}),u=createAlgorithm12({typed:t,DenseMatrix:a}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t});return t("unequal",{"any, any":function(e,t){return null===e?null!==t:null===t?null!==e:void 0===e?void 0!==t:void 0===t?void 0!==e:f(e,t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,f)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,f,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,f,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,f)},"Array, Array":function(e,t){return this(i(e),i(t)).valueOf()},"Array, Matrix":function(e,t){return this(i(e),t)},"Matrix, Array":function(e,t){return this(e,i(t))},"SparseMatrix, any":function(e,t){return u(e,t,f,!1)},"DenseMatrix, any":function(e,t){return l(e,t,f,!1)},"any, SparseMatrix":function(e,t){return u(t,e,f,!0)},"any, DenseMatrix":function(e,t){return l(t,e,f,!0)},"Array, any":function(e,t){return l(i(e),t,f,!1).valueOf()},"any, Array":function(e,t){return l(i(t),e,f,!0).valueOf()}});function f(e,t){return!n(e,t)}}));factory(name$2k,["typed","equalScalar"],(e=>{var{typed:t,equalScalar:r}=e;return t(name$2k,{"any, any":function(e,t){return null===e?null!==t:null===t?null!==e:void 0===e?void 0!==t:void 0===t?void 0!==e:!r(e,t)}})}));var name$2j="partitionSelect",dependencies$2j=["typed","isNumeric","isNaN","compare"],createPartitionSelect=factory(name$2j,dependencies$2j,(e=>{var{typed:t,isNumeric:r,isNaN:n,compare:i}=e,a=i,o=(e,t)=>-i(e,t);return t(name$2j,{"Array | Matrix, number":function(e,t){return s(e,t,a)},"Array | Matrix, number, string":function(e,t,r){if("asc"===r)return s(e,t,a);if("desc"===r)return s(e,t,o);throw new Error('Compare string must be "asc" or "desc"')},"Array | Matrix, number, function":s});function s(e,t,r){if(!isInteger$1(t)||t<0)throw new Error("k must be a non-negative integer");if(isMatrix(e)){if(e.size().length>1)throw new Error("Only one dimensional matrices supported");return u(e.valueOf(),t,r)}if(Array.isArray(e))return u(e,t,r)}function u(e,t,i){if(t>=e.length)throw new Error("k out of bounds");for(var a=0;a=0){var f=e[c];e[c]=e[u],e[u]=f,--c}else++u;i(e[u],l)>0&&--u,t<=u?s=u:o=u+1}return e[t]}})),name$2i="sort",dependencies$2i=["typed","matrix","compare","compareNatural"],createSort=factory(name$2i,dependencies$2i,(e=>{var{typed:t,matrix:r,compare:n,compareNatural:i}=e,a=n,o=(e,t)=>-n(e,t);return t(name$2i,{Array:function(e){return u(e),e.sort(a)},Matrix:function(e){return c(e),r(e.toArray().sort(a),e.storage())},"Array, function":function(e,t){return u(e),e.sort(t)},"Matrix, function":function(e,t){return c(e),r(e.toArray().sort(t),e.storage())},"Array, string":function(e,t){return u(e),e.sort(s(t))},"Matrix, string":function(e,t){return c(e),r(e.toArray().sort(s(t)),e.storage())}});function s(e){if("asc"===e)return a;if("desc"===e)return o;if("natural"===e)return i;throw new Error('String "asc", "desc", or "natural" expected')}function u(e){if(1!==arraySize(e).length)throw new Error("One dimensional array expected")}function c(e){if(1!==e.size().length)throw new Error("One dimensional matrix expected")}})),name$2h="max",dependencies$2h=["typed","config","numeric","larger"],createMax=factory(name$2h,dependencies$2h,(e=>{var{typed:t,config:r,numeric:n,larger:i}=e;return t(name$2h,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return reduce$2(e,t.valueOf(),a)},"...":function(e){if(containsCollections(e))throw new TypeError("Scalar values expected in function max");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw improveErrorMessage(e,"max",t)}}function o(e){var t;if(deepForEach(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw improveErrorMessage(t,"max",e)}})),void 0===t)throw new Error("Cannot calculate max of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),name$2g="min",dependencies$2g=["typed","config","numeric","smaller"],createMin=factory(name$2g,dependencies$2g,(e=>{var{typed:t,config:r,numeric:n,smaller:i}=e;return t(name$2g,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return reduce$2(e,t.valueOf(),a)},"...":function(e){if(containsCollections(e))throw new TypeError("Scalar values expected in function min");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw improveErrorMessage(e,"min",t)}}function o(e){var t;if(deepForEach(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw improveErrorMessage(t,"min",e)}})),void 0===t)throw new Error("Cannot calculate min of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),name$2f="ImmutableDenseMatrix",dependencies$2f=["smaller","DenseMatrix"],createImmutableDenseMatrixClass=factory(name$2f,dependencies$2f,(e=>{var{smaller:t,DenseMatrix:r}=e;function n(e,t){if(!(this instanceof n))throw new SyntaxError("Constructor must be called with the new operator");if(t&&!isString$1(t))throw new Error("Invalid datatype: "+t);if(isMatrix(e)||isArray$1(e)){var i=new r(e,t);this._data=i._data,this._size=i._size,this._datatype=i._datatype,this._min=null,this._max=null}else if(e&&isArray$1(e.data)&&isArray$1(e.size))this._data=e.data,this._size=e.size,this._datatype=e.datatype,this._min=void 0!==e.min?e.min:null,this._max=void 0!==e.max?e.max:null;else{if(e)throw new TypeError("Unsupported type of data ("+typeOf$1(e)+")");this._data=[],this._size=[0],this._datatype=t,this._min=null,this._max=null}}return n.prototype=new r,n.prototype.type="ImmutableDenseMatrix",n.prototype.isImmutableDenseMatrix=!0,n.prototype.subset=function(e){switch(arguments.length){case 1:var t=r.prototype.subset.call(this,e);return isMatrix(t)?new n({data:t._data,size:t._size,datatype:t._datatype}):t;case 2:case 3:throw new Error("Cannot invoke set subset on an Immutable Matrix instance");default:throw new SyntaxError("Wrong number of arguments")}},n.prototype.set=function(){throw new Error("Cannot invoke set on an Immutable Matrix instance")},n.prototype.resize=function(){throw new Error("Cannot invoke resize on an Immutable Matrix instance")},n.prototype.reshape=function(){throw new Error("Cannot invoke reshape on an Immutable Matrix instance")},n.prototype.clone=function(){return new n({data:clone$3(this._data),size:clone$3(this._size),datatype:this._datatype})},n.prototype.toJSON=function(){return{mathjs:"ImmutableDenseMatrix",data:this._data,size:this._size,datatype:this._datatype}},n.fromJSON=function(e){return new n(e)},n.prototype.swapRows=function(){throw new Error("Cannot invoke swapRows on an Immutable Matrix instance")},n.prototype.min=function(){if(null===this._min){var e=null;this.forEach((function(r){(null===e||t(r,e))&&(e=r)})),this._min=null!==e?e:void 0}return this._min},n.prototype.max=function(){if(null===this._max){var e=null;this.forEach((function(r){(null===e||t(e,r))&&(e=r)})),this._max=null!==e?e:void 0}return this._max},n}),{isClass:!0}),name$2e="Index",dependencies$2e=["ImmutableDenseMatrix"],createIndexClass=factory(name$2e,dependencies$2e,(e=>{var{ImmutableDenseMatrix:t}=e;function r(e){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");this._dimensions=[],this._isScalar=!0;for(var t=0,i=arguments.length;t{var{smaller:t,larger:r}=e,n=1/Math.log((1+Math.sqrt(5))/2);function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._minimum=null,this._size=0}function a(e,t,r){t.left.right=t.right,t.right.left=t.left,r.degree--,r.child===t&&(r.child=t.right),0===r.degree&&(r.child=null),t.left=e,t.right=e.right,e.right=t,t.right.left=t,t.parent=null,t.mark=!1}function o(e,t){var r=t.parent;r&&(t.mark?(a(e,t,r),o(r)):t.mark=!0)}i.prototype.type="FibonacciHeap",i.prototype.isFibonacciHeap=!0,i.prototype.insert=function(e,r){var n={key:e,value:r,degree:0};if(this._minimum){var i=this._minimum;n.left=i,n.right=i.right,i.right=n,n.right.left=n,t(e,i.key)&&(this._minimum=n)}else n.left=n,n.right=n,this._minimum=n;return this._size++,n},i.prototype.size=function(){return this._size},i.prototype.clear=function(){this._minimum=null,this._size=0},i.prototype.isEmpty=function(){return 0===this._size},i.prototype.extractMinimum=function(){var e=this._minimum;if(null===e)return e;for(var i=this._minimum,a=e.degree,o=e.child;a>0;){var u=o.right;o.left.right=o.right,o.right.left=o.left,o.left=i,o.right=i.right,i.right=o,o.right.left=o,o.parent=null,o=u,a--}return e.left.right=e.right,e.right.left=e.left,i=e===e.right?null:function(e,i){var a,o=Math.floor(Math.log(i)*n)+1,u=new Array(o),c=0,l=e;if(l)for(c++,l=l.right;l!==e;)c++,l=l.right;for(;c>0;){for(var f=l.degree,p=l.right;a=u[f];){if(r(l.key,a.key)){var m=a;a=l,l=m}s(a,l),u[f]=null,f++}u[f]=l,l=p,c--}e=null;for(var d=0;d{var{addScalar:t,equalScalar:r,FibonacciHeap:n}=e;function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._values=[],this._heap=new n}return i.prototype.type="Spa",i.prototype.isSpa=!0,i.prototype.set=function(e,t){if(this._values[e])this._values[e].value=t;else{var r=this._heap.insert(e,t);this._values[e]=r}},i.prototype.get=function(e){var t=this._values[e];return t?t.value:0},i.prototype.accumulate=function(e,r){var n=this._values[e];n?n.value=t(n.value,r):(n=this._heap.insert(e,r),this._values[e]=n)},i.prototype.forEach=function(e,t,n){var 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e.equalBase(I.NONE)&&null!==e.value&&!a.predictable?e.value:e}w.isValuelessUnit=function(e){return null!==O(e)},w.prototype.hasBase=function(e){if("string"==typeof e&&(e=I[e]),!e)return!1;for(var t=0;t1e-12)return!1;return!0},w.prototype.equalBase=function(e){for(var t=0;t1e-12)return!1;return!0},w.prototype.equals=function(e){return this.equalBase(e)&&d(this.value,e.value)},w.prototype.multiply=function(e){for(var t=this.clone(),r=0;r1e-12&&(hasOwnProperty$2(F,s)?n.push({unit:F[s].unit,prefix:F[s].prefix,power:r.dimensions[o]||0}):a=!0)}n.length1e-12){if(!hasOwnProperty$2(L.si,n))throw new Error("Cannot express custom unit "+n+" in SI units");t.push({unit:L.si[n].unit,prefix:L.si[n].prefix,power:e.dimensions[r]||0})}}return e.units=t,e.fixPrefix=!0,e.skipAutomaticSimplification=!0,e},w.prototype.formatUnits=function(){for(var e="",t="",r=0,n=0,i=0;i0?(r++,e+=" 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0!==t.value&&null!==t.value&&isComplex(t.value)&&(r=Math.abs(t.value.re)<1e-14),t.units)hasOwnProperty$2(t.units,n)&&t.units[n].unit&&("VA"===t.units[n].unit.name&&r?t.units[n].unit=R.VAR:"VAR"!==t.units[n].unit.name||r||(t.units[n].unit=R.VA));1!==t.units.length||t.fixPrefix||Math.abs(t.units[0].power-Math.round(t.units[0].power))<1e-14&&(t.units[0].prefix=t._bestPrefix());var i=t._denormalize(t.value),a=null!==t.value?y(i,e||{}):"",o=t.formatUnits();return t.value&&isComplex(t.value)&&(a="("+a+")"),o.length>0&&a.length>0&&(a+=" "),a+=o},w.prototype._bestPrefix=function(){if(1!==this.units.length)throw new Error("Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!");if(Math.abs(this.units[0].power-Math.round(this.units[0].power))>=1e-14)throw new Error("Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!");var e=null!==this.value?f(this.value):0,t=f(this.units[0].unit.value),r=this.units[0].prefix;if(0===e)return r;var n=this.units[0].power,i=Math.log(e/Math.pow(r.value*t,n))/Math.LN10-1.2;if(i>-2.200001&&i<1.800001)return r;i=Math.abs(i);var a=this.units[0].unit.prefixes;for(var o in a)if(hasOwnProperty$2(a,o)){var s=a[o];if(s.scientific){var 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this.properties)hasOwnProperty$2(this.properties,t)&&(e[t]=this.properties[t]);return new r(e)},r.prototype._toString=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push(stringify(r)+": "+this.properties[r].toString(e));return"{"+t.join(", ")+"}"},r.prototype.toJSON=function(){return{mathjs:"ObjectNode",properties:this.properties}},r.fromJSON=function(e){return new r(e.properties)},r.prototype.toHTML=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push(''+escape$1(r)+':'+this.properties[r].toHTML(e));return'{'+t.join(',')+'}'},r.prototype._toTex=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push("\\mathbf{"+r+":} & 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n.map((function(e){switch(e.getContent().type){case"ArrayNode":case"ConstantNode":case"SymbolNode":case"ParenthesisNode":return!1;default:return!0}}));switch(n.length){case 0:a=[];break;case 1:var u=getPrecedence(n[0],t);if(i&&null!==u){var c,l;if("keep"===t?(c=n[0].getIdentifier(),l=e.getIdentifier()):(c=n[0].getContent().getIdentifier(),l=e.getContent().getIdentifier()),!1===properties[o][l].latexLeftParens){a=[!1];break}if(!1===properties[u][c].latexParens){a=[!1];break}}if(null===u){a=[!1];break}if(u<=o){a=[!0];break}a=[!1];break;case 2:var f,p,m=getPrecedence(n[0],t),d=isAssociativeWith(e,n[0],t);f=null!==m&&(m===o&&"right"===s&&!d||m=2&&"OperatorNode:multiply"===e.getIdentifier()&&e.implicit&&"auto"===t&&"hide"===r&&(a=n.map((function(e,t){var r="ParenthesisNode"===e.getIdentifier();return!(!a[t]&&!r)}))),a}return r.prototype=new t,r.prototype.type="OperatorNode",r.prototype.isOperatorNode=!0,r.prototype._compile=function(e,t){if("string"!=typeof this.fn||!isSafeMethod(e,this.fn))throw e[this.fn]?new Error('No access to function "'+this.fn+'"'):new Error("Function "+this.fn+' missing in provided namespace "math"');var r=getSafeProperty(e,this.fn),n=map$2(this.args,(function(r){return r._compile(e,t)}));if(1===n.length){var i=n[0];return function(e,t,n){return r(i(e,t,n))}}if(2===n.length){var a=n[0],o=n[1];return function(e,t,n){return r(a(e,t,n),o(e,t,n))}}return function(e,t,i){return r.apply(null,map$2(n,(function(r){return r(e,t,i)})))}},r.prototype.forEach=function(e){for(var t=0;t2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())){var f=i.map((function(t,r){return t=t.toString(e),a[r]&&(t="("+t+")"),t}));return this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?f.join(" "):f.join(" "+this.op+" ")}return this.fn+"("+this.args.join(", 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i.length>2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())?this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?l.join(''):l.join(''+escape$1(this.op)+""):''+escape$1(this.fn)+'('+l.join(',')+')'},r.prototype._toTex=function(e){var t=e&&e.parenthesis?e.parenthesis:"keep",r=e&&e.implicit?e.implicit:"hide",i=this.args,a=n(this,t,r,i,!0),o=latexOperators[this.fn];if(o=void 0===o?this.op:o,1===i.length){var s=getAssociativity(this,t),u=i[0].toTex(e);return a[0]&&(u="\\left(".concat(u,"\\right)")),"right"===s?o+u:u+o}if(2===i.length){var c=i[0],l=c.toTex(e);a[0]&&(l="\\left(".concat(l,"\\right)"));var f,p=i[1].toTex(e);switch(a[1]&&(p="\\left(".concat(p,"\\right)")),f="keep"===t?c.getIdentifier():c.getContent().getIdentifier(),this.getIdentifier()){case"OperatorNode:divide":return 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If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]},log10Docs={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]},log1pDocs={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]},log2Docs={name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]},modDocs={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]},multiplyDocs={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]},normDocs={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']},nthRootDocs={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]},nthRootsDocs={name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]},powDocs={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)","math.pow([[1, 2], [4, 3]], 2)","math.pow([[1, 2], [4, 3]], -1)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]},roundDocs={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)"],seealso:["ceil","floor","fix"]},signDocs={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]},sqrtDocs={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]},sqrtmDocs={name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[1, 2], [3, 4]])"],seealso:["sqrt","abs","square","multiply"]},squareDocs={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]},subtractDocs={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]},unaryMinusDocs={name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]},unaryPlusDocs={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]},xgcdDocs={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]},bitAndDocs={name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitNotDocs={name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitOrDocs={name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]},bitXorDocs={name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]},leftShiftDocs={name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]},rightArithShiftDocs={name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]},rightLogShiftDocs={name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]},bellNumbersDocs={name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]},catalanDocs={name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]},compositionDocs={name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]},stirlingS2Docs={name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]},argDocs={name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]},conjDocs={name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]},imDocs={name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]},reDocs={name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]},evaluateDocs={name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(" + 4 + ")")'],seealso:[]},helpDocs={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]},distanceDocs={name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]},intersectDocs={name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])"],seealso:[]},andDocs={name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]},notDocs={name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]},orDocs={name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]},xorDocs={name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]},columnDocs={name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row","matrixFromColumns"]},concatDocs={name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},countDocs={name:"count",category:"Matrix",syntax:["count(x)"],description:"Count the number of elements of a matrix, array or string.",examples:["a = [1, 2; 3, 4; 5, 6]","count(a)","size(a)",'count("hello world")'],seealso:["size"]},crossDocs={name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0], [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4], [5, 6, 7])"],seealso:["multiply","dot"]},ctransposeDocs={name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},detDocs={name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diagDocs={name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diffDocs={name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["diff([1, 2, 4, 7, 0])","diff([1, 2, 4, 7, 0], 0)","diff(matrix([1, 2, 4, 7, 0]))","diff([[1, 2], [3, 4]])","diff([[1, 2], [3, 4]], 0)","diff([[1, 2], [3, 4]], 1)","diff([[1, 2], [3, 4]], bignumber(1))","diff(matrix([[1, 2], [3, 4]]), 1)","diff([[1, 2], matrix([3, 4])], 1)"],seealso:["subtract","partitionSelect"]},dotDocs={name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]},eigsDocs={name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and eigenvectors of a real symmetric matrix",examples:["eigs([[5, 2.3], [2.3, 1]])"],seealso:["inv"]},filterDocs={name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]},flattenDocs={name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]},forEachDocs={name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["numberOfPets = {}","addPet(n) = numberOfPets[n] = (numberOfPets[n] ? numberOfPets[n]:0 ) + 1;",'forEach(["Dog","Cat","Cat"], addPet)',"numberOfPets"],seealso:["map","sort","filter"]},getMatrixDataTypeDocs={name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeOf"]},identityDocs={name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},invDocs={name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]},pinvDocs={name:"pinv",category:"Matrix",syntax:["pinv(x)"],description:"Calculate the Moore–Penrose inverse of a matrix",examples:["pinv([1, 2; 3, 4])","pinv([[1, 0], [0, 1], [0, 1]])","pinv(4)"],seealso:["inv"]},kronDocs={name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]},mapDocs={name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]},matrixFromColumnsDocs={name:"matrixFromColumns",category:"Matrix",syntax:["math.matrixFromColumns(...arr)","math.matrixFromColumns(row1, row2)","math.matrixFromColumns(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual columns.",examples:["matrixFromColumns([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromRows","matrixFromFunction","zeros"]},matrixFromFunctionDocs={name:"matrixFromFunction",category:"Matrix",syntax:["math.matrixFromFunction(size, fn)","math.matrixFromFunction(size, fn, format)","math.matrixFromFunction(size, fn, format, datatype)","math.matrixFromFunction(size, format, fn)","math.matrixFromFunction(size, format, datatype, fn)"],description:"Create a matrix by evaluating a generating function at each index.",examples:["f(I) = I[1] - I[2]","matrixFromFunction([3,3], f)","g(I) = I[1] - I[2] == 1 ? 4 : 0",'matrixFromFunction([100, 100], "sparse", g)',"matrixFromFunction([5], random)"],seealso:["matrix","matrixFromRows","matrixFromColumns","zeros"]},matrixFromRowsDocs={name:"matrixFromRows",category:"Matrix",syntax:["math.matrixFromRows(...arr)","math.matrixFromRows(row1, row2)","math.matrixFromRows(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual rows.",examples:["matrixFromRows([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromColumns","matrixFromFunction","zeros"]},onesDocs={name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]},partitionSelectDocs={name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1)'],seealso:["sort"]},rangeDocs={name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]},reshapeDocs={name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])"],seealso:["size","squeeze","resize"]},resizeDocs={name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]},rotateDocs={name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], math.pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]},rotationMatrixDocs={name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]},rowDocs={name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column","matrixFromRows"]},sizeDocs={name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","count","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]},sortDocs={name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"])',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]},squeezeDocs={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]},subsetDocs={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of the entries of a matrix or characters of a string. Indexes are one-based. There should be one index specification for each dimension of the target. Each specification can be a single index, a list of indices, or a range in colon notation `l:u`. In a range, both the lower bound l and upper bound u are included; and if a bound is omitted it defaults to the most extreme valid value. The cartesian product of the indices specified in each dimension determines the target of the operation.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]","f[[1,2], [1,3]] = [9, 10; 11, 12]","f"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]},traceDocs={name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]},transposeDocs={name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},zerosDocs={name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]},fftDocs={name:"fft",category:"Matrix",syntax:["fft(x)"],description:"Calculate N-dimensional fourier transform",examples:["fft([[1, 0], [1, 0]])"],seealso:["ifft"]},ifftDocs={name:"ifft",category:"Matrix",syntax:["ifft(x)"],description:"Calculate N-dimensional inverse fourier transform",examples:["ifft([[2, 2], [0, 0]])"],seealso:["fft"]},combinationsDocs={name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]},combinationsWithRepDocs={name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]},factorialDocs={name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]},gammaDocs={name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]},lgammaDocs={name:"lgamma",category:"Probability",syntax:["lgamma(n)"],description:"Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers.",examples:["lgamma(4)","lgamma(1/2)","lgamma(math.i)","lgamma(complex(1.1, 2))"],seealso:["gamma"]},kldivergenceDocs={name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]},multinomialDocs={name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]},permutationsDocs={name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]},pickRandomDocs={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]},randomDocs={name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]},randomIntDocs={name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]},compareDocs={name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]},compareNaturalDocs={name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]},compareTextDocs={name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]},deepEqualDocs={name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]},equalDocs={name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]},equalTextDocs={name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]},largerDocs={name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]},largerEqDocs={name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]},smallerDocs={name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]},smallerEqDocs={name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]},unequalDocs={name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]},setCartesianDocs={name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]},setDifferenceDocs={name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]},setDistinctDocs={name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]},setIntersectDocs={name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]},setIsSubsetDocs={name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]},setMultiplicityDocs={name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]},setPowersetDocs={name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]},setSizeDocs={name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]},setSymDifferenceDocs={name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]},setUnionDocs={name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]},erfDocs={name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]},madDocs={name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]},maxDocs={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]},meanDocs={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]},medianDocs={name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]},minDocs={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]},modeDocs={name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]},prodDocs={name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]},quantileSeqDocs={name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.",examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","variance"]},stdDocs={name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","prod","sum","variance"]},cumSumDocs={name:"cumsum",category:"Statistics",syntax:["cumsum(a, b, c, ...)","cumsum(A)"],description:"Compute the cumulative sum of all values.",examples:["cumsum(2, 3, 4, 1)","cumsum([2, 3, 4, 1])","cumsum([1, 2; 3, 4])","cumsum([1, 2; 3, 4], 1)","cumsum([1, 2; 3, 4], 2)"],seealso:["max","mean","median","min","prod","std","sum","variance"]},sumDocs={name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","variance"]},varianceDocs={name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, normalization)"],description:'Compute the variance of all values. 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N("^","pow",[e.args[0].cloneDeep(),new x(a-1)]);e=new N("*","multiply",[s,u])}else e=new N("*","multiply",[e.args[0],e.args[0].cloneDeep()]);i&&("content"===r?t.content=e:t.args[r]=e)}}if("ParenthesisNode"===n)S(e.content,e,"content");else if("ConstantNode"!==n&&"SymbolNode"!==n)for(var c=0;cn&&(t[c]=0),t[c]+=o.cte*("+"===o.oper?1:-1),void(n=Math.max(c,n))}o.cte=c,""===o.fire&&(t[0]+=o.cte*("+"===o.oper?1:-1))}}(e,null,r);for(var a,o=!0,s=n=t.length-1;s>=0;s--)if(0!==t[s]){var u=new x(o?t[s]:Math.abs(t[s])),c=t[s]<0?"-":"+";if(s>0){var l=new $(i);if(s>1){var f=new x(s);l=new N("^","pow",[l,f])}u=-1===t[s]&&o?new N("-","unaryMinus",[l]):1===Math.abs(t[s])?l:new N("*","multiply",[u,l])}a=o?u:"+"===c?new N("+","add",[a,u]):new N("-","subtract",[a,u]),o=!1}return o?new x(0):a}})),name$j="reviver",dependencies$j=["classes"],createReviver=factory(name$j,dependencies$j,(e=>{var{classes:t}=e;return function(e,r){var n=t[r&&r.mathjs];return n&&"function"==typeof n.fromJSON?n.fromJSON(r):r}})),name$i="replacer",dependencies$i=[],createReplacer=factory(name$i,dependencies$i,(()=>function(e,t){return"number"!=typeof t||isFinite(t)&&!isNaN(t)?t:{mathjs:"number",value:String(t)}})),version$2="10.6.4",createTrue=factory("true",[],(()=>!0)),createFalse=factory("false",[],(()=>!1)),createNull=factory("null",[],(()=>null)),createInfinity=recreateFactory("Infinity",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1/0):1/0})),createNaN=recreateFactory("NaN",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(NaN):NaN})),createPi=recreateFactory("pi",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberPi(r):pi$1})),createTau=recreateFactory("tau",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberTau(r):tau$1})),createE=recreateFactory("e",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberE(r):e$1})),createPhi=recreateFactory("phi",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberPhi(r):phi$1})),createLN2=recreateFactory("LN2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(2).ln():Math.LN2})),createLN10=recreateFactory("LN10",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(10).ln():Math.LN10})),createLOG2E=recreateFactory("LOG2E",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1).div(new r(2).ln()):Math.LOG2E})),createLOG10E=recreateFactory("LOG10E",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1).div(new r(10).ln()):Math.LOG10E})),createSQRT1_2=recreateFactory("SQRT1_2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r("0.5").sqrt():Math.SQRT1_2})),createSQRT2=recreateFactory("SQRT2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(2).sqrt():Math.SQRT2})),createI=recreateFactory("i",["Complex"],(e=>{var{Complex:t}=e;return t.I})),createUppercasePi=factory("PI",["pi"],(e=>{var{pi:t}=e;return t})),createUppercaseE=factory("E",["e"],(e=>{var{e:t}=e;return t})),createVersion=factory("version",[],(()=>version$2));function recreateFactory(e,t,r){return factory(e,t,r,{recreateOnConfigChange:!0})}var createSpeedOfLight=unitFactory("speedOfLight","299792458","m s^-1"),createGravitationConstant=unitFactory("gravitationConstant","6.67430e-11","m^3 kg^-1 s^-2"),createPlanckConstant=unitFactory("planckConstant","6.62607015e-34","J s"),createReducedPlanckConstant=unitFactory("reducedPlanckConstant","1.0545718176461565e-34","J s"),createMagneticConstant=unitFactory("magneticConstant","1.25663706212e-6","N A^-2"),createElectricConstant=unitFactory("electricConstant","8.8541878128e-12","F m^-1"),createVacuumImpedance=unitFactory("vacuumImpedance","376.730313667","ohm"),createCoulomb=unitFactory("coulomb","8.987551792261171e9","N m^2 C^-2"),createElementaryCharge=unitFactory("elementaryCharge","1.602176634e-19","C"),createBohrMagneton=unitFactory("bohrMagneton","9.2740100783e-24","J T^-1"),createConductanceQuantum=unitFactory("conductanceQuantum","7.748091729863649e-5","S"),createInverseConductanceQuantum=unitFactory("inverseConductanceQuantum","12906.403729652257","ohm"),createMagneticFluxQuantum=unitFactory("magneticFluxQuantum","2.0678338484619295e-15","Wb"),createNuclearMagneton=unitFactory("nuclearMagneton","5.0507837461e-27","J T^-1"),createKlitzing=unitFactory("klitzing","25812.807459304513","ohm"),createBohrRadius=unitFactory("bohrRadius","5.29177210903e-11","m"),createClassicalElectronRadius=unitFactory("classicalElectronRadius","2.8179403262e-15","m"),createElectronMass=unitFactory("electronMass","9.1093837015e-31","kg"),createFermiCoupling=unitFactory("fermiCoupling","1.1663787e-5","GeV^-2"),createFineStructure=numberFactory("fineStructure",.0072973525693),createHartreeEnergy=unitFactory("hartreeEnergy","4.3597447222071e-18","J"),createProtonMass=unitFactory("protonMass","1.67262192369e-27","kg"),createDeuteronMass=unitFactory("deuteronMass","3.3435830926e-27","kg"),createNeutronMass=unitFactory("neutronMass","1.6749271613e-27","kg"),createQuantumOfCirculation=unitFactory("quantumOfCirculation","3.6369475516e-4","m^2 s^-1"),createRydberg=unitFactory("rydberg","10973731.568160","m^-1"),createThomsonCrossSection=unitFactory("thomsonCrossSection","6.6524587321e-29","m^2"),createWeakMixingAngle=numberFactory("weakMixingAngle",.2229),createEfimovFactor=numberFactory("efimovFactor",22.7),createAtomicMass=unitFactory("atomicMass","1.66053906660e-27","kg"),createAvogadro=unitFactory("avogadro","6.02214076e23","mol^-1"),createBoltzmann=unitFactory("boltzmann","1.380649e-23","J K^-1"),createFaraday=unitFactory("faraday","96485.33212331001","C mol^-1"),createFirstRadiation=unitFactory("firstRadiation","3.7417718521927573e-16","W m^2"),createLoschmidt=unitFactory("loschmidt","2.686780111798444e25","m^-3"),createGasConstant=unitFactory("gasConstant","8.31446261815324","J K^-1 mol^-1"),createMolarPlanckConstant=unitFactory("molarPlanckConstant","3.990312712893431e-10","J s mol^-1"),createMolarVolume=unitFactory("molarVolume","0.022413969545014137","m^3 mol^-1"),createSackurTetrode=numberFactory("sackurTetrode",-1.16487052358),createSecondRadiation=unitFactory("secondRadiation","0.014387768775039337","m K"),createStefanBoltzmann=unitFactory("stefanBoltzmann","5.67037441918443e-8","W m^-2 K^-4"),createWienDisplacement=unitFactory("wienDisplacement","2.897771955e-3","m K"),createMolarMass=unitFactory("molarMass","0.99999999965e-3","kg mol^-1"),createMolarMassC12=unitFactory("molarMassC12","11.9999999958e-3","kg mol^-1"),createGravity=unitFactory("gravity","9.80665","m s^-2"),createPlanckLength=unitFactory("planckLength","1.616255e-35","m"),createPlanckMass=unitFactory("planckMass","2.176435e-8","kg"),createPlanckTime=unitFactory("planckTime","5.391245e-44","s"),createPlanckCharge=unitFactory("planckCharge","1.87554603778e-18","C"),createPlanckTemperature=unitFactory("planckTemperature","1.416785e+32","K");function unitFactory(e,t,r){return factory(e,["config","Unit","BigNumber"],(e=>{var{config:n,Unit:i,BigNumber:a}=e,o=new i("BigNumber"===n.number?new a(t):parseFloat(t),r);return o.fixPrefix=!0,o}))}function numberFactory(e,t){return factory(e,["config","BigNumber"],(e=>{var{config:r,BigNumber:n}=e;return"BigNumber"===r.number?new n(t):t}))}var name$h="apply",dependencies$h=["typed","isInteger"],createApplyTransform=factory(name$h,dependencies$h,(e=>{var{typed:t,isInteger:r}=e,n=createApply({typed:t,isInteger:r});return t("apply",{"...any":function(e){var t=e[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1));try{return n.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$g="column",dependencies$g=["typed","Index","matrix","range"],createColumnTransform=factory(name$g,dependencies$g,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e,a=createColumn({typed:t,Index:r,matrix:n,range:i});return t("column",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)&&(e[t]=r-1);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0});function compileInlineExpression(e,t,r){var n=e.filter((function(e){return isSymbolNode(e)&&!(e.name in t)&&!r.has(e.name)}))[0];if(!n)throw new Error('No undefined variable found in inline expression "'+e+'"');var i=n.name,a=createSubScope(r),o=e.compile();return function(e){return a.set(i,e),o.evaluate(a)}}var name$f="filter",dependencies$f=["typed"],createFilterTransform=factory(name$f,dependencies$f,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("filter",{"Array, function":_filter,"Matrix, function":function(e,t){return e.create(_filter(e.toArray(),t))},"Array, RegExp":filterRegExp,"Matrix, RegExp":function(e,t){return e.create(filterRegExp(e.toArray(),t))}});return r}),{isTransformFunction:!0});function _filter(e,t){var r=maxArgumentCount(t);return filter$2(e,(function(e,n,i){return 1===r?t(e):2===r?t(e,[n+1]):t(e,[n+1],i)}))}var name$e="forEach",dependencies$e=["typed"],createForEachTransform=factory(name$e,dependencies$e,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("forEach",{"Array | Matrix, function":function(e,t){var r=maxArgumentCount(t);!function n(i,a){Array.isArray(i)?forEach$1(i,(function(e,t){n(e,a.concat(t+1))})):1===r?t(i):2===r?t(i,a):t(i,a,e)}(e.valueOf(),[])}});return r}),{isTransformFunction:!0}),name$d="index",dependencies$d=["Index"],createIndexTransform=factory(name$d,dependencies$d,(e=>{var{Index:t}=e;return function(){for(var e=[],r=0,n=arguments.length;r0?0:2;else if(i&&!0===i.isSet)i=i.map((function(e){return e-1}));else if(isArray$1(i)||isMatrix(i))i=i.map((function(e){return e-1}));else if(isNumber$1(i))i--;else if(isBigNumber(i))i=i.toNumber()-1;else if("string"!=typeof i)throw new TypeError("Dimension must be an Array, Matrix, number, string, or Range");e[r]=i}var a=new t;return t.apply(a,e),a}}),{isTransformFunction:!0}),name$c="map",dependencies$c=["typed"],createMapTransform=factory(name$c,dependencies$c,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("map",{"Array, function":function(e,t){return _map(e,t,e)},"Matrix, function":function(e,t){return e.create(_map(e.valueOf(),t,e))}});return r}),{isTransformFunction:!0});function _map(e,t,r){var n=maxArgumentCount(t);return function e(i,a){return Array.isArray(i)?map$2(i,(function(t,r){return e(t,a.concat(r+1))})):1===n?t(i):2===n?t(i,a):t(i,a,r)}(e,[])}function lastDimToZeroBase(e){if(2===e.length&&isCollection(e[0])){var t=(e=e.slice())[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1))}return e}var name$b="max",dependencies$b=["typed","config","numeric","larger"],createMaxTransform=factory(name$b,dependencies$b,(e=>{var{typed:t,config:r,numeric:n,larger:i}=e,a=createMax({typed:t,config:r,numeric:n,larger:i});return t("max",{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$a="mean",dependencies$a=["typed","add","divide"],createMeanTransform=factory(name$a,dependencies$a,(e=>{var{typed:t,add:r,divide:n}=e,i=createMean({typed:t,add:r,divide:n});return t("mean",{"...any":function(e){e=lastDimToZeroBase(e);try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$9="min",dependencies$9=["typed","config","numeric","smaller"],createMinTransform=factory(name$9,dependencies$9,(e=>{var{typed:t,config:r,numeric:n,smaller:i}=e,a=createMin({typed:t,config:r,numeric:n,smaller:i});return t("min",{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$8="range",dependencies$8=["typed","config","?matrix","?bignumber","smaller","smallerEq","larger","largerEq"],createRangeTransform=factory(name$8,dependencies$8,(e=>{var{typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u}=e,c=createRange({typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u});return t("range",{"...any":function(e){return"boolean"!=typeof e[e.length-1]&&e.push(!0),c.apply(null,e)}})}),{isTransformFunction:!0}),name$7="row",dependencies$7=["typed","Index","matrix","range"],createRowTransform=factory(name$7,dependencies$7,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e,a=createRow({typed:t,Index:r,matrix:n,range:i});return t("row",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)&&(e[t]=r-1);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$6="subset",dependencies$6=["typed","matrix"],createSubsetTransform=factory(name$6,dependencies$6,(e=>{var{typed:t,matrix:r}=e,n=createSubset({typed:t,matrix:r});return t("subset",{"...any":function(e){try{return n.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$5="concat",dependencies$5=["typed","matrix","isInteger"],createConcatTransform=factory(name$5,dependencies$5,(e=>{var{typed:t,matrix:r,isInteger:n}=e,i=createConcat({typed:t,matrix:r,isInteger:n});return t("concat",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)?e[t]=r-1:isBigNumber(r)&&(e[t]=r.minus(1));try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$4="diff",dependencies$4=["typed","matrix","subtract","number","bignumber"],createDiffTransform=factory(name$4,dependencies$4,(e=>{var{typed:t,matrix:r,subtract:n,number:i,bignumber:a}=e,o=createDiff({typed:t,matrix:r,subtract:n,number:i,bignumber:a});return t(name$4,{"...any":function(e){e=lastDimToZeroBase(e);try{return o.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$3="std",dependencies$3=["typed","sqrt","variance"],createStdTransform=factory(name$3,dependencies$3,(e=>{var{typed:t,sqrt:r,variance:n}=e,i=createStd({typed:t,sqrt:r,variance:n});return t("std",{"...any":function(e){e=lastDimToZeroBase(e);try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$2="sum",dependencies$2=["typed","config","add","numeric"],createSumTransform=factory(name$2,dependencies$2,(e=>{var{typed:t,config:r,add:n,numeric:i}=e,a=createSum({typed:t,config:r,add:n,numeric:i});return t(name$2,{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$1="cumsum",dependencies$1=["typed","add","unaryPlus"],createCumSumTransform=factory(name$1,dependencies$1,(e=>{var{typed:t,add:r,unaryPlus:n}=e,i=createCumSum({typed:t,add:r,unaryPlus:n});return t(name$1,{"...any":function(e){if(2===e.length&&isCollection(e[0])){var t=e[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1))}try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name="variance",dependencies=["typed","add","subtract","multiply","divide","apply","isNaN"],createVarianceTransform=factory(name,dependencies,(e=>{var{typed:t,add:r,subtract:n,multiply:i,divide:a,apply:o,isNaN:s}=e,u=createVariance({typed:t,add:r,subtract:n,multiply:i,divide:a,apply:o,isNaN:s});return t(name,{"...any":function(e){e=lastDimToZeroBase(e);try{return u.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),allFactories=Object.freeze({__proto__:null,createTyped:createTyped,createResultSet:createResultSet,createBigNumberClass:createBigNumberClass,createComplexClass:createComplexClass,createFractionClass:createFractionClass,createRangeClass:createRangeClass,createMatrixClass:createMatrixClass,createDenseMatrixClass:createDenseMatrixClass,createClone:createClone,createIsInteger:createIsInteger,createIsNegative:createIsNegative,createIsNumeric:createIsNumeric,createHasNumericValue:createHasNumericValue,createIsPositive:createIsPositive,createIsZero:createIsZero,createIsNaN:createIsNaN,createTypeOf:createTypeOf,createEqualScalar:createEqualScalar,createSparseMatrixClass:createSparseMatrixClass,createNumber:createNumber,createString:createString,createBoolean:createBoolean,createBignumber:createBignumber,createComplex:createComplex,createFraction:createFraction,createMatrix:createMatrix,createMatrixFromFunction:createMatrixFromFunction,createMatrixFromRows:createMatrixFromRows,createMatrixFromColumns:createMatrixFromColumns,createSplitUnit:createSplitUnit,createUnaryMinus:createUnaryMinus,createUnaryPlus:createUnaryPlus,createAbs:createAbs,createApply:createApply,createAddScalar:createAddScalar,createCbrt:createCbrt,createCeil:createCeil,createCube:createCube,createExp:createExp,createExpm1:createExpm1,createFix:createFix,createFloor:createFloor,createGcd:createGcd,createLcm:createLcm,createLog10:createLog10,createLog2:createLog2,createMod:createMod,createMultiplyScalar:createMultiplyScalar,createMultiply:createMultiply,createNthRoot:createNthRoot,createSign:createSign,createSqrt:createSqrt,createSquare:createSquare,createSubtract:createSubtract,createXgcd:createXgcd,createInvmod:createInvmod,createDotMultiply:createDotMultiply,createBitAnd:createBitAnd,createBitNot:createBitNot,createBitOr:createBitOr,createBitXor:createBitXor,createArg:createArg,createConj:createConj,createIm:createIm,createRe:createRe,createNot:createNot,createOr:createOr,createXor:createXor,createConcat:createConcat,createColumn:createColumn,createCount:createCount,createCross:createCross,createDiag:createDiag,createFilter:createFilter,createFlatten:createFlatten,createForEach:createForEach,createGetMatrixDataType:createGetMatrixDataType,createIdentity:createIdentity,createKron:createKron,createMap:createMap,createDiff:createDiff,createOnes:createOnes,createRange:createRange,createReshape:createReshape,createResize:createResize,createRotate:createRotate,createRotationMatrix:createRotationMatrix,createRow:createRow,createSize:createSize,createSqueeze:createSqueeze,createSubset:createSubset,createTranspose:createTranspose,createCtranspose:createCtranspose,createZeros:createZeros,createFft:createFft,createIfft:createIfft,createErf:createErf,createMode:createMode,createProd:createProd,createFormat:createFormat,createBin:createBin,createOct:createOct,createHex:createHex,createPrint:createPrint,createTo:createTo,createIsPrime:createIsPrime,createNumeric:createNumeric,createDivideScalar:createDivideScalar,createPow:createPow,createRound:createRound,createLog:createLog,createLog1p:createLog1p,createNthRoots:createNthRoots,createDotPow:createDotPow,createDotDivide:createDotDivide,createLsolve:createLsolve,createUsolve:createUsolve,createLsolveAll:createLsolveAll,createUsolveAll:createUsolveAll,createLeftShift:createLeftShift,createRightArithShift:createRightArithShift,createRightLogShift:createRightLogShift,createAnd:createAnd,createCompare:createCompare,createCompareNatural:createCompareNatural,createCompareText:createCompareText,createEqual:createEqual,createEqualText:createEqualText,createSmaller:createSmaller,createSmallerEq:createSmallerEq,createLarger:createLarger,createLargerEq:createLargerEq,createDeepEqual:createDeepEqual,createUnequal:createUnequal,createPartitionSelect:createPartitionSelect,createSort:createSort,createMax:createMax,createMin:createMin,createImmutableDenseMatrixClass:createImmutableDenseMatrixClass,createIndexClass:createIndexClass,createFibonacciHeapClass:createFibonacciHeapClass,createSpaClass:createSpaClass,createUnitClass:createUnitClass,createUnitFunction:createUnitFunction,createSparse:createSparse,createCreateUnit:createCreateUnit,createAcos:createAcos,createAcosh:createAcosh,createAcot:createAcot,createAcoth:createAcoth,createAcsc:createAcsc,createAcsch:createAcsch,createAsec:createAsec,createAsech:createAsech,createAsin:createAsin,createAsinh:createAsinh,createAtan:createAtan,createAtan2:createAtan2,createAtanh:createAtanh,createCos:createCos,createCosh:createCosh,createCot:createCot,createCoth:createCoth,createCsc:createCsc,createCsch:createCsch,createSec:createSec,createSech:createSech,createSin:createSin,createSinh:createSinh,createTan:createTan,createTanh:createTanh,createSetCartesian:createSetCartesian,createSetDifference:createSetDifference,createSetDistinct:createSetDistinct,createSetIntersect:createSetIntersect,createSetIsSubset:createSetIsSubset,createSetMultiplicity:createSetMultiplicity,createSetPowerset:createSetPowerset,createSetSize:createSetSize,createSetSymDifference:createSetSymDifference,createSetUnion:createSetUnion,createAdd:createAdd,createHypot:createHypot,createNorm:createNorm,createDot:createDot,createTrace:createTrace,createIndex:createIndex,createNode:createNode,createAccessorNode:createAccessorNode,createArrayNode:createArrayNode,createAssignmentNode:createAssignmentNode,createBlockNode:createBlockNode,createConditionalNode:createConditionalNode,createConstantNode:createConstantNode,createFunctionAssignmentNode:createFunctionAssignmentNode,createIndexNode:createIndexNode,createObjectNode:createObjectNode,createOperatorNode:createOperatorNode,createParenthesisNode:createParenthesisNode,createRangeNode:createRangeNode,createRelationalNode:createRelationalNode,createSymbolNode:createSymbolNode,createFunctionNode:createFunctionNode,createParse:createParse,createCompile:createCompile,createEvaluate:createEvaluate,createParserClass:createParserClass,createParser:createParser,createLup:createLup,createQr:createQr,createSlu:createSlu,createLusolve:createLusolve,createHelpClass:createHelpClass,createChainClass:createChainClass,createHelp:createHelp,createChain:createChain,createDet:createDet,createInv:createInv,createPinv:createPinv,createEigs:createEigs,createExpm:createExpm,createSqrtm:createSqrtm,createDivide:createDivide,createDistance:createDistance,createIntersect:createIntersect,createSum:createSum,createCumSum:createCumSum,createMean:createMean,createMedian:createMedian,createMad:createMad,createVariance:createVariance,createQuantileSeq:createQuantileSeq,createStd:createStd,createCombinations:createCombinations,createCombinationsWithRep:createCombinationsWithRep,createGamma:createGamma,createLgamma:createLgamma,createFactorial:createFactorial,createKldivergence:createKldivergence,createMultinomial:createMultinomial,createPermutations:createPermutations,createPickRandom:createPickRandom,createRandom:createRandom,createRandomInt:createRandomInt,createStirlingS2:createStirlingS2,createBellNumbers:createBellNumbers,createCatalan:createCatalan,createComposition:createComposition,createLeafCount:createLeafCount,createSimplify:createSimplify,createSimplifyCore:createSimplifyCore,createResolve:createResolve,createSymbolicEqual:createSymbolicEqual,createDerivative:createDerivative,createRationalize:createRationalize,createReviver:createReviver,createReplacer:createReplacer,createE:createE,createUppercaseE:createUppercaseE,createFalse:createFalse,createI:createI,createInfinity:createInfinity,createLN10:createLN10,createLN2:createLN2,createLOG10E:createLOG10E,createLOG2E:createLOG2E,createNaN:createNaN,createNull:createNull,createPhi:createPhi,createPi:createPi,createUppercasePi:createUppercasePi,createSQRT1_2:createSQRT1_2,createSQRT2:createSQRT2,createTau:createTau,createTrue:createTrue,createVersion:createVersion,createAtomicMass:createAtomicMass,createAvogadro:createAvogadro,createBohrMagneton:createBohrMagneton,createBohrRadius:createBohrRadius,createBoltzmann:createBoltzmann,createClassicalElectronRadius:createClassicalElectronRadius,createConductanceQuantum:createConductanceQuantum,createCoulomb:createCoulomb,createDeuteronMass:createDeuteronMass,createEfimovFactor:createEfimovFactor,createElectricConstant:createElectricConstant,createElectronMass:createElectronMass,createElementaryCharge:createElementaryCharge,createFaraday:createFaraday,createFermiCoupling:createFermiCoupling,createFineStructure:createFineStructure,createFirstRadiation:createFirstRadiation,createGasConstant:createGasConstant,createGravitationConstant:createGravitationConstant,createGravity:createGravity,createHartreeEnergy:createHartreeEnergy,createInverseConductanceQuantum:createInverseConductanceQuantum,createKlitzing:createKlitzing,createLoschmidt:createLoschmidt,createMagneticConstant:createMagneticConstant,createMagneticFluxQuantum:createMagneticFluxQuantum,createMolarMass:createMolarMass,createMolarMassC12:createMolarMassC12,createMolarPlanckConstant:createMolarPlanckConstant,createMolarVolume:createMolarVolume,createNeutronMass:createNeutronMass,createNuclearMagneton:createNuclearMagneton,createPlanckCharge:createPlanckCharge,createPlanckConstant:createPlanckConstant,createPlanckLength:createPlanckLength,createPlanckMass:createPlanckMass,createPlanckTemperature:createPlanckTemperature,createPlanckTime:createPlanckTime,createProtonMass:createProtonMass,createQuantumOfCirculation:createQuantumOfCirculation,createReducedPlanckConstant:createReducedPlanckConstant,createRydberg:createRydberg,createSackurTetrode:createSackurTetrode,createSecondRadiation:createSecondRadiation,createSpeedOfLight:createSpeedOfLight,createStefanBoltzmann:createStefanBoltzmann,createThomsonCrossSection:createThomsonCrossSection,createVacuumImpedance:createVacuumImpedance,createWeakMixingAngle:createWeakMixingAngle,createWienDisplacement:createWienDisplacement,createApplyTransform:createApplyTransform,createColumnTransform:createColumnTransform,createFilterTransform:createFilterTransform,createForEachTransform:createForEachTransform,createIndexTransform:createIndexTransform,createMapTransform:createMapTransform,createMaxTransform:createMaxTransform,createMeanTransform:createMeanTransform,createMinTransform:createMinTransform,createRangeTransform:createRangeTransform,createRowTransform:createRowTransform,createSubsetTransform:createSubsetTransform,createConcatTransform:createConcatTransform,createDiffTransform:createDiffTransform,createStdTransform:createStdTransform,createSumTransform:createSumTransform,createCumSumTransform:createCumSumTransform,createVarianceTransform:createVarianceTransform}),BigNumber=createBigNumberClass({config:config$2}),Complex=createComplexClass({}),e=createE({BigNumber:BigNumber,config:config$2}),_false=createFalse({}),fineStructure=createFineStructure({BigNumber:BigNumber,config:config$2}),Fraction=createFractionClass({}),i=createI({Complex:Complex}),_Infinity=createInfinity({BigNumber:BigNumber,config:config$2}),LN10=createLN10({BigNumber:BigNumber,config:config$2}),LOG10E=createLOG10E({BigNumber:BigNumber,config:config$2}),Matrix=createMatrixClass({}),_NaN=createNaN({BigNumber:BigNumber,config:config$2}),_null=createNull({}),phi=createPhi({BigNumber:BigNumber,config:config$2}),Range=createRangeClass({}),ResultSet=createResultSet({}),SQRT1_2=createSQRT1_2({BigNumber:BigNumber,config:config$2}),sackurTetrode=createSackurTetrode({BigNumber:BigNumber,config:config$2}),tau=createTau({BigNumber:BigNumber,config:config$2}),_true=createTrue({}),version$1=createVersion({}),DenseMatrix=createDenseMatrixClass({Matrix:Matrix}),efimovFactor=createEfimovFactor({BigNumber:BigNumber,config:config$2}),LN2=createLN2({BigNumber:BigNumber,config:config$2}),pi=createPi({BigNumber:BigNumber,config:config$2}),replacer=createReplacer({}),SQRT2=createSQRT2({BigNumber:BigNumber,config:config$2}),typed=createTyped({BigNumber:BigNumber,Complex:Complex,DenseMatrix:DenseMatrix,Fraction:Fraction}),unaryPlus=createUnaryPlus({BigNumber:BigNumber,config:config$2,typed:typed}),weakMixingAngle=createWeakMixingAngle({BigNumber:BigNumber,config:config$2}),abs$1=createAbs({typed:typed}),acos$1=createAcos({Complex:Complex,config:config$2,typed:typed}),acot$1=createAcot({BigNumber:BigNumber,typed:typed}),acsc$1=createAcsc({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),addScalar=createAddScalar({typed:typed}),arg=createArg({typed:typed}),asech$1=createAsech({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),asinh$1=createAsinh({typed:typed}),atan$1=createAtan({typed:typed}),atanh$1=createAtanh({Complex:Complex,config:config$2,typed:typed}),bignumber=createBignumber({BigNumber:BigNumber,typed:typed}),bitNot=createBitNot({typed:typed}),boolean=createBoolean({typed:typed}),clone$1=createClone({typed:typed}),combinations=createCombinations({typed:typed}),complex=createComplex({Complex:Complex,typed:typed}),conj$1=createConj({typed:typed}),cosh$1=createCosh({typed:typed}),coth$1=createCoth({BigNumber:BigNumber,typed:typed}),csc$1=createCsc({BigNumber:BigNumber,typed:typed}),cube=createCube({typed:typed}),equalScalar=createEqualScalar({config:config$2,typed:typed}),erf$1=createErf({typed:typed}),exp$1=createExp({typed:typed}),expm1=createExpm1({Complex:Complex,typed:typed}),filter$1=createFilter({typed:typed}),forEach=createForEach({typed:typed}),format=createFormat({typed:typed}),getMatrixDataType=createGetMatrixDataType({typed:typed}),hex=createHex({format:format,typed:typed}),im$1=createIm({typed:typed}),isInteger=createIsInteger({typed:typed}),isNegative=createIsNegative({typed:typed}),isPositive=createIsPositive({typed:typed}),isZero=createIsZero({typed:typed}),LOG2E=createLOG2E({BigNumber:BigNumber,config:config$2}),lgamma=createLgamma({Complex:Complex,typed:typed}),log10$1=createLog10({Complex:Complex,config:config$2,typed:typed}),log2=createLog2({Complex:Complex,config:config$2,typed:typed}),map$1=createMap({typed:typed}),multiplyScalar=createMultiplyScalar({typed:typed}),not=createNot({typed:typed}),number=createNumber({typed:typed}),oct=createOct({format:format,typed:typed}),pickRandom=createPickRandom({config:config$2,typed:typed}),print=createPrint({typed:typed}),random$1=createRandom({config:config$2,typed:typed}),re$1=createRe({typed:typed}),sec$1=createSec({BigNumber:BigNumber,typed:typed}),sign$1=createSign({BigNumber:BigNumber,Fraction:Fraction,complex:complex,typed:typed}),sin$1=createSin({typed:typed}),SparseMatrix=createSparseMatrixClass({Matrix:Matrix,equalScalar:equalScalar,typed:typed}),splitUnit=createSplitUnit({typed:typed}),square=createSquare({typed:typed}),string=createString({typed:typed}),tan$1=createTan({typed:typed}),typeOf=createTypeOf({typed:typed}),acosh$1=createAcosh({Complex:Complex,config:config$2,typed:typed}),acsch$1=createAcsch({BigNumber:BigNumber,typed:typed}),apply=createApply({isInteger:isInteger,typed:typed}),asec$1=createAsec({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),bin=createBin({format:format,typed:typed}),combinationsWithRep=createCombinationsWithRep({typed:typed}),cos$1=createCos({typed:typed}),csch$1=createCsch({BigNumber:BigNumber,typed:typed}),isNaN$2=createIsNaN({typed:typed}),isPrime=createIsPrime({typed:typed}),randomInt=createRandomInt({config:config$2,typed:typed}),sech$1=createSech({BigNumber:BigNumber,typed:typed}),sinh$1=createSinh({typed:typed}),sparse=createSparse({SparseMatrix:SparseMatrix,typed:typed}),sqrt$1=createSqrt({Complex:Complex,config:config$2,typed:typed}),tanh$1=createTanh({typed:typed}),unaryMinus=createUnaryMinus({typed:typed}),acoth$1=createAcoth({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),cot$1=createCot({BigNumber:BigNumber,typed:typed}),fraction=createFraction({Fraction:Fraction,typed:typed}),isNumeric=createIsNumeric({typed:typed}),matrix$2=createMatrix({DenseMatrix:DenseMatrix,Matrix:Matrix,SparseMatrix:SparseMatrix,typed:typed}),matrixFromFunction=createMatrixFromFunction({isZero:isZero,matrix:matrix$2,typed:typed}),mod$1=createMod({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),nthRoot=createNthRoot({BigNumber:BigNumber,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),numeric=createNumeric({bignumber:bignumber,fraction:fraction,number:number}),or=createOr({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),prod=createProd({config:config$2,multiplyScalar:multiplyScalar,numeric:numeric,typed:typed}),reshape=createReshape({isInteger:isInteger,matrix:matrix$2,typed:typed}),size$1=createSize({matrix:matrix$2,config:config$2,typed:typed}),smaller=createSmaller({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),squeeze=createSqueeze({matrix:matrix$2,typed:typed}),subset=createSubset({matrix:matrix$2,typed:typed}),subtract$1=createSubtract({DenseMatrix:DenseMatrix,addScalar:addScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed,unaryMinus:unaryMinus}),to=createTo({matrix:matrix$2,typed:typed}),transpose=createTranspose({matrix:matrix$2,typed:typed}),xgcd=createXgcd({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),zeros=createZeros({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),and=createAnd({equalScalar:equalScalar,matrix:matrix$2,not:not,typed:typed,zeros:zeros}),bitAnd=createBitAnd({equalScalar:equalScalar,matrix:matrix$2,typed:typed}),bitXor=createBitXor({DenseMatrix:DenseMatrix,matrix:matrix$2,typed:typed}),cbrt=createCbrt({BigNumber:BigNumber,Complex:Complex,Fraction:Fraction,config:config$2,isNegative:isNegative,matrix:matrix$2,typed:typed,unaryMinus:unaryMinus}),compare=createCompare({BigNumber:BigNumber,DenseMatrix:DenseMatrix,Fraction:Fraction,config:config$2,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),compareText=createCompareText({matrix:matrix$2,typed:typed}),concat=createConcat({isInteger:isInteger,matrix:matrix$2,typed:typed}),count=createCount({prod:prod,size:size$1,typed:typed}),ctranspose=createCtranspose({conj:conj$1,transpose:transpose,typed:typed}),diag=createDiag({DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,matrix:matrix$2,typed:typed}),divideScalar=createDivideScalar({numeric:numeric,typed:typed}),dotDivide=createDotDivide({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),equal$1=createEqual({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),fft=createFft({addScalar:addScalar,divideScalar:divideScalar,exp:exp$1,i:i,matrix:matrix$2,multiplyScalar:multiplyScalar,tau:tau,typed:typed}),flatten$3=createFlatten({matrix:matrix$2,typed:typed}),gcd=createGcd({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),hasNumericValue=createHasNumericValue({isNumeric:isNumeric,typed:typed}),hypot=createHypot({abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,isPositive:isPositive,multiplyScalar:multiplyScalar,smaller:smaller,sqrt:sqrt$1,typed:typed}),ifft=createIfft({conj:conj$1,dotDivide:dotDivide,fft:fft,typed:typed}),kron=createKron({matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),largerEq=createLargerEq({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),leftShift=createLeftShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),lsolve=createLsolve({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),matrixFromColumns=createMatrixFromColumns({flatten:flatten$3,matrix:matrix$2,size:size$1,typed:typed}),min$1=createMin({config:config$2,numeric:numeric,smaller:smaller,typed:typed}),mode=createMode({isNaN:isNaN$2,isNumeric:isNumeric,typed:typed}),nthRoots=createNthRoots({Complex:Complex,config:config$2,divideScalar:divideScalar,typed:typed}),ones=createOnes({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),partitionSelect=createPartitionSelect({compare:compare,isNaN:isNaN$2,isNumeric:isNumeric,typed:typed}),resize=createResize({config:config$2,matrix:matrix$2}),rightArithShift=createRightArithShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),round$1=createRound({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),smallerEq=createSmallerEq({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),unequal=createUnequal({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),usolve=createUsolve({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),xor=createXor({DenseMatrix:DenseMatrix,matrix:matrix$2,typed:typed}),add$1=createAdd({DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,addScalar:addScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),atan2$1=createAtan2({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),bitOr=createBitOr({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),catalan=createCatalan({addScalar:addScalar,combinations:combinations,divideScalar:divideScalar,isInteger:isInteger,isNegative:isNegative,multiplyScalar:multiplyScalar,typed:typed}),compareNatural=createCompareNatural({compare:compare,typed:typed}),cumsum=createCumSum({add:add$1,typed:typed,unaryPlus:unaryPlus}),deepEqual=createDeepEqual({equal:equal$1,typed:typed}),diff=createDiff({matrix:matrix$2,number:number,subtract:subtract$1,typed:typed}),dot=createDot({addScalar:addScalar,conj:conj$1,multiplyScalar:multiplyScalar,size:size$1,typed:typed}),equalText=createEqualText({compareText:compareText,isZero:isZero,typed:typed}),floor=createFloor({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,round:round$1,typed:typed,zeros:zeros}),identity$1=createIdentity({BigNumber:BigNumber,DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,config:config$2,matrix:matrix$2,typed:typed}),invmod=createInvmod({BigNumber:BigNumber,add:add$1,config:config$2,equal:equal$1,isInteger:isInteger,mod:mod$1,smaller:smaller,typed:typed,xgcd:xgcd}),larger=createLarger({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),log$1=createLog({Complex:Complex,config:config$2,divideScalar:divideScalar,typed:typed}),lsolveAll=createLsolveAll({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),matrixFromRows=createMatrixFromRows({flatten:flatten$3,matrix:matrix$2,size:size$1,typed:typed}),multiply$1=createMultiply({addScalar:addScalar,dot:dot,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),qr=createQr({addScalar:addScalar,complex:complex,conj:conj$1,divideScalar:divideScalar,equal:equal$1,identity:identity$1,isZero:isZero,matrix:matrix$2,multiplyScalar:multiplyScalar,sign:sign$1,sqrt:sqrt$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus,zeros:zeros}),range$1=createRange({bignumber:bignumber,matrix:matrix$2,config:config$2,larger:larger,largerEq:largerEq,smaller:smaller,smallerEq:smallerEq,typed:typed}),rightLogShift=createRightLogShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),setSize=createSetSize({compareNatural:compareNatural,typed:typed}),slu=createSlu({SparseMatrix:SparseMatrix,abs:abs$1,add:add$1,divideScalar:divideScalar,larger:larger,largerEq:largerEq,multiply:multiply$1,subtract:subtract$1,transpose:transpose,typed:typed}),sum=createSum({add:add$1,config:config$2,numeric:numeric,typed:typed}),trace=createTrace({add:add$1,matrix:matrix$2,typed:typed}),usolveAll=createUsolveAll({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),asin$1=createAsin({Complex:Complex,config:config$2,typed:typed}),ceil=createCeil({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,round:round$1,typed:typed,zeros:zeros}),composition=createComposition({addScalar:addScalar,combinations:combinations,isInteger:isInteger,isNegative:isNegative,isPositive:isPositive,larger:larger,typed:typed}),cross=createCross({matrix:matrix$2,multiply:multiply$1,subtract:subtract$1,typed:typed}),det=createDet({divideScalar:divideScalar,isZero:isZero,matrix:matrix$2,multiply:multiply$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),distance=createDistance({abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,multiplyScalar:multiplyScalar,sqrt:sqrt$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),dotMultiply=createDotMultiply({equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),FibonacciHeap=createFibonacciHeapClass({larger:larger,smaller:smaller}),fix=createFix({Complex:Complex,DenseMatrix:DenseMatrix,ceil:ceil,equalScalar:equalScalar,floor:floor,matrix:matrix$2,typed:typed,zeros:zeros}),ImmutableDenseMatrix=createImmutableDenseMatrixClass({DenseMatrix:DenseMatrix,smaller:smaller}),Index=createIndexClass({ImmutableDenseMatrix:ImmutableDenseMatrix}),intersect=createIntersect({abs:abs$1,add:add$1,addScalar:addScalar,config:config$2,divideScalar:divideScalar,equalScalar:equalScalar,flatten:flatten$3,isNumeric:isNumeric,isZero:isZero,matrix:matrix$2,multiply:multiply$1,multiplyScalar:multiplyScalar,smaller:smaller,subtract:subtract$1,typed:typed}),lcm=createLcm({equalScalar:equalScalar,matrix:matrix$2,typed:typed}),log1p=createLog1p({Complex:Complex,config:config$2,divideScalar:divideScalar,log:log$1,typed:typed}),max$1=createMax({config:config$2,larger:larger,numeric:numeric,typed:typed}),quantileSeq=createQuantileSeq({add:add$1,compare:compare,multiply:multiply$1,partitionSelect:partitionSelect,typed:typed}),row=createRow({Index:Index,matrix:matrix$2,range:range$1,typed:typed}),setCartesian=createSetCartesian({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setDistinct=createSetDistinct({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setIsSubset=createSetIsSubset({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setPowerset=createSetPowerset({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),sort=createSort({compare:compare,compareNatural:compareNatural,matrix:matrix$2,typed:typed}),column=createColumn({Index:Index,matrix:matrix$2,range:range$1,typed:typed}),index=createIndex({Index:Index,typed:typed}),inv=createInv({abs:abs$1,addScalar:addScalar,det:det,divideScalar:divideScalar,identity:identity$1,matrix:matrix$2,multiply:multiply$1,typed:typed,unaryMinus:unaryMinus}),pinv=createPinv({Complex:Complex,add:add$1,ctranspose:ctranspose,deepEqual:deepEqual,divideScalar:divideScalar,dot:dot,dotDivide:dotDivide,equal:equal$1,inv:inv,matrix:matrix$2,multiply:multiply$1,typed:typed}),pow$1=createPow({Complex:Complex,config:config$2,fraction:fraction,identity:identity$1,inv:inv,matrix:matrix$2,multiply:multiply$1,number:number,typed:typed}),setDifference=createSetDifference({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setMultiplicity=createSetMultiplicity({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),Spa=createSpaClass({FibonacciHeap:FibonacciHeap,addScalar:addScalar,equalScalar:equalScalar}),sqrtm=createSqrtm({abs:abs$1,add:add$1,identity:identity$1,inv:inv,max:max$1,multiply:multiply$1,size:size$1,sqrt:sqrt$1,subtract:subtract$1,typed:typed}),Unit=createUnitClass({BigNumber:BigNumber,Complex:Complex,Fraction:Fraction,abs:abs$1,addScalar:addScalar,config:config$2,divideScalar:divideScalar,equal:equal$1,fix:fix,format:format,isNumeric:isNumeric,multiplyScalar:multiplyScalar,number:number,pow:pow$1,round:round$1,subtract:subtract$1}),vacuumImpedance=createVacuumImpedance({BigNumber:BigNumber,Unit:Unit,config:config$2}),wienDisplacement=createWienDisplacement({BigNumber:BigNumber,Unit:Unit,config:config$2}),atomicMass=createAtomicMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),bohrMagneton=createBohrMagneton({BigNumber:BigNumber,Unit:Unit,config:config$2}),boltzmann=createBoltzmann({BigNumber:BigNumber,Unit:Unit,config:config$2}),conductanceQuantum=createConductanceQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),createUnit=createCreateUnit({Unit:Unit,typed:typed}),deuteronMass=createDeuteronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),dotPow=createDotPow({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,pow:pow$1,typed:typed}),electricConstant=createElectricConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),elementaryCharge=createElementaryCharge({BigNumber:BigNumber,Unit:Unit,config:config$2}),expm=createExpm({abs:abs$1,add:add$1,identity:identity$1,inv:inv,multiply:multiply$1,typed:typed}),faraday=createFaraday({BigNumber:BigNumber,Unit:Unit,config:config$2}),firstRadiation=createFirstRadiation({BigNumber:BigNumber,Unit:Unit,config:config$2}),gamma$1=createGamma({BigNumber:BigNumber,Complex:Complex,config:config$2,multiplyScalar:multiplyScalar,pow:pow$1,typed:typed}),gravitationConstant=createGravitationConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),hartreeEnergy=createHartreeEnergy({BigNumber:BigNumber,Unit:Unit,config:config$2}),klitzing=createKlitzing({BigNumber:BigNumber,Unit:Unit,config:config$2}),loschmidt=createLoschmidt({BigNumber:BigNumber,Unit:Unit,config:config$2}),magneticConstant=createMagneticConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarMass=createMolarMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarPlanckConstant=createMolarPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),neutronMass=createNeutronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),nuclearMagneton=createNuclearMagneton({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckCharge=createPlanckCharge({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckLength=createPlanckLength({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckTemperature=createPlanckTemperature({BigNumber:BigNumber,Unit:Unit,config:config$2}),protonMass=createProtonMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),reducedPlanckConstant=createReducedPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),rydberg=createRydberg({BigNumber:BigNumber,Unit:Unit,config:config$2}),setIntersect=createSetIntersect({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),speedOfLight=createSpeedOfLight({BigNumber:BigNumber,Unit:Unit,config:config$2}),stefanBoltzmann=createStefanBoltzmann({BigNumber:BigNumber,Unit:Unit,config:config$2}),thomsonCrossSection=createThomsonCrossSection({BigNumber:BigNumber,Unit:Unit,config:config$2}),avogadro=createAvogadro({BigNumber:BigNumber,Unit:Unit,config:config$2}),bohrRadius=createBohrRadius({BigNumber:BigNumber,Unit:Unit,config:config$2}),coulomb=createCoulomb({BigNumber:BigNumber,Unit:Unit,config:config$2}),divide$1=createDivide({divideScalar:divideScalar,equalScalar:equalScalar,inv:inv,matrix:matrix$2,multiply:multiply$1,typed:typed}),electronMass=createElectronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),factorial$1=createFactorial({gamma:gamma$1,typed:typed}),gravity=createGravity({BigNumber:BigNumber,Unit:Unit,config:config$2}),inverseConductanceQuantum=createInverseConductanceQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),lup=createLup({DenseMatrix:DenseMatrix,Spa:Spa,SparseMatrix:SparseMatrix,abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,equalScalar:equalScalar,larger:larger,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),magneticFluxQuantum=createMagneticFluxQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarMassC12=createMolarMassC12({BigNumber:BigNumber,Unit:Unit,config:config$2}),multinomial=createMultinomial({add:add$1,divide:divide$1,factorial:factorial$1,isInteger:isInteger,isPositive:isPositive,multiply:multiply$1,typed:typed}),permutations=createPermutations({factorial:factorial$1,typed:typed}),planckMass=createPlanckMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),quantumOfCirculation=createQuantumOfCirculation({BigNumber:BigNumber,Unit:Unit,config:config$2}),secondRadiation=createSecondRadiation({BigNumber:BigNumber,Unit:Unit,config:config$2}),stirlingS2=createStirlingS2({bignumber:bignumber,addScalar:addScalar,combinations:combinations,divideScalar:divideScalar,factorial:factorial$1,isInteger:isInteger,isNegative:isNegative,larger:larger,multiplyScalar:multiplyScalar,number:number,pow:pow$1,subtract:subtract$1,typed:typed}),unit=createUnitFunction({Unit:Unit,typed:typed}),bellNumbers=createBellNumbers({addScalar:addScalar,isInteger:isInteger,isNegative:isNegative,stirlingS2:stirlingS2,typed:typed}),eigs=createEigs({abs:abs$1,add:add$1,addScalar:addScalar,atan:atan$1,bignumber:bignumber,column:column,complex:complex,config:config$2,cos:cos$1,diag:diag,divideScalar:divideScalar,dot:dot,equal:equal$1,flatten:flatten$3,im:im$1,inv:inv,larger:larger,matrix:matrix$2,matrixFromColumns:matrixFromColumns,multiply:multiply$1,multiplyScalar:multiplyScalar,number:number,qr:qr,re:re$1,sin:sin$1,smaller:smaller,sqrt:sqrt$1,subtract:subtract$1,typed:typed,usolve:usolve,usolveAll:usolveAll}),fermiCoupling=createFermiCoupling({BigNumber:BigNumber,Unit:Unit,config:config$2}),mean=createMean({add:add$1,divide:divide$1,typed:typed}),molarVolume=createMolarVolume({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckConstant=createPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),setSymDifference=createSetSymDifference({Index:Index,concat:concat,setDifference:setDifference,size:size$1,subset:subset,typed:typed}),classicalElectronRadius=createClassicalElectronRadius({BigNumber:BigNumber,Unit:Unit,config:config$2}),lusolve=createLusolve({DenseMatrix:DenseMatrix,lsolve:lsolve,lup:lup,matrix:matrix$2,slu:slu,typed:typed,usolve:usolve}),median=createMedian({add:add$1,compare:compare,divide:divide$1,partitionSelect:partitionSelect,typed:typed}),setUnion=createSetUnion({Index:Index,concat:concat,setIntersect:setIntersect,setSymDifference:setSymDifference,size:size$1,subset:subset,typed:typed}),variance=createVariance({add:add$1,apply:apply,divide:divide$1,isNaN:isNaN$2,multiply:multiply$1,subtract:subtract$1,typed:typed}),kldivergence=createKldivergence({divide:divide$1,dotDivide:dotDivide,isNumeric:isNumeric,log:log$1,matrix:matrix$2,multiply:multiply$1,sum:sum,typed:typed}),norm=createNorm({abs:abs$1,add:add$1,conj:conj$1,ctranspose:ctranspose,eigs:eigs,equalScalar:equalScalar,larger:larger,matrix:matrix$2,multiply:multiply$1,pow:pow$1,smaller:smaller,sqrt:sqrt$1,typed:typed}),planckTime=createPlanckTime({BigNumber:BigNumber,Unit:Unit,config:config$2}),rotationMatrix=createRotationMatrix({BigNumber:BigNumber,DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,addScalar:addScalar,config:config$2,cos:cos$1,matrix:matrix$2,multiplyScalar:multiplyScalar,norm:norm,sin:sin$1,typed:typed,unaryMinus:unaryMinus}),gasConstant=createGasConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),std=createStd({sqrt:sqrt$1,typed:typed,variance:variance}),mad=createMad({abs:abs$1,map:map$1,median:median,subtract:subtract$1,typed:typed}),rotate=createRotate({multiply:multiply$1,rotationMatrix:rotationMatrix,typed:typed}),math$2={},mathWithTransform={},classes={},Chain=createChainClass({math:math$2}),Node=createNode({mathWithTransform:mathWithTransform}),ObjectNode=createObjectNode({Node:Node}),OperatorNode=createOperatorNode({Node:Node}),ParenthesisNode=createParenthesisNode({Node:Node}),RelationalNode=createRelationalNode({Node:Node}),ArrayNode=createArrayNode({Node:Node}),BlockNode=createBlockNode({Node:Node,ResultSet:ResultSet}),ConditionalNode=createConditionalNode({Node:Node}),ConstantNode=createConstantNode({Node:Node}),RangeNode=createRangeNode({Node:Node}),reviver=createReviver({classes:classes}),chain$1=createChain({Chain:Chain,typed:typed}),FunctionAssignmentNode=createFunctionAssignmentNode({Node:Node,typed:typed}),AccessorNode=createAccessorNode({Node:Node,subset:subset}),AssignmentNode=createAssignmentNode({matrix:matrix$2,Node:Node,subset:subset}),IndexNode=createIndexNode({Node:Node,size:size$1}),SymbolNode=createSymbolNode({Unit:Unit,Node:Node,math:math$2}),FunctionNode=createFunctionNode({Node:Node,SymbolNode:SymbolNode,math:math$2}),parse$2=createParse({AccessorNode:AccessorNode,ArrayNode:ArrayNode,AssignmentNode:AssignmentNode,BlockNode:BlockNode,ConditionalNode:ConditionalNode,ConstantNode:ConstantNode,FunctionAssignmentNode:FunctionAssignmentNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,RangeNode:RangeNode,RelationalNode:RelationalNode,SymbolNode:SymbolNode,config:config$2,numeric:numeric,typed:typed}),resolve=createResolve({ConstantNode:ConstantNode,FunctionNode:FunctionNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,parse:parse$2}),simplifyCore=createSimplifyCore({AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,divide:divide$1,equal:equal$1,isZero:isZero,multiply:multiply$1,pow:pow$1,subtract:subtract$1}),compile=createCompile({parse:parse$2,typed:typed}),Help=createHelpClass({parse:parse$2}),leafCount=createLeafCount({parse:parse$2,typed:typed}),simplify$2=createSimplify({bignumber:bignumber,fraction:fraction,AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,config:config$2,divide:divide$1,equal:equal$1,isZero:isZero,mathWithTransform:mathWithTransform,matrix:matrix$2,multiply:multiply$1,parse:parse$2,pow:pow$1,resolve:resolve,simplifyCore:simplifyCore,subtract:subtract$1,typed:typed}),symbolicEqual=createSymbolicEqual({OperatorNode:OperatorNode,parse:parse$2,simplify:simplify$2,typed:typed}),evaluate$1=createEvaluate({parse:parse$2,typed:typed}),help=createHelp({Help:Help,mathWithTransform:mathWithTransform,typed:typed}),Parser=createParserClass({evaluate:evaluate$1}),rationalize=createRationalize({bignumber:bignumber,fraction:fraction,AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,config:config$2,divide:divide$1,equal:equal$1,isZero:isZero,mathWithTransform:mathWithTransform,matrix:matrix$2,multiply:multiply$1,parse:parse$2,pow:pow$1,simplify:simplify$2,simplifyCore:simplifyCore,subtract:subtract$1,typed:typed}),derivative$1=createDerivative({ConstantNode:ConstantNode,FunctionNode:FunctionNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,config:config$2,equal:equal$1,isZero:isZero,numeric:numeric,parse:parse$2,simplify:simplify$2,typed:typed}),parser=createParser({Parser:Parser,typed:typed});_extends$1(math$2,{e:e,false:_false,fineStructure:fineStructure,i:i,Infinity:_Infinity,LN10:LN10,LOG10E:LOG10E,NaN:_NaN,null:_null,phi:phi,SQRT1_2:SQRT1_2,sackurTetrode:sackurTetrode,tau:tau,true:_true,E:e,version:version$1,efimovFactor:efimovFactor,LN2:LN2,pi:pi,replacer:replacer,reviver:reviver,SQRT2:SQRT2,typed:typed,unaryPlus:unaryPlus,PI:pi,weakMixingAngle:weakMixingAngle,abs:abs$1,acos:acos$1,acot:acot$1,acsc:acsc$1,addScalar:addScalar,arg:arg,asech:asech$1,asinh:asinh$1,atan: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o=a.length,s=Array(o+1);for(s[0]=0,r=0;r=u){if(i[l]=m[c],0===c)return;++l,s=f[--c],u=p[c]}else 0===n[o=a[r[s]]]?(n[o]=1,f[c]=s,m[++c]=o,s=t[o],p[c]=u=t[o+1]):++s},numeric.ccsLPSolve=function(e,t,r,n,i,a,o){var s=e[0],u=e[1],c=e[2];s.length;var l,f,p,m,d,h,y,g,v,x=t[0],b=t[1],_=t[2];for(f=x[i],p=x[i+1],n.length=0,l=f;la&&(o=i,a=s);for(_(v[r])=c){if(i[f]=a[d[l]],0===l)return;++f,u=p[--l],c=m[l]}else 0===n[s=r[u]]?(n[s]=1,p[l]=u,d[++l]=s,u=t[s=a[s]],m[l]=c=t[s+1]):++u}},numeric.ccsLPSolve0=function(e,t,r,n,i,a,o,s){var u=e[0],c=e[1],l=e[2];u.length;var f,p,m,d,h,y,g,v,x,b=t[0],_=t[1],w=t[2];for(p=b[i],m=b[i+1],n.length=0,f=p;fa&&(o=i,a=s);for(_(v[w[r]])r[n]&&(r[n]=t.length),t)t.hasOwnProperty(i)&&e(t[i],r,n+1);return r},numeric.sclone=function e(t,r,n){void 0===r&&(r=0),void 0===n&&(n=numeric.sdim(t).length);var i,a=Array(t.length);if(r===n-1){for(i in t)t.hasOwnProperty(i)&&(a[i]=t[i]);return a}for(i in t)t.hasOwnProperty(i)&&(a[i]=e(t[i],r+1,n));return a},numeric.sdiag=function(e){var t,r,n=e.length,i=Array(n);for(t=n-1;t>=1;t-=2)r=t-1,i[t]=[],i[t][t]=e[t],i[r]=[],i[r][r]=e[r];return 0===t&&(i[0]=[],i[0][0]=e[t]),i},numeric.sidentity=function(e){return numeric.sdiag(numeric.rep([e],1))},numeric.stranspose=function(e){var t,r,n,i=[];for(t in e.length,e)if(e.hasOwnProperty(t))for(r in n=e[t])n.hasOwnProperty(r)&&("object"!=typeof i[r]&&(i[r]=[]),i[r][t]=n[r]);return i},numeric.sLUP=function(e,t){throw new Error("The function numeric.sLUP had a bug in it and has been removed. 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numeric.sdotMM(e,t);default:throw new Error("numeric.sdot not implemented for tensors of order "+r+" and "+n)}},numeric.sscatter=function(e){var t,r,n,i,a=e[0].length,o=e.length,s=[];for(r=a-1;r>=0;--r)if(e[o-1][r]){for(i=s,n=0;n=0;--a)r[a]=[];for(a=i;a>=0;--a)r[a].push(n[a]);r[i+1].push(o)}}else e(o,r,n);return n.length>i&&n.pop(),r},numeric.cLU=function(e){var t,r,n,i,a,o,s=e[0],u=e[1],c=e[2],l=s.length,f=0;for(t=0;tf&&(f=s[t]);f++;var p,m=Array(f),d=Array(f),h=numeric.rep([f],1/0),y=numeric.rep([f],-1/0);for(n=0;ny[t]&&(y[t]=r);for(t=0;ty[t+1]&&(y[t+1]=y[t]);for(t=f-1;t>=1;t--)h[t]=0;p--){for(;c[m]>p;)i[p]-=l[m]*i[c[m]],m--;i[p]/=l[m],m--}return i},numeric.cgrid=function(e,t){"number"==typeof e&&(e=[e,e]);var r,n,i,a=numeric.rep(e,-1);if("function"!=typeof t)if("L"===t)t=function(t,r){return t>=e[0]/2||ri&&(i=a[n]);for(i++,r=numeric.rep([i],0),n=0;n1;)i[n=o((t+r)/2)]<=e?t=n:r=n;return this._at(e,t)}a=e.length;var s,u=Array(a);for(s=a-1;-1!==s;--s)u[s]=this.at(e[s]);return u},numeric.Spline.prototype.diff=function(){var e,t,r,n=this.x,i=this.yl,a=this.yr,o=this.kl,s=this.kr,u=i.length,c=o,l=s,f=Array(u),p=Array(u),m=numeric.add,d=numeric.mul,h=numeric.div,y=numeric.sub;for(e=u-1;-1!==e;--e)t=n[e+1]-n[e],r=y(a[e+1],i[e]),f[e]=h(m(d(r,6),d(o[e],-4*t),d(s[e+1],-2*t)),t*t),p[e+1]=h(m(d(r,-6),d(o[e],2*t),d(s[e+1],4*t)),t*t);return new numeric.Spline(n,c,l,f,p)},numeric.Spline.prototype.roots=function(){function e(e){return e*e}var t=[],r=this.x,n=this.yl,i=this.yr,a=this.kl,o=this.kr;"number"==typeof n[0]&&(n=[n],i=[i],a=[a],o=[o]);var s,u,c,l,f,p,m,d,h,y,g,v,x,b,_,w,N,$,A,M,S,E,T,O=n.length,C=r.length-1,k=(t=Array(O),Math.sqrt);for(s=0;s!==O;++s){for(l=n[s],f=i[s],p=a[s],m=o[s],d=[],u=0;u!==C;u++){for(u>0&&f[u]*l[u]<0&&d.push(r[u]),w=r[u+1]-r[u],r[u],g=l[u],v=f[u+1],h=p[u]/w,x=(y=m[u+1]/w)+3*g+2*h-3*v,b=3*(y+h+2*(g-v)),(_=e(h-y+3*(g-v))+12*y*g)<=0?N=($=x/b)>r[u]&&$r[u]&&$r[u]&&A0)S=E,$=A;else{for(var D=0;!((T=($*E-A*S)/($-A))<=S||T>=E);)if((M=this._at(T,u))*A>0)E=T,A=M,-1===D&&($*=.5),D=-1;else{if(!(M*$>0))break;S=T,$=M,1===D&&(A*=.5),D=1}d.push(T),S=N[c+1],$=this._at(S,u)}else d.push(S),S=E,$=A;0===A&&d.push(E)}t[s]=d}return"number"==typeof this.yl[0]?t[0]:t},numeric.spline=function(e,t,r,n){var i,a=e.length,o=[],s=[],u=[],c=numeric.sub,l=numeric.mul,f=numeric.add;for(i=a-2;i>=0;i--)s[i]=e[i+1]-e[i],u[i]=c(t[i+1],t[i]);"string"!=typeof r&&"string"!=typeof n||(r=n="periodic");var p=[[],[],[]];switch(typeof r){case"undefined":o[0]=l(3/(s[0]*s[0]),u[0]),p[0].push(0,0),p[1].push(0,1),p[2].push(2/s[0],1/s[0]);break;case"string":o[0]=f(l(3/(s[a-2]*s[a-2]),u[a-2]),l(3/(s[0]*s[0]),u[0])),p[0].push(0,0,0),p[1].push(a-2,0,1),p[2].push(1/s[a-2],2/s[a-2]+2/s[0],1/s[0]);break;default:o[0]=r,p[0].push(0),p[1].push(0),p[2].push(1)}for(i=1;i20)throw new Error("Numerical gradient 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s,u,c,l,f,p,m,d,h,y,g,v,x,b=[e],_=[r],w=[n(e,r)],N=[],$=[3/40,9/40],A=[44/45,-56/15,32/9],M=[19372/6561,-25360/2187,64448/6561,-212/729],S=[9017/3168,-355/33,46732/5247,49/176,-5103/18656],E=[35/384,0,500/1113,125/192,-2187/6784,11/84],T=[.10013431883002395,0,.3918321794184259,-.02982460176594817,.05893268337240795,-.04497888809104361,5618549.5/235043384],O=[.2,.3,.8,8/9,1,1],C=[-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,1/40],k=0,D=(t-e)/10,I=0,B=numeric.add,z=numeric.mul,R=Math.min,P=Math.abs,q=numeric.norminf,L=Math.pow,F=numeric.any,j=numeric.lt,U=numeric.and;numeric.sub;var G=new numeric.Dopri(b,_,w,N,-1,"");for("function"==typeof o&&(g=o(e,r));et&&(D=t-e),s=n(e+O[0]*D,B(r,z(.2*D,w[k]))),u=n(e+O[1]*D,B(B(r,z($[0]*D,w[k])),z($[1]*D,s))),c=n(e+O[2]*D,B(B(B(r,z(A[0]*D,w[k])),z(A[1]*D,s)),z(A[2]*D,u))),l=n(e+O[3]*D,B(B(B(B(r,z(M[0]*D,w[k])),z(M[1]*D,s)),z(M[2]*D,u)),z(M[3]*D,c))),f=n(e+O[4]*D,B(B(B(B(B(r,z(S[0]*D,w[k])),z(S[1]*D,s)),z(S[2]*D,u)),z(S[3]*D,c)),z(S[4]*D,l))),p=n(e+D,h=B(B(B(B(B(r,z(w[k],D*E[0])),z(u,D*E[2])),z(c,D*E[3])),z(l,D*E[4])),z(f,D*E[5]))),(y="number"==typeof(m=B(B(B(B(B(z(w[k],D*C[0]),z(u,D*C[2])),z(c,D*C[3])),z(l,D*C[4])),z(f,D*C[5])),z(p,D*C[6])))?P(m):q(m))>i){if(e+(D=.2*D*L(i/y,.25))===e){G.msg="Step size became too small";break}}else{if(N[k]=B(B(B(B(B(B(r,z(w[k],D*T[0])),z(u,D*T[2])),z(c,D*T[3])),z(l,D*T[4])),z(f,D*T[5])),z(p,D*T[6])),b[++k]=e+D,_[k]=h,w[k]=p,"function"==typeof o){var V,Z,H=e,X=e+.5*D;if(v=o(X,N[k-1]),F(x=U(j(g,0),j(0,v)))||(H=X,g=v,v=o(X=e+D,h),x=U(j(g,0),j(0,v))),F(x)){for(var W,Q,Y=0,J=1,K=1;;){if("number"==typeof g)Z=(K*v*H-J*g*X)/(K*v-J*g);else 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t=e[0],r=e.slice(1);if("apply"===t){if("string"!=typeof r[0])throw Error("Non string functions not implemented for conversion to mathjs");if("factorial"===r[0])return new math.OperatorNode("!","factorial",[this.convert(r[1])]);let e=functionConverstions[r[0]];e||(e=r[0]);const t=new math.SymbolNode(e),n=r[1];let i;return i="tuple"===n[0]?n.slice(1).map(function(e,t){return this.convert(e)}.bind(this)):[this.convert(n)],new math.FunctionNode(t,i)}if("lts"===t||"gts"===t){const e=r[0],n=r[1];if("tuple"!==e[0]||"tuple"!==n[0])throw new Error("Badly formed ast");const i=e.slice(1).map(function(e,t){return this.convert(e)}.bind(this));let a=[];for(let r=1;r","larger",i.slice(r-1,r+1))):"lts"===t?a.push(new math.OperatorNode("<=","smallerEq",i.slice(r-1,r+1))):a.push(new math.OperatorNode(">=","largerEq",i.slice(r-1,r+1)));let o=new math.OperatorNode("and","and",a.slice(0,2));for(let e=2;e=","largerEq",[e,o])):u.push(new math.OperatorNode(">","larger",[e,o])),a[2]?u.push(new 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math.OperatorNode("and","and",p);return"notsubset"!==t&&"notsuperset"!==t||(m=new math.OperatorNode("not","not",[m])),m}if("matrix"===t){let e=r[0],t=e[1],n=e[2],i=r[1];if(!Number.isInteger(t)||!Number.isInteger(n))throw Error("Matrix must have integer dimensions");let a=[];for(let e=1;e<=t;e++){let t=[];for(let r=1;r<=n;r++)t.push(this.convert(i[e][r]));a.push(new math.ArrayNode(t))}return new math.ArrayNode(a)}if(t in operators$2)return operators$2[t](r.map(function(e,t){return this.convert(e)}.bind(this)));throw Error("Operator "+t+" not implemented for conversion to mathjs")}}var function_normalizations={ln:"log",arccos:"acos",arccosh:"acosh",arcsin:"asin",arcsinh:"asinh",arctan:"atan",arctanh:"atanh",arcsec:"asec",arcsech:"asech",arccsc:"acsc",arccsch:"acsch",arccot:"acot",arccoth:"acoth",cosec:"csc"},create_trig_inverses_for=["cos","cosh","sin","sinh","tan","tanh","sec","sech","csc","csch","cot","coth"],move_exponents_outside_for=["cos","cosh","sin","sinh","tan","tanh","sec","sech","csc","csch","cot","coth"];function normalize_function_names(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("apply"===r){if("sqrt"===n[0])return["^",normalize_function_names(n[1]),.5];var i=normalize_function_names_sub(n[0]);i=["apply",i];var a=n.slice(1).map((function(e){return normalize_function_names(e)}));return a=a.length>1?["tuple"].concat(a):a[0],i.push(a),i}return"^"===r&&"e"===n[0]&&math$1.define_e?["apply","exp",normalize_function_names(n[1])]:"binom"===r?["apply","nCr",["tuple",normalize_function_names(n[0]),normalize_function_names(n[1])]]:[r].concat(n.map((function(e){return normalize_function_names(e)})))}function normalize_function_names_sub(e){if("string"==typeof e)return e in function_normalizations?function_normalizations[e]:e;if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if("^"===t&&2===r.length&&-1===r[1]){let e=normalize_function_names_sub(r[0]);if(create_trig_inverses_for.includes(e))return"a"+e}return[t].concat(r.map((function(e){return normalize_function_names_sub(e)})))}function normalize_applied_functions(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("apply"===r){let e=n[0];if("^"===e[0]){let t=e[1],r=e[2];return-1!==r&&move_exponents_outside_for.includes(t)?["^",["apply",t,normalize_applied_functions(n[1])],r]:["apply",e,normalize_applied_functions(n[1])]}let t=0;for(;"prime"===e[0];)t+=1,e=e[1];let r=["apply",e,normalize_applied_functions(n[1])];for(let e=0;e2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_integer_ast(e,o[0],r),is_integer_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_integer_ast(a[0],n,r);if("*"===i){return!!a.every((function(e){return is_integer_ast(e,n,r)}))||void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!is_positive_ast(a[1],n,!0,r))return;if(!1===e)return!0}let t=is_integer_ast(a[0],n,r),i=is_integer_ast(a[1],n,r);if(!t)return t;if(!i)return;return!!is_positive_ast(a[1],n,!1,r)||void 0}if("+"===i){let e=0;for(let t=0;t0)return;e+=1}if(void 0===i)return}return 0===e}if("apply"===i)return!!(functions.C.Z&&functions.C.Z.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.Z&&functions.R.Z.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.Z&&functions.nonzeroC.Z.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.Z&&functions.nonneg.Z.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.Z&&functions.pos.Z.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("/"===i||"prime"===i)return;return!1}return!1}function is_real_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e)return Number.isFinite(e);var n=evaluate_to_constant(e,{remove_units_first:!1,nan_for_non_numeric:!1});if(null!==n)return"number"==typeof n&&Number.isFinite(n);if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}if("in"===a&&o[0]===e&&"R"===o[1])return negate_adjust(!0,s);if("notin"===a&&o[0]===e&&"R"===o[1])return negate_adjust(!1,s);if(!1===s){if("in"===a&&o[0]===e&&"Z"===o[1])return!0}else if("notin"===a&&o[0]===e&&"Z"===o[1])return!0;if("<"===a||"le"===a){let t=variables(n),r=functions$2(n);if(-1!==t.indexOf(e)&&0===r.length)return!0}if("="===a&&!s||"ne"===a&&s){let t=narrow_assumptions(i,r);if(o[0]===e)return is_real_ast(o[1],t);if(o[1]===e)return is_real_ast(o[0],t)}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_real_ast(e,o[0],r),is_real_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_real_ast(a[0],n,r);if("*"===i||"+"===i){if(a.length>2&&(a=(e=unflattenRight(e)).slice(1)),"*"===i&&(!1===is_nonzero_ast(a[0],n,r)||!1===is_nonzero_ast(a[1],n,r)))return!0;let t=is_real_ast(a[0],n,r),o=is_real_ast(a[1],n,r);return!(!t||!o)||!(t&&!1===o||o&&!1===t)&&void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r),t=is_positive_ast(a[1],n,!0,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!t)return;if(!1===e)return!0}let i=is_real_ast(a[0],n,r),o=is_real_ast(a[1],n,r);if(!i||!o)return;if(!is_positive_ast(a[0],n,!1,r)){return!!is_integer_ast(a[1],n,r)||void 0}return!!is_positive_ast(a[0],n,!0,r)||(!!t||void 0)}if("/"===i){if(!is_nonzero_ast(a[1],n,r))return;if(!1===is_nonzero_ast(a[0],n,r))return!0;if(!is_real_ast(a[0],n,r)||!is_real_ast(a[1],n,r))return;return!0}if("apply"===i)return!!(functions.C.R&&functions.C.R.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.R&&functions.R.R.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.R&&functions.nonzeroC.R.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.R&&functions.nonneg.R.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.R&&functions.pos.R.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("prime"===i)return;return!1}return!1}function is_complex_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e)return Number.isFinite(e);var n=evaluate_to_constant(e,{remove_units_first:!1,nan_for_non_numeric:!1});if(null!==n)return"number"==typeof n?Number.isFinite(n):!(void 0===n.re||!Number.isFinite(n.re)||void 0===n.im||!Number.isFinite(n.im));if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}if("in"===a&&o[0]===e&&"C"===o[1])return negate_adjust(!0,s);if("notin"===a&&o[0]===e&&"C"===o[1])return negate_adjust(!1,s);if(!1===s){if("in"===a){if(o[0]===e&&"Z"===o[1])return!0;if(o[0]===e&&"R"===o[1])return!0}}else if("notin"===a){if(o[0]===e&&"Z"===o[1])return!0;if(o[0]===e&&"R"===o[1])return!0}if("<"===a||"le"===a){let t=variables(n),r=functions$2(n);if(-1!==t.indexOf(e)&&0===r.length)return!0}if("="===a&&!s||"ne"===a&&s){let t=narrow_assumptions(i,r);if(o[0]===e)return is_complex_ast(o[1],t);if(o[1]===e)return is_complex_ast(o[0],t)}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_complex_ast(e,o[0],r),is_complex_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_complex_ast(a[0],n,r);if("*"===i||"+"===i){if("*"===i&&!a.every((e=>!1!==is_nonzero_ast(e,n,r))))return!0;return!!a.every((e=>is_complex_ast(e,n,r)))||void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r),t=is_positive_ast(a[1],n,!0,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!t)return;if(!1===e)return!0}let i=is_complex_ast(a[0],n,r),o=is_complex_ast(a[1],n,r);return!(!i||!o)||void 0}if("/"===i){if(!is_nonzero_ast(a[1],n,r))return;if(!1===is_nonzero_ast(a[0],n,r))return!0;if(!is_complex_ast(a[0],n,r)||!is_complex_ast(a[1],n,r))return;return!0}if("apply"===i)return!!(functions.C.C&&functions.C.C.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.C&&functions.R.C.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.C&&functions.nonzeroC.C.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.C&&functions.nonneg.C.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.C&&functions.pos.C.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("prime"===i)return;return!1}return!1}function is_nonzero_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e){if(Number.isFinite(e))return 0!==e;if(Number.isNaN(e))return;return!0}var n=evaluate_to_constant(e,{remove_units_first:!1,nan_for_non_numeric:!1});if(null!==n){if("number"==typeof n){if(Number.isFinite(n))return 0!==n;if(Number.isNaN(n))return;return!0}return void 0!==n.re&&void 0!==n.im&&(0!==n.re||0!==n.im)||void 0}if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}let u=narrow_assumptions(i,r);if("="===a&&!s||"ne"===a&&s){if(o[0]===e)return is_nonzero_ast(o[1],u);if(o[1]===e)return 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is_nonzero_ast(a[0],n,r);if("+"===i){if(a.length>2&&(a=(e=unflattenRight(e)).slice(1)),equal(a[0],simplify(["-",a[1]],r)))return!1;let t=is_nonzero_ast(a[0],n,r),i=is_nonzero_ast(a[1],n,r);if(!1===t)return i;if(!1===i)return t;let o=is_real_ast(a[0],n,r),s=is_real_ast(a[1],n,r);if(!o||!s)return!0===o?!1===s||void 0:!0===s&&!1===o||void 0;let u=is_positive_ast(a[0],n,!1,r),c=is_positive_ast(a[1],n,!1,r),l=is_positive_ast(a[0],n,!0,r),f=is_positive_ast(a[1],n,!0,r);return!!(u&&f||l&&c)||(!1===u&&!1===f||!1===l&&!1===c||void 0)}if("*"===i){let e=!0;for(let t=0;t0:e>=0);var i=is_real_ast(e,t,n);if(!i)return i;var a=evaluate_to_constant(e,{remove_units_first:!1,nan_for_non_numeric:!1});if(null!==a)return"number"==typeof a&&(!!Number.isFinite(a)&&(r?a>0:a>=0));if("string"==typeof e){let i;if(i=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(i))return;let a=i,o=i[0],s=i.slice(1),u=!1;for(;"not"===o;){if(u=!u,i=s[0],!Array.isArray(i))return;o=i[0],s=i.slice(1)}let c=narrow_assumptions(a,n);if("="===o&&!u||"ne"===o&&u){if(s[0]===e)return is_positive_ast(s[1],c,r);if(s[1]===e)return is_positive_ast(s[0],c,r)}if("<"===o)if(u){if(s[0]===e&&is_positive_ast(s[1],c,r))return!0;if(s[1]===e&&is_negative_ast(s[0],c,!r))return!1}else{if(s[0]===e&&is_negative_ast(s[1],c,!1))return!1;if(s[1]===e&&is_positive_ast(s[0],c,!1))return!0}if("le"===o)if(u){if(s[0]===e&&is_positive_ast(s[1],c,!1))return!0;if(s[1]===e&&is_negative_ast(s[0],c,!1))return!1}else{if(s[0]===e&&is_negative_ast(s[1],c,!r))return!1;if(s[1]===e&&is_positive_ast(s[0],c,r))return!0}if("and"!==o&&"or"!==o)return;if(u)return;return s.length>2&&(i=unflattenRight(i),s=i.slice(1)),simple_assumption_combination(o,is_positive_ast(e,s[0],r,n),is_positive_ast(e,s[1],r,n))}if(Array.isArray(e)){let i;i=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let a=e[0],o=e.slice(1);if("-"===a)return is_negative_ast(o[0],i,r,n);if("+"===a){o.length>2&&(o=(e=unflattenRight(e)).slice(1));let t=is_positive_ast(o[0],i,!1,n),a=is_positive_ast(o[1],i,!1,n),s=is_positive_ast(o[0],i,!0,n),u=is_positive_ast(o[1],i,!0,n);if(r){if(t&&u||s&&a)return!0}else if(t&&a)return!0;if(r){if(!1===s&&!1===u)return!1}else if(!1===t&&!1===u||!1===s&&!1===a)return!1;return}if("*"===a){if(!o.every((e=>!1!==is_nonzero_ast(e,i,n))))return!r;o.length>2&&(o=(e=unflattenRight(e)).slice(1));let t=is_real_ast(o[0],i,n),a=is_real_ast(o[1],i,n);if(void 0===t||void 0===a)return;if(!1===t)return!1===a&&void 0;if(!1===a)return!1;let s=is_positive_ast(o[0],i,!1,n),u=is_positive_ast(o[1],i,!1,n),c=is_positive_ast(o[0],i,!0,n),l=is_positive_ast(o[1],i,!0,n);if(r){if(c&&l||!1===s&&!1===u)return!0;if(!1===c&&u||s&&!1===l)return!1}else{if(s&&u||!1===c&&!1===l)return!0;if(c&&!1===u||!1===s&&l)return!1}return}if("/"===a){if(!is_nonzero_ast(o[1],i,n))return;if(!1===is_nonzero_ast(o[0],i,n))return!r;let e=is_positive_ast(o[1],i,!0,n);if(void 0===e)return;let t=e?r:!r,a=is_positive_ast(o[0],i,t,n);if(void 0===a)return;return!0===a?!0===e:!0!==e}if("^"===a){let e=is_nonzero_ast(o[0],i,n);if(e){if(!1===is_nonzero_ast(o[1],i,n)){if(o[0]===1/0||o[0]===-1/0)return;return!0}}else{if(!is_positive_ast(o[1],i,!0,n))return;if(!1===e)return!r;if(r)return}if(!0!==is_real_ast(o[0],i,n))return;if(!is_positive_ast(o[0],i,r,n)){return!!is_integer_ast(simplify(["/",o[1],2],n),i,n)||void 0}return!!is_real_ast(o[1],i,n)||void 0}if("apply"===a&&!r)return!!(functions.C.nonneg&&functions.C.nonneg.includes(o[0])&&is_complex_ast(o[1],i,n))||(!!(functions.R.nonneg&&functions.R.nonneg.includes(o[0])&&is_real_ast(o[1],i,n))||(!!(functions.nonzeroC.nonneg&&functions.nonzeroC.nonneg.includes(o[0])&&is_nonzero_ast(o[1],i,n)&&is_complex_ast(o[1],i,n))||(!!(functions.nonneg.nonneg&&functions.nonneg.nonneg.includes(o[0])&&is_positive_ast(o[1],i,!1,n))||(!!(functions.pos.nonneg&&functions.pos.nonneg.includes(o[0])&&is_positive_ast(o[1],i,!0,n))||void 0))));if("apply"===a&&r)return!!(functions.C.pos&&functions.C.pos.includes(o[0])&&is_complex_ast(o[1],i,n))||(!!(functions.R.pos&&functions.R.pos.includes(o[0])&&is_real_ast(o[1],i,n))||(!!(functions.nonzeroC.pos&&functions.nonzeroC.pos.includes(o[0])&&is_nonzero_ast(o[1],i,n)&&is_complex_ast(o[1],i,n))||(!!(functions.nonneg.pos&&functions.nonneg.pos.includes(o[0])&&is_positive_ast(o[1],i,!1,n))||(!!(functions.pos.pos&&functions.pos.pos.includes(o[0])&&is_positive_ast(o[1],i,!0,n))||void 0))));if("prime"===a)return;return!1}return!1}function is_negative_ast(e,t,r,n){void 0===r&&(r=!0);var i=is_real_ast(e,t,n);if(!0===i){let i=is_positive_ast(e,t,!r,n);return!1===i||!0!==i&&void 0}return i}function tuples_to_vectors(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("tuple"===r){return["vector"].concat(n.map((function(e,t){return tuples_to_vectors(e)})))}if("apply"===r){if("tuple"===n[1][0]){let e=tuples_to_vectors(n[0]),t=n[1].slice(1);return["apply",e,["tuple"].concat(t.map((function(e,t){return tuples_to_vectors(e)})))]}}else if("gts"===r||"lts"===r||"interval"===r){let e=n[0],t=n[1];if("tuple"!==e[0]||"tuple"!==t[0])throw new Error("Badly formed ast");return[r,["tuple"].concat(e.slice(1).map((function(e,t){return tuples_to_vectors(e)}))),t]}return[r].concat(n.map((function(e,t){return tuples_to_vectors(e)})))}function to_intervals(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("tuple"===r&&2===n.length){let e=["tuple"].concat(n.map((function(e,t){return to_intervals(e)})));return e=["interval",e,["tuple",!1,!1]],e}if("array"===r&&2===n.length){let e=["tuple"].concat(n.map((function(e,t){return to_intervals(e)})));return e=["interval",e,["tuple",!0,!0]],e}if("apply"===r){if("tuple"===n[1][0]){let e=to_intervals(n[0]),t=n[1].slice(1);return["apply",e,["tuple"].concat(t.map((function(e,t){return to_intervals(e)})))]}}else if("gts"===r||"lts"===r||"interval"===r){let e=n[0],t=n[1];if("tuple"!==e[0]||"tuple"!==t[0])throw new Error("Badly formed ast");return[r,["tuple"].concat(e.slice(1).map((function(e,t){return to_intervals(e)}))),t]}return[r].concat(n.map((function(e,t){return to_intervals(e)})))}function altvectors_to_vectors(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("altvector"===r){return["vector"].concat(n.map((function(e,t){return altvectors_to_vectors(e)})))}return[r].concat(n.map((function(e,t){return altvectors_to_vectors(e)})))}function ParseError(e,t){this.name="ParseError",this.message=e||"Error parsing input",this.stack=(new Error).stack,this.location=t}functions.C.nonneg=["abs"],functions.C.nonzero=["exp"],functions.C.R=["abs","arg"],functions.C.C=["abs","arg","exp","sign","cos","cosh","sin","sinh","erf","sqrt","log","ln","log10"],functions.R.pos=["exp"],functions.R.nonneg=["abs","exp","arg"],functions.R.R=["abs","arg","exp","sign","cos","cosh","sin","sinh","erf"],functions.R.Z=["sign"],functions.nonzeroC.pos=["abs"],functions.nonneg.nonneg=["abs","exp","arg","sqrt","erf"],functions.nonzeroC.nonzero=["abs"],functions.nonneg.R=[...new Set(functions.R.R.concat(functions.nonneg.nonneg))],functions.pos.pos=["abs","exp","sqrt","erf"],functions.pos.nonneg=functions.pos.pos,functions.pos.nonzero=["abs","exp","sqrt","erf"],functions.pos.R=functions.nonneg.R.concat(["log","ln","log10"]),ParseError.prototype=Object.create(Error.prototype),ParseError.prototype.constructor=ParseError;class lexer{constructor(e,t="\\s"){this.input="",this.location=0,this.token_rules=[],this.initial_whitespace=new RegExp("^("+t+")+");for(let t of e)this.token_rules.push([new RegExp("^"+t[0])].concat(t.slice(1)))}set_input(e){if("string"!=typeof e)throw new Error("Input must be a string");this.input=e,this.location=0}return_state(){return{input:this.input,location:this.location}}set_state({input:e=null,location:t=0}={}){null!==e&&(this.input=e,this.location=t)}advance({remove_initial_space:e=!0}={}){let t=this.initial_whitespace.exec(this.input);if(t){let r=t[0].length;if(this.input=this.input.slice(r),this.location+=r,!e)return{token_type:"SPACE",token_text:t[0],original_text:t[0]}}if(0===this.input.length)return{token_type:"EOF",token_text:"",original_text:""};for(var r of(t=null,this.token_rules))if(t=r[0].exec(this.input),t){let e=t[0].length;this.input=this.input.slice(e),this.location+=e;break}return null===t?{token_type:"INVALID",token_text:this.input[0],original_text:this.input[0]}:r.length>2?{token_type:r[1],token_text:r[2],original_text:t[0]}:{token_type:r[1],token_text:t[0],original_text:t[0]}}unput(e){if("string"!=typeof e)throw new Error("Input must be a string");this.location-=e.length,this.input=e+this.input}}var is_associative={"+":!0,"*":!0,and:!0,or:!0,union:!0,intersect:!0};function flatten(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if(r=r.map((function(e,t){return flatten(e)})),is_associative[t]){for(var n=[],i=0;i2?n=n.concat(r[i].slice(1)):n.push(r[i]);r=n}return[t].concat(r)}const sci_notat_exp_regex$1="(E[+\\-]?[0-9]+\\s*($|(?=\\,|\\||\\)|\\}|\\])))?",number_rules_sci$1=[["[0-9]+(\\.[0-9]*)?"+sci_notat_exp_regex$1,"NUMBER"],["\\.[0-9]+"+sci_notat_exp_regex$1,"NUMBER"]],number_rules_non_sci$1=[["[0-9]+(\\.[0-9]*)?","NUMBER"],["\\.[0-9]+","NUMBER"]],base_text_rules=[["\\*\\*","^"],["\\*","*"],["\\xB7","*"],["·","*"],["•","*"],["⋅","*"],["×","*"],["/","/"],["-","-"],["֊","-"],["־","-"],["᠆","-"],["‐","-"],["‑","-"],["‒","-"],["–","-"],["—","-"],["―","-"],["⁻","-"],["₋","-"],["−","-"],["⸺","-"],["⸻","-"],["﹘","-"],["﹣","-"],["－","-"],["\\+","+"],["\\^","^"],["‸","^"],["ʌ","^"],["\\|","|"],["\\(","("],["\\)",")"],["\\[","["],["\\]","]"],["\\{","{"],["\\}","}"],["⟨","LANGLE"],["⟩","RANGLE"],["〈","LANGLE"],["〉","RANGLE"],[",",","],[":",":"],["α","VARMULTICHAR","alpha"],["β","VARMULTICHAR","beta"],["ϐ","VARMULTICHAR","beta"],["Γ","VARMULTICHAR","Gamma"],["γ","VARMULTICHAR","gamma"],["Δ","VARMULTICHAR","Delta"],["δ","VARMULTICHAR","delta"],["ε","VARMULTICHAR","epsilon"],["ϵ","VARMULTICHAR","epsilon"],["ζ","VARMULTICHAR","zeta"],["η","VARMULTICHAR","eta"],["Θ","VARMULTICHAR","Theta"],["ϴ","VARMULTICHAR","Theta"],["θ","VARMULTICHAR","theta"],["ᶿ","VARMULTICHAR","theta"],["ϑ","VARMULTICHAR","theta"],["ι","VARMULTICHAR","iota"],["κ","VARMULTICHAR","kappa"],["Λ","VARMULTICHAR","Lambda"],["λ","VARMULTICHAR","lambda"],["μ","VARMULTICHAR","mu"],["µ","VARMULTICHAR","mu"],["ν","VARMULTICHAR","nu"],["Ξ","VARMULTICHAR","Xi"],["ξ","VARMULTICHAR","xi"],["Π","VARMULTICHAR","Pi"],["π","VARMULTICHAR","pi"],["ϖ","VARMULTICHAR","pi"],["ρ","VARMULTICHAR","rho"],["ϱ","VARMULTICHAR","rho"],["Σ","VARMULTICHAR","Sigma"],["σ","VARMULTICHAR","sigma"],["ς","VARMULTICHAR","sigma"],["τ","VARMULTICHAR","tau"],["Υ","VARMULTICHAR","Upsilon"],["υ","VARMULTICHAR","upsilon"],["Φ","VARMULTICHAR","Phi"],["φ","VARMULTICHAR","phi"],["ϕ","VARMULTICHAR","phi"],["Ψ","VARMULTICHAR","Psi"],["ψ","VARMULTICHAR","psi"],["Ω","VARMULTICHAR","Omega"],["ω","VARMULTICHAR","omega"],["oo(?![a-zA-Z0-9])","INFINITY"],["OO(?![a-zA-Z0-9])","INFINITY"],["infty(?![a-zA-Z0-9])","INFINITY"],["infinity(?![a-zA-Z0-9])","INFINITY"],["Infinity(?![a-zA-Z0-9])","INFINITY"],["∞","INFINITY"],["ℯ","VAR","e"],["♠","VARMULTICHAR","spade"],["♡","VARMULTICHAR","heart"],["♢","VARMULTICHAR","diamond"],["♣","VARMULTICHAR","club"],["★","VARMULTICHAR","bigstar"],["◯","VARMULTICHAR","bigcirc"],["◊","VARMULTICHAR","lozenge"],["△","VARMULTICHAR","bigtriangleup"],["▽","VARMULTICHAR","bigtriangledown"],["⧫","VARMULTICHAR","blacklozenge"],["■","VARMULTICHAR","blacksquare"],["▲","VARMULTICHAR","blacktriangle"],["▼","VARMULTICHAR","blacktriangledown"],["◀","VARMULTICHAR","blacktriangleleft"],["▶","VARMULTICHAR","blacktriangleright"],["□","VARMULTICHAR","Box"],["∘","VARMULTICHAR","circ"],["⋆","VARMULTICHAR","star"],["and(?![a-zA-Z0-9])","AND"],["\\&\\&?","AND"],["∧","AND"],["or(?![a-zA-Z0-9])","OR"],["∨","OR"],["not(?![a-zA-Z0-9])","NOT"],["¬","NOT"],["=","="],["᐀","="],["゠","="],["!=","NE"],["≠","NE"],["<=","LE"],["≤","LE"],[">=","GE"],["≥","GE"],["<","<"],[">",">"],["forall(?![a-zA-Z0-9])","FORALL"],["∀","FORALL"],["exists(?![a-zA-Z0-9])","EXISTS"],["∃","EXISTS"],["elementof(?![a-zA-Z0-9])","IN"],["∈","IN"],["notelementof(?![a-zA-Z0-9])","NOTIN"],["∉","NOTIN"],["containselement(?![a-zA-Z0-9])","NI"],["∋","NI"],["notcontainselement(?![a-zA-Z0-9])","NOTNI"],["∌","NOTNI"],["subset(?![a-zA-Z0-9])","SUBSET"],["⊂","SUBSET"],["subseteq(?![a-zA-Z0-9])","SUBSETEQ"],["⊆","SUBSETEQ"],["notsubset(?![a-zA-Z0-9])","NOTSUBSET"],["⊄","NOTSUBSET"],["notsubseteq(?![a-zA-Z0-9])","NOTSUBSETEQ"],["⊈","NOTSUBSETEQ"],["superset(?![a-zA-Z0-9])","SUPERSET"],["⊃","SUPERSET"],["superseteq(?![a-zA-Z0-9])","SUPERSETEQ"],["⊇","SUPERSETEQ"],["notsuperset(?![a-zA-Z0-9])","NOTSUPERSET"],["⊅","NOTSUPERSET"],["notsuperseteq(?![a-zA-Z0-9])","NOTSUPERSETEQ"],["⊉","NOTSUPERSETEQ"],["union(?![a-zA-Z0-9])","UNION"],["∪","UNION"],["intersect(?![a-zA-Z0-9])","INTERSECT"],["∩","INTERSECT"],["perp(?![a-zA-Z0-9])","PERP"],["⟂","PERP"],["parallel(?![a-zA-Z0-9])","PARALLEL"],["∥","PARALLEL"],["angle(?![a-zA-Z0-9])","ANGLE"],["∠","ANGLE"],["int(?![a-zA-Z0-9])","INT"],["∫","INT"],["!","!"],["'","'"],["_","_"],["\\.\\.\\.","LDOTS"],["[a-zA-Z∂][a-zA-Z∂0-9]*","VAR"],["[＿$%]","VAR"]],allowSimplifiedFunctionApplicationDefault$1=!0,splitSymbolsDefault=!0,unsplitSymbolsDefault=["alpha","beta","gamma","Gamma","delta","Delta","epsilon","zeta","eta","theta","Theta","iota","kappa","lambda","Lambda","mu","nu","xi","Xi","pi","Pi","rho","sigma","Sigma","tau","Tau","upsilon","Upsilon","phi","Phi","chi","psi","Psi","omega","Omega","angle","deg"],appliedFunctionSymbolsDefault$1=["abs","exp","log","ln","log10","sign","sqrt","erf","cos","cosh","acos","acosh","arccos","arccosh","cot","coth","acot","acoth","arccot","arccoth","csc","csch","acsc","acsch","arccsc","arccsch","sec","sech","asec","asech","arcsec","arcsech","sin","sinh","asin","asinh","arcsin","arcsinh","tan","tanh","atan","atan2","atanh","arctan","arctanh","arg","conj","re","im","det"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textToAst$4{constructor({allowSimplifiedFunctionApplication:e=allowSimplifiedFunctionApplicationDefault$1,splitSymbols:t=splitSymbolsDefault,unsplitSymbols:r=unsplitSymbolsDefault,appliedFunctionSymbols:n=appliedFunctionSymbolsDefault$1,functionSymbols:i=functionSymbolsDefault$1,operatorSymbols:a=operatorSymbolsDefault$1,units:o=unitsDefault$1,parseLeibnizNotation:s=parseLeibnizNotationDefault$1,parseScientificNotation:u=!0}={}){this.allowSimplifiedFunctionApplication=e,this.splitSymbols=t,this.unsplitSymbols=r,this.appliedFunctionSymbols=n,this.functionSymbols=i,this.operatorSymbols=a,this.units=o,this.parseLeibnizNotation=s;let c=base_text_rules;c=u?[...number_rules_sci$1,...c]:[...number_rules_non_sci$1,...c],this.lexer=new lexer(c)}advance(e){if(this.token=this.lexer.advance(e),"INVALID"===this.token.token_type)throw new ParseError("Invalid symbol '"+this.token.original_text+"'",this.lexer.location)}return_state(){return{lexer_state:this.lexer.return_state(),token:Object.assign({},this.token)}}set_state(e){this.lexer.set_state(e.lexer_state),this.token=Object.assign({},e.token)}convert(e){this.lexer.set_input(e),this.advance();var t=this.statement_list();if("EOF"!==this.token.token_type)throw new ParseError("Invalid location of '"+this.token.original_text+"'",this.lexer.location);return flatten(t)}statement_list(){for(var e=[this.statement()];","===this.token.token_type;)this.advance(),e.push(this.statement());return e=e.length>1?["list"].concat(e):e[0]}statement({inside_absolute_value:e=0}={}){if("LDOTS"===this.token.token_type)return this.advance(),["ldots"];var t;try{t=this.return_state();let r=this.statement_a({inside_absolute_value:e});return":"!==this.token.token_type?r:(this.advance(),[":",r,this.statement_a()])}catch(e){try{this.set_state(t);let r=this.statement_a({parse_absolute_value:!1});if("|"!==this.token.token_type)throw e;return this.advance(),["|",r,this.statement_a({parse_absolute_value:!1})]}catch(t){throw e}}}statement_a({inside_absolute_value:e=0,parse_absolute_value:t=!0}={}){for(var r=this.statement_b({inside_absolute_value:e,parse_absolute_value:t});"OR"===this.token.token_type;){let n=this.token.token_type.toLowerCase();this.advance(),r=[n,r,this.statement_b({inside_absolute_value:e,parse_absolute_value:t})]}return r}statement_b(e){for(var t=this.relation(e);"AND"===this.token.token_type;){let r=this.token.token_type.toLowerCase();this.advance(),t=[r,t,this.relation(e)]}return t}relation(e){if("NOT"===this.token.token_type||"!"===this.token.token_type)return this.advance(),["not",this.relation(e)];if("FORALL"===this.token.token_type||"EXISTS"===this.token.token_type){let t=this.token.token_type.toLowerCase();return this.advance(),[t,this.relation(e)]}for(var t=this.expression(e);"="===this.token.token_type||"NE"===this.token.token_type||"<"===this.token.token_type||">"===this.token.token_type||"LE"===this.token.token_type||"GE"===this.token.token_type||"IN"===this.token.token_type||"NOTIN"===this.token.token_type||"NI"===this.token.token_type||"NOTNI"===this.token.token_type||"SUBSET"===this.token.token_type||"NOTSUBSET"===this.token.token_type||"SUBSETEQ"===this.token.token_type||"NOTSUBSETEQ"===this.token.token_type||"SUPERSET"===this.token.token_type||"NOTSUPERSET"===this.token.token_type||"SUPERSETEQ"===this.token.token_type||"NOTSUPERSETEQ"===this.token.token_type;){let r=this.token.token_type.toLowerCase(),n=0;"<"===this.token.token_type||"LE"===this.token.token_type?n=-1:">"!==this.token.token_type&&"GE"!==this.token.token_type||(n=1),this.advance();let i=this.expression(e);if(-1===n)if("<"===this.token.token_type||"LE"===this.token.token_type){let n=["tuple"];"<"===r?n.push(!0):n.push(!1);let a=["tuple",t,i];for(;"<"===this.token.token_type||"LE"===this.token.token_type;)"<"===this.token.token_type?n.push(!0):n.push(!1),this.advance(),a.push(this.expression(e));t=["lts",a,n]}else t=[r,t,i];else if(1===n)if(">"===this.token.token_type||"GE"===this.token.token_type){let n=["tuple"];">"===r?n.push(!0):n.push(!1);let a=["tuple",t,i];for(;">"===this.token.token_type||"GE"===this.token.token_type;)">"===this.token.token_type?n.push(!0):n.push(!1),this.advance(),a.push(this.expression(e));t=["gts",a,n]}else t=[r,t,i];else if("="===r)for(t=["=",t,i];"="===this.token.token_type;)this.advance(),t.push(this.expression(e));else t=[r,t,i]}return t}expression(e){let t=!1;"+"===this.token.token_type&&(t=!0,this.advance());let r=!1;"-"===this.token.token_type&&(r=!0,this.advance());var n=this.term(e);if(r||t){if(!1===n)return(t?"+":"")+(r?"-":"");if("string"==typeof n&&[...n].every((e=>["+","-"].includes(e))))return(t?"+":"")+(r?"-":"")+n}for(!1===n&&(n="＿"),r&&(n=n>0?-n:["-",n]),t&&(n=["+",n]);["+","-","UNION","INTERSECT","PERP","PARALLEL"].includes(this.token.token_type);){let t=this.token.token_type.toLowerCase(),r=!1,i=!1;"-"===this.token.token_type?(t="+",r=!0,this.advance()):(this.advance(),"+"===t&&"-"===this.token.token_type&&(r=!0,i=!0,this.advance()));let a=this.term(e);if("+"===t){if(!1===a&&("number"==typeof n||"string"==typeof n))return i?n+"+-":r?n+"-":n+"+";if("string"==typeof a&&[...a].every((e=>["+","-"].includes(e)))&&("number"==typeof n||"string"==typeof n))return i?n+"+-"+a:r?n+"-"+a:n+"+"+a}!1===a&&(a="＿"),r&&(a=a>0?-a:["-",a]),n=[t,n,a]}return n}term(e){var t=this.factor(e),r=!1;do{if(r=!1,"*"===this.token.token_type){this.advance(),!1===t&&(t="＿");let n=this.factor(e);!1===n&&(n="＿"),t=["*",t,n],r=!0}else if("/"===this.token.token_type){this.advance(),!1===t&&(t="＿");let n=this.factor(e);!1===n&&(n="＿"),t=["/",t,n],r=!0}else{let n=Object.assign({},e);n.allow_absolute_value_closing=!0;let i=this.nonMinusFactor(n);!1!==i&&(!1===t&&(t="＿"),t=["*",t,i],r=!0)}}while(r);return this.convert_units_in_term(flatten(t))}convert_units_in_term(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("*"===t){let t=r.length;for(let[e,n]of r.entries()){let i=this.units[n];if(i){if(i.prefix&&e0){let a,o=n;return i.substitute&&(o=i.substitute),a=1===e?["unit",r[0],o]:["unit",["*",...r.slice(0,e)],o],e===t-1?a:this.convert_units_in_term(["*",a,...r.slice(e+1)])}}}return e}return"/"===t?["/",this.convert_units_in_term(r[0]),this.convert_units_in_term(r[1])]:e}factor(e){if("+"===this.token.token_text){this.advance();let t=this.factor(e);return!1===t?"+":"string"==typeof t&&[...t].every((e=>["+","-"].includes(e)))?"+"+t:["+",t]}if("-"===this.token.token_type){this.advance();let t=this.factor(e);return t>0?-t:!1===t?"-":"string"==typeof t&&[...t].every((e=>["+","-"].includes(e)))?"-"+t:["-",t]}let t=this.nonMinusFactor(e);return!1===t&&"PERP"===this.token.token_type&&(t="perp",this.advance()),t}nonMinusFactor(e){for(var t=this.baseFactor(e);"^"===this.token.token_type||"!"===this.token.token_type||"'"===this.token.token_type;)if(!1===t&&(t="＿"),"^"===this.token.token_type){this.advance(),t=["^",t,this.get_subsuperscript(e)]}else"!"===this.token.token_type?(t=["apply","factorial",t],this.advance()):(t=["prime",t],this.advance());return t}get_subsuperscript({parse_absolute_value:e}){if(["+","-","PERP"].includes(this.token.token_type)){let e=this.token.token_type.toLowerCase();return this.advance(),e}{let t=this.baseFactor({parse_absolute_value:e,in_subsuperscript_with_no_delimiters:!0});return!1===t&&(t="＿"),t}}baseFactor({inside_absolute_value:e=0,parse_absolute_value:t=!0,allow_absolute_value_closing:r=!1,in_subsuperscript_with_no_delimiters:n=!1}={}){var i=!1;if("NUMBER"===this.token.token_type)i=parseFloat(this.token.token_text),this.advance();else if("INFINITY"===this.token.token_type)i=1/0,this.advance();else if("VAR"===this.token.token_type||"VARMULTICHAR"===this.token.token_type){if(i=this.token.token_text,this.appliedFunctionSymbols.includes(i)||this.functionSymbols.includes(i)){let e=!1;if(this.appliedFunctionSymbols.includes(i)&&(e=!0),this.advance(),"_"===this.token.token_type){this.advance();let e=this.get_subsuperscript({parse_absolute_value:t});i="log"===i&&10===e?"log10":["_",i,e]}if(n)e&&(i=["apply",i,"＿"]);else{for(;"'"===this.token.token_type;)i=["prime",i],this.advance();for(;"^"===this.token.token_type;){this.advance(),i=["^",i,this.get_subsuperscript({parse_absolute_value:t})]}if("("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),"list"===e[0]&&(e[0]="tuple"),i=["apply",i,e]}else if(e){if(!this.allowSimplifiedFunctionApplication)throw new ParseError("Expecting ( after function",this.lexer.location);let e=this.factor({parse_absolute_value:t});!1===e&&(e="＿"),i=["apply",i,e]}}return i}if(this.operatorSymbols.includes(i))if(this.advance(),"("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),i="list"===e[0]?[i,...e.slice(1)]:[i,e]}else{let e=this.factor({parse_absolute_value:t});!1===e&&(e="＿"),i=[i,e]}else{if(this.parseLeibnizNotation){let e=this.return_state(),t=this.leibniz_notation();if(t)return t;this.set_state(e)}let n=this.splitSymbols;if(n&&("VARMULTICHAR"===this.token.token_type||this.unsplitSymbols.includes(i)||1===i.length||i.match(/[\d]/g))&&(n=!1),n){for(let e=i.length-1;e>=0;e--)this.lexer.unput(" "),this.lexer.unput(i[e]);return this.advance(),this.baseFactor({inside_absolute_value:e,parse_absolute_value:t,allow_absolute_value_closing:r})}this.advance()}}else if("("===this.token.token_type||"["===this.token.token_type||"{"===this.token.token_type||"LANGLE"===this.token.token_type){let e,t,r=this.token.token_type;"("===this.token.token_type?(e=")",t="]"):"["===this.token.token_type?(e="]",t=")"):"{"===this.token.token_type?(e="}",t=null):(e="RANGLE",t=null),this.advance();let n=1;if("list"===(i=this.statement_list())[0]&&(n=i.length-1),this.token.token_type!==e){if(2!==n||null===t)throw new ParseError("Expecting "+e,this.lexer.location);if(this.token.token_type!==t)throw new ParseError("Expecting ) or ]",this.lexer.location);let a;i[0]="tuple",a="("===r?["tuple",!1,!0]:["tuple",!0,!1],(i=["interval",i]).push(a)}else n>=2?i[0]="("===r?"tuple":"["===r?"array":"{"===r?"set":"altvector":"{"===r&&(i=("|"===i[0]||i[0],["set",i]));this.advance()}else if("|"!==this.token.token_type||!t||0!==e&&r){if("ANGLE"===this.token.token_type)if(this.advance(),"("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),"list"===e[0]?i=["angle",...e.slice(1)]:"*"===e[0]&&(i=["angle",e])}else{let e=[],r=this.nonMinusFactor({parse_absolute_value:t});for(;!1!==r;)e.push(r),r=this.nonMinusFactor({parse_absolute_value:t});i=0===e.length?"angle":["angle",...e]}else if("INT"===this.token.token_type){this.advance();let e="int";if("_"===this.token.token_type){this.advance(),e=["_",e,this.get_subsuperscript({parse_absolute_value:t})]}if("^"===this.token.token_type){this.advance(),e=["^",e,this.get_subsuperscript({parse_absolute_value:t})]}let r=flatten(this.term({parse_absolute_value:t}));if(Array.isArray(r)&&"*"===r[0]){let e=[];for(let t=0;t2&&(this.lexer.unput(this.token.token_text.slice(2)),this.token.token_text=this.token.token_text.slice(0,2));let s=this.token.token_text;if(2===s.length){if(!/[a-zA-Z]/.exec(s[1]))return!1;i.push(s[1])}else{if(this.advance(),("VAR"!==this.token.token_type||this.token.token_text.includes("∂"))&&"VARMULTICHAR"!==this.token.token_type)return!1;i.push(this.token.token_text)}let u=1,c=!1;if(this.advance({remove_initial_space:!1}),"SPACE"===this.token.token_type&&(c=!0,this.advance()),"^"===this.token.token_type){if(this.advance(),"NUMBER"!==this.token.token_type)return!1;if(u=parseFloat(this.token.token_text),!Number.isInteger(u))return!1;c=!1,this.advance({remove_initial_space:!1}),"SPACE"===this.token.token_type&&(c=!0,this.advance())}if(a.push(u),o+=u,o>r)return!1;if(o===r){if(!c&&("VAR"===this.token.token_type||"VARMULTICHAR"===this.token.token_type))return!1;"SPACE"===this.token.token_type&&this.advance();let o="derivative_leibniz";"∂"===t&&(o="partial_"+o),e=[o],1===r?e.push(n):e.push(["tuple",n,r]);let s=[];for(let e=0;et[e+1]));if(t.length!==n||i.length!==n)return subtree;let a=["+",...t.map(((e,t)=>["*",e,i[t]]))];r.push(a)}s.push(r)}return{success:!0,newMatrix:["matrix",["tuple",r,i],s]}}function a(e,t){let r=e[1][1],n=e[1][2],i=e[2],a=["tuple"];for(let e=0;e=0;t--){let n=r[t][0];if("matrix"===n){let n=i(r[t],e);if(!n.success)break;e=n.newMatrix,r.pop()}else{if(["tuple","list","vector","altvector","interval","set","array"].includes(n))break;1!==r[t]&&(e=a(e,r[t])),r.pop()}}for(;n.length>0;){let t=n[0][0];if("matrix"===t){let t=i(e,n[0]);if(!t.success)break;e=t.newMatrix,n.splice(0,1)}else{if(["tuple","list","vector","altvector","interval","set","array"].includes(t))break;1!==n[0]&&(e=a(e,n[0])),n.splice(0,1)}}return r.length>0||n.length>0?["*",...r,e,...n]:e}return e})),(t||r)&&(o=["*",["matrix",["tuple","m","n"],"matrixData"],"b"],s={variables:{n:Number.isInteger,m:Number.isInteger,matrixData:!0,b:!0}},n=transform(n,(function(e){let n=match$2(e,o,s);if(n){let i,a=n.m,o=n.n,s=n.b,u=n.matrixData,c=[];t&&(c.push("vector"),c.push("altvector")),r&&c.push("tuple");let l=[];if(c.includes(s[0]))i=s;else{if(!Array.isArray(s)||"*"!==s[0]||!c.includes(s[1][0]))return e;i=s[1],l=s.slice(2)}let f=i.slice(1);if(f.length!==o)return e;let p=[i[0]];for(let e=0;e["*",e,f[t]]))];p.push(t)}return l.length>0?["*",p,...l]:p}return e}))),n}function perform_vector_scalar_multiplications(e,t=!0){var r=get_tree(e);let n=function(e,t){let r=["*","a",[t,"vectorData"],"b"],n={allow_implicit_identities:["a","b"]};return e=transform(e,(function(e){let i=match$2(e,r,n);if(i){if(1===i.a&&1===i.b)return e;let r=i.vectorData;r=Array.isArray(r)&&r[0]===t?r.slice(1):[r];let n=[],a=[];Array.isArray(i.a)&&"*"===i.a[0]?n.push(...i.a.slice(1)):n.push(i.a),Array.isArray(i.b)&&"*"===i.b[0]?a.push(...i.b.slice(1)):a.push(i.b);for(let e=n.length-1;e>=0;e--){let t=n[e][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t))break;1!==n[e]&&(r=r.map((t=>["*",t,n[e]]))),n.pop()}for(;a.length>0;){let e=a[0][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(e))break;1!==a[0]&&(r=r.map((e=>["*",e,a[0]]))),a.splice(0,1)}let o=[t,...r];return n.length>0||a.length>0?["*",...n,o,...a]:o}return e})),e};return r=n(r,"vector"),r=n(r,"altvector"),t&&(r=n(r,"tuple")),r}function perform_matrix_scalar_multiplications(e){var t=get_tree(e);let r=["*","a",["matrix","size","matrixData"],"b"],n={allow_implicit_identities:["a","b"]};return t=transform(t,(function(e){let t=match$2(e,r,n);if(t){if(1===t.a&&1===t.b)return e;let r=t.matrixData,n=[],i=[];Array.isArray(t.a)&&"*"===t.a[0]?n.push(...t.a.slice(1)):n.push(t.a),Array.isArray(t.b)&&"*"===t.b[0]?i.push(...t.b.slice(1)):i.push(t.b);for(let e=n.length-1;e>=0;e--){let t=n[e][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t))break;1!==n[e]&&(r=r.map((t=>"tuple"===t?t:t.map((t=>"tuple"===t?t:["*",t,n[e]]))))),n.pop()}for(;i.length>0;){let e=i[0][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(e))break;1!==i[0]&&(r=r.map((e=>"tuple"===e?e:e.map((e=>"tuple"===e?e:["*",e,i[0]]))))),i.splice(0,1)}let a=["matrix",t.size,r];return n.length>0||i.length>0?["*",...n,a,...i]:a}return e})),t}function expand_relations(e){var t=get_tree(e);return transform(t,expand_relations_transform)}function expand_relations_transform(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if("="===t){if(r.length<=2)return e;let t=["and"];for(let e=0;e":"lts"===t?"le":"ge",i.push([a,e[r],e[r+1]])}let a=["and",i[0],i[1]];for(let e=2;e",n,c]),s[2]?a?f.push([">",n,l]):f.push(["le",n,l]):a?f.push(["ge",n,l]):f.push(["<",n,l]),u=a?["or"].concat(f):["and"].concat(f),u}if("subset"===t||"notsubset"===t||"superset"===t||"notsuperset"===t){let n,i,a=!1;if("notsubset"!==t&&"notsuperset"!==t||(a=!0),"subset"===t||"notsubset"===t?(n=r[0],i=r[1]):(n=r[1],i=r[0]),n=to_intervals(n),i=to_intervals(i),"interval"!==n[0]||"interval"!==i[0])return e;let o=n[1],s=n[2],u=i[1],c=i[2];if("tuple"!==o[0]||"tuple"!==s[0]||"tuple"!==u[0]||"tuple"!==c[0])throw new Error("Badly formed ast");let l,f=o[1],p=o[2],m=u[1],d=u[2],h=[];return s[1]&&!c[1]?a?h.push(["le",f,m]):h.push([">",f,m]):a?h.push(["<",f,m]):h.push(["ge",f,m]),s[2]&&!c[2]?a?h.push(["ge",p,d]):h.push(["<",p,d]):a?h.push([">",p,d]):h.push(["le",p,d]),l=a?["or"].concat(h):["and"].concat(h),l}return e}function substitute(e,t){var r=get_tree(e),n={};for(let e in t)n[e]=get_tree(t[e]);return substitute$1(r,n)}function substitute_component(e,t,r){let n=get_tree(e);if(get_tree(r),"number"==typeof t)t=[t];else if(!Array.isArray(t))throw Error("Invalid substitute_component: "+t);let i=["list","tuple","vector","altvector","array"];return function e(t,n,a){if(0===n.length)return r;if(!Array.isArray(t))throw Error("Invalid substitute_component: expected list, tuple, vector, or array");let o=t[0],s=t.slice(1);if(!i.includes(o))throw Error("Invalid substitute_component: expected list, tuple, vector, or array");let u=n[0];if(u<0||u>s.length-1)throw Error("Invalid substitute_component: component out of range");let c=n.slice(1),l=e(s[u],c);return[o,...s.slice(0,u),l,...s.slice(u+1)]}(n,t)}function get_component(e,t){let r=get_tree(e);if("number"==typeof t)t=[t];else if(!Array.isArray(t))throw Error("Invalid get_component: "+t);let n=["list","tuple","vector","altvector","array"];return function e(t,r){if(0===r.length)return t;if(!Array.isArray(t))throw Error("Invalid get_component: expected list, tuple, vector, or array");let i=t[0],a=t.slice(1);if(!n.includes(i))throw Error("Invalid get_component: expected list, tuple, vector, or array");let o=r[0];if(o<0||o>a.length-1)throw Error("Invalid get_component: component out of range");let s=r.slice(1);return e(a[o],s)}(r,t)}var transformation=Object.freeze({__proto__:null,expand:expand,expand_relations:expand_relations,substitute:substitute,substitute_component:substitute_component,get_component:get_component,perform_vector_scalar_multiplications:perform_vector_scalar_multiplications,perform_matrix_scalar_multiplications:perform_matrix_scalar_multiplications,perform_matrix_multiplications:perform_matrix_multiplications});function clean(e){return flatten$5(get_tree(e))}function evalf(e,t){return parseFloat(math$1.format(e,{notation:"exponential",precision:t}))}function collapse_unary_minus(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if(n=n.map((e=>collapse_unary_minus(e))),"-"===r){if("number"==typeof n[0])return-n[0];if(Array.isArray(n[0])&&"*"===n[0][0]&&"number"==typeof n[0][1])return["*",-n[0][1]].concat(n[0].slice(2));if(Array.isArray(n[0])&&"/"===n[0][0]){if("number"==typeof n[0][1])return["/",-n[0][1],n[0][2]];if(Array.isArray(n[0][1])&&"*"===n[0][1][0]&&"number"==typeof n[0][1][1])return["/",["*",-n[0][1][1]].concat(n[0][1].slice(2)),n[0][2]]}}return[r].concat(n)}function simplify(e,t,r){var n=get_tree(e);return contains_blank(n)?n:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),n=evaluate_numbers(n,{assumptions:t,max_digits:r,evaluate_functions:!0}),Array.isArray(n)?n=collect_like_terms_factors(n=perform_vector_matrix_additions_scalar_multiplications(n=simplify_logical(n,t)),t,r):n)}function simplify_logical(e,t){var r=get_tree(e);if(contains_blank(r))return r;void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),r=evaluate_numbers(r,{assumptions:t}),r=unflattenRight(r);var n=[];return n.push([["not",["not","a"]],"a"]),n.push([["not",["and","a","b"]],["or",["not","a"],["not","b"]]]),n.push([["not",["or","a","b"]],["and",["not","a"],["not","b"]]]),n.push([["not",["=","a","b"]],["ne","a","b"]]),n.push([["not",["ne","a","b"]],["=","a","b"]]),n.push([["not",["<","a","b"]],["le","b","a"]]),n.push([["not",["le","a","b"]],["not",["le","a","b"]]]),n.push([["not",["in","a","b"]],["notin","a","b"]]),n.push([["not",["subset","a","b"]],["notsubset","a","b"]]),r=flatten$5(r=applyAllTransformations(r,n,20))}function perform_vector_matrix_additions_scalar_multiplications(e,t=!0){var r=get_tree(e);r=perform_vector_scalar_multiplications(r=perform_matrix_scalar_multiplications(r),t);let n=["+","a","b"];return r=transform(r,(function(e){let r=match$2(e,n,{allow_permutations:!0});if(r){let n=["vector","altvector"];t&&n.push("tuple");let i={},a={},o=[];if(n.includes(r.a[0])){let e=r.a.length-1;i[e]||(i[e]=[]),i[e].push(r.a)}else if("matrix"===r.a[0]){let e=r.a[1].slice(1).toString();a[e]||(a[e]=[]),a[e].push(r.a)}else o.push(r.a);if(n.includes(r.b[0])){let e=r.b.length-1;i[e]||(i[e]=[]),i[e].push(r.b)}else if("matrix"===r.b[0]){let e=r.b[1].slice(1).toString();a[e]||(a[e]=[]),a[e].push(r.b)}else if("+"===r.b[0])for(let e of r.b.slice(1))if(n.includes(e[0])){let t=e.length-1;i[t]||(i[t]=[]),i[t].push(e)}else if("matrix"===e[0]){let t=e[1].slice(1).toString();a[t]||(a[t]=[]),a[t].push(e)}else o.push(e);else o.push(r.b);if(Object.values(i).every((e=>e.length<2))&&Object.values(a).every((e=>e.length<2)))return e;let s=o;for(let e in i)if(i[e].length<2)s.push(...i[e]);else{let t,r=i[e].some((e=>"vector"===e[0])),n=i[e].some((e=>"tuple"===e[0])),a=i[e].some((e=>"altvector"===e[0]));t=r||n&&a?["vector"]:a?["altvector"]:["tuple"];for(let r=0;re[r+1]))]);s.push(t)}for(let e in a)if(a[e].length<2)s.push(...a[e]);else{let[t,r]=e.split(",").map(Number),n=["tuple"];for(let i=0;ie[2][i+1][n+1]))]);n.push(t)}let i=["matrix",["tuple",t,r],n];s.push(i)}return 1===s.length?s[0]:["+",...s]}return e})),r}function contains_decimal_number(e){return"string"!=typeof e&&("number"==typeof e?!(!Number.isFinite(e)||Number.isInteger(e)):!!Array.isArray(e)&&e.slice(1).some((e=>contains_decimal_number(e))))}function contains_only_numbers(e,{include_number_symbols:t=!1,evaluate_functions:r=!1}={}){if("string"==typeof e){if(t){if("e"===e&&math$1.define_e)return!0;if("pi"===e&&math$1.define_pi)return!0}return!("i"!==e||!math$1.define_i)}return"number"==typeof e||!!Array.isArray(e)&&(r&&"apply"===e[0]?e.slice(2).every((e=>contains_only_numbers(e,{include_number_symbols:t}))):e.slice(1).every((e=>contains_only_numbers(e,{include_number_symbols:t}))))}function try_evaluate_sum_of_numbers(e,t,r){if("number"==typeof e){if(0===e)return t;if("number"==typeof t)return e+t;if(Array.isArray(t)&&"+"===t[0]&&"number"==typeof t[1])return["+",e+t[1],t[2]];if(!r&&Array.isArray(t)&&"+"===t[0]&&"number"==typeof t[2])return["+",e+t[2],t[1]]}return"number"==typeof t&&0===t?e:null}function try_evaluate_negate_number(e){if("number"==typeof e)return-e;if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1])return["*",-e[1]].concat(e.slice(2));if(Array.isArray(e)&&"/"===e[0]){if("number"==typeof e[1])return["/",-e[1],e[2]];if(Array.isArray(e[1])&&"*"===e[1][0]&&"number"==typeof e[1][1])return["/",["*",-e[1][1]].concat(e[1].slice(2)),e[2]]}return null}function try_evaluate_product_of_numbers(e,t){if("number"==typeof e){if(isNaN(e))return NaN;if("number"==typeof t)return e*t;if(!isFinite(e))return e===1/0&&is_negative_ast(t)||e===-1/0&&is_positive_ast(t)?-1/0:!1===is_nonzero_ast(t)?NaN:1/0;if(0===e)return 0;if(1===e)return t;if(-1===e)return["-",t];if(Array.isArray(t)&&"*"===t[0]&&"number"==typeof t[1])return e*=t[1],t=t[2],1===e?t:-1===e?["-",t]:["*",e,t]}if("number"==typeof t){if(isNaN(t))return NaN;if(!isFinite(t))return t===1/0&&is_negative_ast(e)||t===-1/0&&is_positive_ast(e)?-1/0:!1===is_nonzero_ast(e)?NaN:1/0;if(0===t)return 0;if(1===t)return e;if(-1===t)return["-",e];if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1])return t*=e[1],e=e[2],1===t?e:-1===t?["-",e]:["*",e,t]}if(math$1.define_i&&"i"===e){if("i"===t)return-1;if(Array.isArray(t)&&"*"===t[0]&&"i"===t[1])return["-",t[2]]}else if(math$1.define_i&&"i"===t&&Array.isArray(e)&&"*"===e[0]&&"i"===e[1])return["-",e[2]];return null}function try_evaluate_quotient_of_numbers(e,t,r,n){if("number"==typeof e){if(0===e){let e=is_nonzero_ast(t,r);if(e)return 0;if(!1===e)return NaN}if("number"==typeof t){let r=e/t;if(n===1/0||math$1.round(r,n)===r)return r;if(t<0)return["/",-e,-t]}if(Array.isArray(t)&&"*"===t[0]&&"number"==typeof t[1]){let r=e/t[1];if(n===1/0||math$1.round(r,n)===r)return["/",r,t[2]]}}else if("number"==typeof t){if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1]){let r=e[1]/t;if(n===1/0||math$1.round(r,n)===r)return 1===r?e[2]:["*",r,e[2]];if(t<0)return["/",["*",-e[1],e[2]],-t]}let r=1/t;if(n===1/0||math$1.round(r,n)===r)return["*",r,e];if(t<0)return Array.isArray(e)&&"-"===e[0]?["/",e[1],-t]:["-",["/",e,-t]]}return null}function evaluate_numbers_sub(e,t,r,n,i,a){if(void 0===e)return e;if("number"==typeof e)return a>0&&math$1.abs(e)0&&math$1.abs(t)evaluate_numbers_sub(e,t,r,n,i,a)));if("+"===s){let e=u[0],t=u[1];if(void 0===t)return e;let r=try_evaluate_sum_of_numbers(e,t,n);if(null!==r)return r;if("unit"===e[0]&&"unit"===t[0]){let r=get_unit_of_tree(e),i=get_unit_of_tree(t);if(r&&r===i){let i=try_evaluate_sum_of_numbers(remove_units(e,!1),remove_units(t,!1),n);if(null!==i)return add_unit(i,r)}}return[s].concat(u)}if("-"===s){let e=try_evaluate_negate_number(u[0]);if(null!==e)return e;if("unit"===u[0][0]){let e=get_unit_of_tree(u[0]);if(e){let t=try_evaluate_negate_number(remove_units(u[0],!1));if(null!==t)return add_unit(t,e)}}return[s].concat(u)}if("*"===s){let e=u[0],t=u[1];if(void 0===t)return e;let r=try_evaluate_product_of_numbers(e,t);if(null!==r)return r;if("unit"===e[0]&&"unit"!==t[0]){let r=get_unit_of_tree(e);if(r){let n=try_evaluate_product_of_numbers(remove_units(e,!1),t);if(null!==n)return add_unit(n,r)}}if("unit"!==e[0]&&"unit"===t[0]){let r=get_unit_of_tree(t);if(r){let n=try_evaluate_product_of_numbers(e,remove_units(t,!1));if(null!==n)return add_unit(n,r)}}return[s].concat(u)}if("/"===s){let e=u[0],n=u[1],i=try_evaluate_quotient_of_numbers(e,n,t,r);if(null!==i)return i;if("unit"===e[0]&&"unit"!==n[0]){let i=get_unit_of_tree(e);if(i){let a=try_evaluate_quotient_of_numbers(remove_units(e,!1),n,t,r);if(null!==a)return add_unit(a,i)}}return[s].concat(u)}if("^"===s){let e=u[0],n=u[1];if("number"==typeof n)if(0===n){if(!math$1.pow_strict)return 1;let r=is_nonzero_ast(e,t);if(r&&e!==1/0&&e!==-1/0)return 1;if(!1===r)return NaN}else{if(1===n)return e;if("number"==typeof e){let t=math$1.pow(e,n);if(r===1/0||math$1.round(t,r)===t)return t}}else if(1===e)return 1;return[s].concat(u)}return[s].concat(u)}function evaluate_numbers(e,{assumptions:t,max_digits:r,skip_ordering:n=!1,evaluate_functions:i=!1,set_small_zero:a=0}={}){(void 0===r||!Number.isInteger(r)&&r!==1/0)&&(r=0),!0===a&&(a=1e-14);var o,s=get_tree(e);return contains_blank(s)?s:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),n?o=evaluate_numbers_sub(s=unflattenRight(flatten$5(s)),t,r,n,i,a):(s=move_units_outside_products(s),s=unflattenRight(default_order(flatten$5(s))),o=default_order(evaluate_numbers_sub(s,t,r,n,i,a)),o=default_order(evaluate_numbers_sub(unflattenRight(o),t,r,n,i,a))),flatten$5(o=set_negative_zeros_to_zero(o)))}function set_negative_zeros_to_zero(e){return 0===e?0:Array.isArray(e)?[e[0],...e.slice(1).map(set_negative_zeros_to_zero)]:e}function collect_like_terms_factors(e,t,r){function n(e){return"number"==typeof e||!(!Array.isArray(e)||"-"!==e[0]||"number"!=typeof e[1])}function i(e){return"number"==typeof e&&e<0||!(!Array.isArray(e)||"-"!==e[0]||"number"!=typeof e[1])}function a(e){if("number"==typeof e)return!0;if(Array.isArray(e)&&"-"===e[0]&&"number"==typeof e[1])return!0;var t=evaluate_to_constant(e,{remove_units_first:!1});return!!Number.isFinite(t)}var o=get_tree(e);if(contains_blank(o))return o;void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),o=evaluate_numbers(o,{assumptions:t,max_digits:r,evaluate_functions:!0});var s=[];s.push([["/","x",["^","y","a"]],["*","x",["^","y",["-","a"]]],{evaluate_numbers:!0,max_digits:r}]),s.push([["/","x",["apply","exp","a"]],["*","x",["apply","exp",["-","a"]]],{evaluate_numbers:!0,max_digits:r,variables:{x:!0,a:!0}}]),s.push([["/","x","y"],["*","x",["^","y",["-",1]]],{evaluate_numbers:!0,max_digits:r}]),o=applyAllTransformations(o,s,40),s=[];for(let e in all_units){all_units[e].prefix?(s.push([["+",["unit",e,"x"],["unit",e,"y"]],["unit",e,["+","x","y"]],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["unit",e,"x"],["-",["unit",e,"y"]]],["unit",e,["+","x",["-","y"]]],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}])):(s.push([["+",["unit","x",e],["unit","y",e]],["unit",["+","x","y"],e],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["unit","x",e],["-",["unit","y",e]]],["unit",["+","x",["-","y"]],e],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]))}return s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:e=>is_nonzero_ast(e,t),n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:!0,n:e=>n(e)&&is_positive_ast(e,t),m:e=>n(e)&&is_positive_ast(e,t)},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:!0,n:e=>n(e)&&is_negative_ast(e,t),m:e=>n(e)&&is_negative_ast(e,t)},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["apply","exp","n"],["apply","exp","m"]],["apply","exp",["+","n","m"]],{variables:{n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n","x"],["*","m","x"]],["*",["+","n","m"],"x"],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n1","x"],["*",["/","n2","m2"],"x"]],["*",["+","n1",["/","n2","m2"]],"x"],{variables:{x:!0,n1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n1","x"],["*",["-",["/","n2","m2"]],"x"]],["*",["+","n1",["-",["/","n2","m2"]]],"x"],{variables:{x:!0,n1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*",["/","n1","m1"],"x"],["*",["/","n2","m2"],"x"]],["*",["+",["/","n1","m1"],["/","n2","m2"]],"x"],{variables:{x:!0,n1:n,m1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m1","m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*",["/","n1","m1"],"x"],["*",["-",["/","n2","m2"]],"x"]],["*",["+",["/","n1","m1"],["-",["/","n2","m2"]]],"x"],{variables:{x:!0,n1:n,m1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m1","m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n","x"],["-",["*","m","x"]]],["*",["+","n",["-","m"]],"x"],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["^",["*","x","y"],"a"],["*",["^","x","a"],["^","y","a"]],{allow_permutations:!0}]),s.push([["^",["^","x","n"],"m"],["^","x",["*","n","m"]],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_permutations:!0}]),s.push([["-",["+","a","b"]],["+",["-","a"],["-","b"]]]),s.push([["*","x","y"],["*","x","y"],{variables:{x:a,y:a},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),o=applyAllTransformations(o,s,40),(s=[]).push([["*","x",["^","y",["-","a"]]],["/","x",["^","y","a"]],{allow_extended_match:!0,allow_permutations:!0,evaluate_numbers:!0,max_digits:r,max_group:1}]),s.push([["*","x",["apply","exp",["-","a"]]],["/","x",["apply","exp","a"]],{allow_extended_match:!0,allow_permutations:!0,evaluate_numbers:!0,max_digits:r,max_group:1,variables:{x:!0,a:!0}}]),s.push([["*","x",["^","y","n"]],["/","x",["^","y",["-","n"]]],{variables:{x:!0,y:!0,n:i},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*","x",["apply","exp","n"]],["/","x",["apply","exp",["-","n"]]],{variables:{x:!0,n:i},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),o=applyAllTransformations(o,s,40),(s=[]).push([["^","y","n"],["/",1,["^","y",["-","n"]]],{variables:{y:!0,n:i},evaluate_numbers:!0,max_digits:r}]),s.push([["apply","exp","n"],["/",1,["apply","exp",["-","n"]]],{variables:{n:i},evaluate_numbers:!0,max_digits:r}]),o=applyAllTransformations(o,s,40),(s=[]).push([["*","x",["/","y","z"]],["/",["*","x","y"],"z"],{allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["/",["/","x","y"],"z"],["/","x",["*","y","z"]],{allow_extended_match:!0,allow_permutations:!0}]),s.push([["/","x",["/","y","z"]],["/",["*","x","z"],"y"],{allow_extended_match:!0,allow_permutations:!0}]),o=evaluate_numbers(o=applyAllTransformations(o,s,40),{assumptions:t,max_digits:r})}function simplify_ratios(e,t){function r(e){var t=1;return e=e.map((function(e){if("number"==typeof e)return e<0?(t*=-1,-e):e;if(!Array.isArray(e))return e;if("-"===e[0])return t*=-1,e[1];if("+"!==e[0])return e;var r=!1;if(("number"==typeof e[1]&&e[1]<0||Array.isArray(e[1])&&"-"===e[1][0]||Array.isArray(e[1])&&"*"===e[1][0]&&Number(e[1][1])<0)&&(r=!0),r){t*=-1;var n=e.slice(1).map((e=>["-",e]));return evaluate_numbers(["+"].concat(n))}return e})),{factors:e,sign_change:t}}var n=get_tree(e);return contains_blank(n)?n:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),function e(t,n){if(!Array.isArray(t))return n?["-",t]:t;var i=t[0];if("-"===i)return e(t[1],n=!0);var a=t.slice(1).map((t=>e(t)));if("/"!==i)return n?["-",[i,...a]]:[i,...a];var o,s=a[0],u=a[1];s=default_order(s,{ignore_negatives:!0});var c,l=r(o=Array.isArray(s)&&"*"===s[0]?s.slice(1):[s]);o=l.factors,n&&(l.sign_change*=-1),u=default_order(u,{ignore_negatives:!0});var f=r(c=Array.isArray(u)&&"*"===u[0]?u.slice(1):[u]);return c=f.factors,l.sign_change*f.sign_change<0&&(o[0]=["-",o[0]]),["/",s=1===o.length?o[0]:["*"].concat(o),u=1===c.length?c[0]:["*"].concat(c)]}(n))}function contains_blank(e){return"＿"===e||!!Array.isArray(e)&&e.some(contains_blank)}let all_units=get_all_units();function remove_units(e,t=!0){var r=get_tree(e);if(!Array.isArray(r))return r;let n=r[0],i=r.slice(1);if("unit"===n){let e=all_units[get_unit_of_tree(r)];if(!e)return r;let n=remove_units(e.prefix?i[1]:i[0],t);return t?e.scale(n):n}return[n,...i.map((e=>remove_units(e,t)))]}function remove_scaling_units(e){var t=get_tree(e);if(!Array.isArray(t))return t;let r=t[0],n=t.slice(1);if("unit"===r){let e=all_units[get_unit_of_tree(t)];if(!e||!e.only_scales)return t;let r=remove_scaling_units(e.prefix?n[1]:n[0]);return e.scale(r)}return[r,...n.map((e=>remove_scaling_units(e)))]}function add_unit(e,t){var r=get_tree(e);let n=all_units[t];return n?n.prefix?["unit",t,r]:["unit",r,t]:r}function move_units_outside_products(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("*"===t){let e=[],t=[];for(let n of r){let r=get_unit_value_of_tree(n);r?(e.push(r[0]),t.push(r[1])):t.push(n)}let n=["*",...t];for(let t of e)n=add_unit(n,t);return n}return[t,...r.map(move_units_outside_products)]}var simplify$1=Object.freeze({__proto__:null,clean:clean,simplify:simplify,simplify_logical:simplify_logical,evaluate_numbers:evaluate_numbers,collect_like_terms_factors:collect_like_terms_factors,collapse_unary_minus:collapse_unary_minus,simplify_ratios:simplify_ratios,default_order:default_order,perform_vector_matrix_additions_scalar_multiplications:perform_vector_matrix_additions_scalar_multiplications,remove_units:remove_units,add_unit:add_unit,remove_scaling_units:remove_scaling_units});function solve_linear(e,t,r){if("string"==typeof t){void 0===r&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(r=e.context.get_assumptions([e.variables()]));var n=simplify(get_tree(e),r);if(Array.isArray(n)){var i=n[0],a=n.slice(1);if("="===i||"ne"===i||"<"===i||"le"===i||">"===i||"ge"===i){var o=simplify(["+",a[0],["-",a[1]]],r),s=e=>!variables(e).includes(t);if(variables(o=simplify(applyAllTransformations(o,[[["+",["*","_a",t],["*","_b",t]],["*",["+","_a","_b"],t],{variables:{_a:s,_b:s},allow_permutations:!0,allow_extended_match:!0,allow_implicit_identities:["_a","_b"],evaluate_numbers:!0}]],20))).includes(t)){var u=match$2(o,["+",["*","_a",t],"_b"],{variables:{_a:s,_b:s},allow_permutations:!0,allow_implicit_identities:["_a","_b"]});if(u){var c=simplify(u._a),l=simplify(u._b);if(is_nonzero_ast(c,r)){if("="===i||"ne"===i||is_positive_ast(c,r)){let e=simplify(["/",["-",l],c]);return[i,t,e]}if(is_negative_ast(c,r)){var f=simplify(["/",["-",l],c]);return[i="<"===i?">":"le"===i?"ge":">"===i?"<":"le",t,f]}}}}}}}}var 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n=this.factor(e);this.simple_factor_or_function_or_parens(e)||"_"===e[0]&&"string"==typeof e[1]||(n="\\left("+n+"\\right)");for(let e=0;e1?s=s.trimRight()+"^{"+a+"}"+this.stringConvert(o):s+=this.stringConvert(o),s="\\frac{ "+s+" }{ ";let u=1;Array.isArray(i)&&(u=i.length-1);for(let t=1;t<=u;t++){let r=i[t],n=1,a="";Array.isArray(r)?(a=r[1],n=r[2]):a=r,s=s+e+this.stringConvert(a),n>1&&(s=s+"^{"+n+"}"),s+=" "}return s+="}",s}if("apply"===t){if("abs"===r[0])return"\\left|"+this.statement(r[1])+"\\right|";if("floor"===r[0])return"\\left\\lfloor "+this.statement(r[1])+" \\right\\rfloor";if("ceil"===r[0])return"\\left\\lceil "+this.statement(r[1])+" \\right\\rceil";if("factorial"===r[0]){let e=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||"_"===r[1][0]&&"string"==typeof r[1][1]?e+"!":"\\left("+e+"\\right)!"}if("sqrt"===r[0])return"\\sqrt{"+this.statement(r[1])+"}";let e,t=r[0];if("^"===t[0]&&(t=t[1]),"_"===t[0]&&(t=t[1]),"int"===t){let e,t=this.factor(r[0]),n=r[1];if(Array.isArray(n)&&"*"===n[0]){let t=[],r=["*"];for(let e=1;e0&&(e[e.length-1].match(/[a-zA-Z]/)&&(e+="\\,"),e+=t.map((e=>"d"+this.factor(e[1]))).join("\\,"))}return e||(e=this.term(r[1])),t+" "+e}e="log10"===r[0]?"\\log_{10}":"re"===r[0]?"\\Re":"im"===r[0]?"\\Im":this.factor(r[0]);let n=this.statement(r[1]);return"tuple"!==r[1][0]&&(n="\\left("+n+"\\right)"),e+n}if("angle"===t){let e=r.every((e=>{if("string"==typeof e&&1===e.length)return!0;if(!Array.isArray(e))return!1;let t=e[0];return"_"===t||"^"===t||"prime"===t}));return operators$1[t](r.map(function(e,t){return this.statement(e)}.bind(this)),e)}return"+"===t&&2===e.length?"+ "+this.factor(e[1]):"\\left("+this.statement(e)+"\\right)"}factorWithParenthesesIfNegatedOrExplicitPlus(e){var t=this.factor(e);return t.match(/^-/)||t.match(/^\+/)?"\\left("+t+"\\right)":t}termWithPlusIfNotNegated(e){var t=this.term(e);return t.match(/^-/)?t.match(/^-[^ ]/)?"- "+t.slice(1):t:"+ "+t}}const textToAst$2=new textToAst$4,astToLatex=new astToLatex$1;var derivatives={sin:textToAst$2.convert("cos x"),cos:textToAst$2.convert("-(sin x)"),tan:textToAst$2.convert("(sec x)^2"),cot:textToAst$2.convert("-((csc x)^2)"),sec:textToAst$2.convert("(sec x)*(tan x)"),csc:textToAst$2.convert("-(csc x)*(cot x)"),sqrt:textToAst$2.convert("1/(2*sqrt(x))"),log:textToAst$2.convert("1/x"),ln:textToAst$2.convert("1/x"),exp:textToAst$2.convert("exp(x)"),arcsin:textToAst$2.convert("1/sqrt(1 - x^2)"),arccos:textToAst$2.convert("-1/sqrt(1 - x^2)"),arctan:textToAst$2.convert("1/(1 + x^2)"),arccsc:textToAst$2.convert("-1/(sqrt(-1/x^2 + 1)*x^2)"),arcsec:textToAst$2.convert("1/(sqrt(-1/x^2 + 1)*x^2)"),arccot:textToAst$2.convert("-1/(1 + x^2)"),abs:textToAst$2.convert("abs(x)/x")};function derivative(e,t,r=[]){var n=get_tree(e),i="\\frac{d}{d"+t+"} ";if("number"==typeof n)return r.push("The derivative of a constant is zero, that is, \\("+i+astToLatex.convert(n)+" = 0\\)."),0;if(variables(n).indexOf(t)<0)return r.push("The derivative of a constant is zero, that is, \\("+i+astToLatex.convert(n)+" = 0\\)."),0;if("string"==typeof n)return t===n?(r.push("We know the derivative of the identity function is one, that is, \\("+i+astToLatex.convert(n)+" = 1\\)."),1):(r.push("As far as \\("+astToLatex.convert(t)+"\\) is concerned, \\("+astToLatex.convert(n)+"\\) is constant, so "+i+astToLatex.convert(n)+" = 0\\)."),0);if(!Array.isArray(n))return null;var a=n[0],o=n.slice(1);if("+"===a||"-"===a||"~"===a){r.push("Using the sum rule, \\("+i+astToLatex.convert(n)+" = "+o.map((function(e,t){return i+astToLatex.convert(e)})).join(" + ")+"\\).");let e=[a].concat(o.map((function(e,n){return derivative(e,t,r)})));return e=simplify(e),r.push("So using the sum rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("*"===a){let e=[],a=[];for(let r=0;r0){if(0===e.length){return r.push("Since the derivative of a constant is zero, \\("+i+astToLatex.convert(n)+" = 0.\\)"),0}let o=["*"].concat(e);if(1===e.length&&(o=e[0]),o===t){r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+a.map((function(e,t){return astToLatex.convert(e)})).join(" \\cdot ")+"\\).");let e=["*"].concat(a);return e=simplify(e),e}r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+a.map((function(e,t){return astToLatex.convert(e)})).join(" \\cdot ")+" \\cdot "+i+"\\left("+astToLatex.convert(o)+"\\right)\\).");let s=derivative(o,t,r),u=["*"].concat(a.concat([s]));return u=simplify(u),r.push("And so \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}r.push("Using the product rule, \\("+i+astToLatex.convert(n)+" = "+o.map((function(e,t){return o.map((function(r,n){return t===n?i+"\\left("+astToLatex.convert(e)+"\\right)":astToLatex.convert(r)})).join(" \\cdot ")})).join(" + ")+"\\).");let s=o.slice(),u=["+"].concat(o.map((function(e,n){return["*"].concat(s.map((function(e,i){if(n===i){let n=derivative(e,t,r);return 1===n?null:n}return e})).filter((function(e){return null!=e})))})));return u=simplify(u),r.push("So using the product rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if("/"===a){let e=o[0],a=o[1];if(variables(a).indexOf(t)<0){r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(["/",1,a])+" \\cdot "+i+"\\left("+astToLatex.convert(e)+"\\right)\\).");let o=derivative(e,t,r),s=textToAst$2.convert("(1/g)*d"),u=substitute$1(s,{d:o,g:a});return u=simplify(u),r.push("So \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if(variables(e).indexOf(t)<0){1!==e&&r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+" \\cdot "+i+"\\left("+astToLatex.convert(["/",1,a])+"\\right)\\)."),r.push("Since \\(\\frac{d}{du} \\frac{1}{u}\\) is \\(\\frac{-1}{u^2}\\), the chain rule gives \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\cdot \\frac{-1}{ "+astToLatex.convert(a)+"^2} \\cdot "+i+astToLatex.convert(a)+"\\).");let o=derivative(a,t,r),s=textToAst$2.convert("f * (-a/(g^2))"),u=substitute$1(s,{f:e,a:o,g:a});return u=simplify(u),r.push("So since \\(\\frac{d}{du} \\frac{1}{u}\\) is \\(\\frac{-1}{u^2}\\), the chain rule gives \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}r.push("Using the quotient rule, \\("+i+astToLatex.convert(n)+" = \\frac{"+i+"\\left("+astToLatex.convert(e)+"\\right) \\cdot "+astToLatex.convert(a)+" - "+astToLatex.convert(e)+"\\cdot "+i+"\\left("+astToLatex.convert(a)+"\\right)}{ \\left( "+astToLatex.convert(a)+" \\right)^2} \\).");let s=derivative(e,t,r),u=derivative(a,t,r),c=textToAst$2.convert("(a * g - f * b)/(g^2)"),l=substitute$1(c,{a:s,b:u,f:e,g:a});return l=simplify(l),r.push("So using the quotient rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(l)+"\\)."),l}if("^"===a){let e=o[0],a=o[1];if(variables(a).indexOf(t)<0){if("string"==typeof e&&"x"===e){if("number"==typeof a){let t=textToAst$2.convert("n * (f^m)"),o=substitute$1(t,{n:a,m:a-1,f:e});return o=simplify(o),r.push("By the power rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"}\\)."),o}let t=textToAst$2.convert("n * (f^(n-1))"),o=substitute$1(t,{n:a,f:e});return o=simplify(o),r.push("By the power rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"}\\)."),o}1!==a&&r.push("By the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"} \\cdot "+i+astToLatex.convert(e)+"\\).");let o=derivative(e,t,r);if(1===a)return o;if("number"==typeof a){let t=textToAst$2.convert("n * (f^m) * a"),s=substitute$1(t,{n:a,m:a-1,f:e,a:o});return s=simplify(s),r.push("So by the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}let s=textToAst$2.convert("n * (f^(n-1)) * a"),u=substitute$1(s,{n:a,f:e,a:o});return u=simplify(u),r.push("So by the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if("e"===e&&math$1.define_e){if("string"==typeof a&&a===t){let e=textToAst$2.convert("e^(f)"),o=substitute$1(e,{f:a});return o=simplify(o),r.push("The derivative of \\(e^"+astToLatex.convert(t)+"\\) is itself, that is, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(n)+"\\)."),o}r.push("Using the rule for \\(e^x\\) and the chain rule, we know \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(n)+" \\cdot "+i+astToLatex.convert(a)+"\\).");let e=textToAst$2.convert("e^(f)*d"),o=derivative(a,t,r),s=substitute$1(e,{f:a,d:o});return s=simplify(s),r.push("So using the rule for \\(e^x\\) and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}if("number"==typeof e){if("string"==typeof a&&a===t){let o=textToAst$2.convert("a^(f) * log(a)"),s=substitute$1(o,{a:e,f:a});return s=simplify(s),r.push("The derivative of \\(a^"+astToLatex.convert(t)+"\\) is \\(a^{"+astToLatex.convert(t)+"} \\, \\log a\\), that is, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}let o=textToAst$2.convert("a^(f) * log(a)"),s=substitute$1(o,{a:e,f:a});r.push("Using the rule for \\(a^x\\) and the chain rule, we know \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+" \\cdot "+i+astToLatex.convert(a)+"\\).");let u=textToAst$2.convert("a^(b)*log(a)*d"),c=derivative(a,t,r),l=substitute$1(u,{a:e,b:a,d:c});return l=simplify(l),r.push("So using the rule for \\(a^x\\) and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(l)+"\\)."),l}let s=e,u=a;r.push("Recall the general rule for exponents, namely that \\(\\frac{d}{dx} u(x)^{v(x)} = u(x)^{v(x)} \\cdot \\left( v'(x) \\cdot \\log u(x) + \\frac{v(x) \\cdot u'(x)}{u(x)} \\right)\\). In this case, \\(u(x) = "+astToLatex.convert(s)+"\\) and \\(v(x) = "+astToLatex.convert(u)+"\\).");let c=derivative(s,t,r),l=derivative(u,t,r),f=textToAst$2.convert("(f^g)*(b * log(f) + (g * a)/f)"),p=substitute$1(f,{a:c,b:l,f:s,g:u});return p=simplify(p),r.push("So by the general rule for exponents, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(p)+"\\)."),p}if("apply"===a&&!(o[0]in derivatives)){let e=o[1];r.push("By the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(substitute$1(["apply",o[0]+"'","x"],{x:e}))+" \\cdot "+i+astToLatex.convert(e)+"\\).");let a=["*",substitute$1(["apply",o[0]+"'","x"],{x:e}),derivative(e,t,r)];return a=simplify(a),r.push("So by the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+"\\)."),a}if("apply"===a&&o[0]in derivatives||a in derivatives){let e=!1;"apply"===a&&(a=o[0],o=o.slice(1),e=!0);let s=o[0];if("number"==typeof s){let e=0;return r.push("The derivative of a constant is zero so \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("string"==typeof s&&s===t){let e=["*",substitute$1(derivatives[a],{x:s})];return e=simplify(e),r.push("It is the case that \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("string"==typeof s&&s!==t){let e=0;return r.push("Since the derivative of a constant is zero, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}{let o=[a,"u"];e&&(o=["apply"].concat(o)),r.push("Recall \\(\\frac{d}{du}"+astToLatex.convert(o)+" = "+astToLatex.convert(derivative(o,"u",[]))+"\\)."),r.push("By the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(substitute$1(derivatives[a],{x:s}))+" \\cdot "+i+astToLatex.convert(s)+"\\).");let u=["*",substitute$1(derivatives[a],{x:s}),derivative(s,t,r)];return u=simplify(u),r.push("So by the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}}return 0}function lowercaseFirstLetter(e){return e.charAt(0).toLowerCase()+e.slice(1)}function simplify_story(e){for(let t=e.length-1;t>=1;t--)e[t]===e[t-1]&&e.splice(t,1);for(let t=0;t":function(e){return e.join(" > ")},lts:function(e){return e.join(" < ")},gts:function(e){return e.join(" > ")},le:function(e){return e.join(" ≤ ")},ge:function(e){return e.join(" ≥ ")},ne:function(e){return e.join(" ≠ ")},forall:function(e){return"∀ "+e[0]},exists:function(e){return"∃ "+e[0]},in:function(e){return e[0]+" ∈ "+e[1]},notin:function(e){return e[0]+" ∉ "+e[1]},ni:function(e){return e[0]+" ∋ "+e[1]},notni:function(e){return e[0]+" ∌ "+e[1]},subset:function(e){return e[0]+" ⊂ "+e[1]},subseteq:function(e){return e[0]+" ⊆ "+e[1]},notsubset:function(e){return e[0]+" ⊄ "+e[1]},notsubseteq:function(e){return e[0]+" ⊈ "+e[1]},superset:function(e){return e[0]+" ⊃ "+e[1]},superseteq:function(e){return e[0]+" ⊇ "+e[1]},notsuperset:function(e){return e[0]+" ⊅ "+e[1]},notsuperseteq:function(e){return e[0]+" ⊉ "+e[1]},union:function(e){return e.join(" ∪ ")},intersect:function(e){return e.join(" ∩ ")},perp:function(e){return e.join(" ⟂ ")},parallel:function(e){return e.join(" ∥ ")},derivative_leibniz:function(e){return"d"+e[0]+"/d"+e[1]},partial_derivative_leibniz:function(e){return"∂"+e[0]+"/∂"+e[1]},"|":function(e){return e[0]+" | "+e[1]},":":function(e){return e[0]+" : "+e[1]},binom:function(e){return"binom( "+e[0]+", "+e[1]+" )"},vec:function(e){return"vec("+e[0]+")"},linesegment:function(e){return"linesegment( "+e.join(", ")+" )"},angle:function(e,t){return t?"∠"+e.join(""):"∠( "+e.join(", ")+" )"},unit:function(e){return e[0]+" "+e[1]}},nonunicode_operators={"+":function(e){return e.join(" ")},"-":function(e){return"-"+e[0]},"*":function(e){return e.join(" ")},"/":function(e){return e[0]+"/"+e[1]},_:function(e){return e[0]+"_"+e[1]},"^":function(e){return e[0]+"^"+e[1]},prime:function(e){return e[0]+"'"},tuple:function(e){return"( "+e.join(", ")+" )"},array:function(e){return"[ "+e.join(", ")+" ]"},list:function(e){return e.join(", ")},set:function(e){return"{ "+e.join(", ")+" }"},vector:function(e){return"( "+e.join(", ")+" )"},altvector:function(e){return"( "+e.join(", ")+" )"},interval:function(e){return"( "+e.join(", ")+" )"},matrix:function(e){return"( "+e.join(", ")+" )"},and:function(e){return e.join(" and ")},or:function(e){return e.join(" or ")},not:function(e){return"not "+e[0]},"=":function(e){return e.join(" = ")},"<":function(e){return e.join(" < ")},">":function(e){return e.join(" > ")},lts:function(e){return e.join(" < ")},gts:function(e){return e.join(" > ")},le:function(e){return e.join(" <= ")},ge:function(e){return e.join(" >= ")},ne:function(e){return e.join(" ne ")},forall:function(e){return"forall "+e[0]},exists:function(e){return"exists "+e[0]},in:function(e){return e[0]+" elementof "+e[1]},notin:function(e){return e[0]+" notelementof "+e[1]},ni:function(e){return e[0]+" containselement "+e[1]},notni:function(e){return e[0]+" notcontainselement "+e[1]},subset:function(e){return e[0]+" subset "+e[1]},subseteq:function(e){return e[0]+" subseteq "+e[1]},notsubset:function(e){return e[0]+" notsubset "+e[1]},notsubseteq:function(e){return e[0]+" notsubseteq "+e[1]},superset:function(e){return e[0]+" superset "+e[1]},superseteq:function(e){return e[0]+" superseteq "+e[1]},notsuperset:function(e){return e[0]+" notsuperset "+e[1]},notsuperseteq:function(e){return e[0]+" notsuperseteq "+e[1]},union:function(e){return e.join(" union ")},intersect:function(e){return e.join(" intersect ")},perp:function(e){return e.join(" perp ")},parallel:function(e){return e.join(" parallel ")},derivative_leibniz:function(e){return"d"+e[0]+"/d"+e[1]},partial_derivative_leibniz:function(e){return"∂"+e[0]+"/∂"+e[1]},"|":function(e){return e[0]+" | "+e[1]},":":function(e){return e[0]+" : "+e[1]},binom:function(e){return"binom( "+e[0]+", "+e[1]+" )"},vec:function(e){return"vec("+e[0]+")"},linesegment:function(e){return"linesegment( "+e.join(", ")+" )"},angle:function(e,t){return t?"angle "+e.join(""):"angle( "+e.join(", ")+" )"},unit:function(e){return e[0]+" "+e[1]}},output_unicodeDefault=!0;class astToText$2{constructor({output_unicode:e=output_unicodeDefault,padToDigits:t=null,padToDecimals:r=null,showBlanks:n=!0}={}){this.output_unicode=e,this.operators=unicode_operators,e||(this.operators=nonunicode_operators),this.padToDigits=t,this.padToDecimals=r,this.showBlanks=n}convert(e){return this.statement(e)}statement(e){if(!Array.isArray(e))return this.single_statement(e);let t=e[0],r=e.slice(1);if("ldots"===t)return"...";if(!(t in this.operators)&&"apply"!==t)throw new Error("Badly formed ast: operator "+t+" not recognized.");return"and"===t||"or"===t?this.operators[t](r.map(function(e,t){let r=this.single_statement(e);return r.match(/ /)&&!r.match(/^\(.*\)$/)?"("+r+")":r}.bind(this))):this.single_statement(e)}single_statement(e){if(!Array.isArray(e))return this.expression(e);let t=e[0],r=e.slice(1);if("not"===t)return this.operators[t](r.map(function(e,t){let r=this.single_statement(e);return r.match(/ /)&&!r.match(/^\(.*\)$/)?"("+r+")":r}.bind(this)));if("exists"===t||"forall"===t)return this.operators[t]([this.single_statement(r[0])]);if("="===t||"ne"===t||"<"===t||">"===t||"le"===t||"ge"===t||"in"===t||"notin"===t||"ni"===t||"notni"===t||"subset"===t||"notsubset"===t||"subseteq"===t||"notsubseteq"===t||"superset"===t||"notsuperset"===t||"superseteq"===t||"notsuperseteq"===t)return this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this)));if("lts"===t||"gts"===t){let e=r[0],n=r[1];if("tuple"!==e[0]||"tuple"!==n[0])throw new Error("Badly formed ast");let i=this.expression(e[1]);for(let r=1;r ":"lts"===t?this.output_unicode?i+=" ≤ ":i+=" <= ":this.output_unicode?i+=" ≥ ":i+=" >= ",i+=this.expression(e[r+1]);return i}return this.expression(e)}expression(e){if(!Array.isArray(e))return this.term(e);let t=e[0],r=e.slice(1);return"+"===t?1===r.length?"+"+this.term(r[0]):this.operators[t](r.map(function(e,t){return t>0?this.termWithPlusIfNotNegated(e):this.term(e)}.bind(this))):["union","intersect","perp","parallel"].includes(t)?this.operators[t](r.map(function(e,t){return this.term(e)}.bind(this))):this.term(e)}term(e){if(!Array.isArray(e))return this.factor(e);let t=e[0],r=e.slice(1);if("-"===t)return this.operators[t](r.map(function(e,t){return this.term(e)}.bind(this)));if("*"===t)return this.operators[t](r.map(function(e,t){let n;return t>0?(n=this.factorWithParenthesesIfNegatedOrExplicitPlus(e),n.match(/^[0-9]/)?"* "+n:"angle"===e[0]&&r.length>1?"( "+n+" )":n):(n=this.factor(e),"angle"===e[0]&&r.length>1?"( "+n+" )":n)}.bind(this)));if("/"===t){let e=this.factor(r[0]),n=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[0])||(e="("+e+")"),this.simple_factor_or_function_or_parens(r[1])||(n="("+n+")"),this.operators[t]([e,n])}return"unit"===t?this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this))):this.factor(e)}symbolConvert(e){let t={alpha:"α",beta:"β",Gamma:"Γ",gamma:"γ",Delta:"Δ",delta:"δ",epsilon:"ε",zeta:"ζ",eta:"η",Theta:"ϴ",theta:"θ",iota:"ι",kappa:"κ",Lambda:"Λ",lambda:"λ",mu:"μ",nu:"ν",Xi:"Ξ",xi:"ξ",Pi:"Π",pi:"π",rho:"ρ",Sigma:"Σ",sigma:"σ",tau:"τ",Upsilon:"Υ",upsilon:"υ",Phi:"Φ",phi:"ϕ",Psi:"Ψ",psi:"ψ",Omega:"Ω",omega:"ω",perp:"⟂",int:"∫"};return this.output_unicode&&e in t?t[e]:this.showBlanks||"＿"!==e?e:""}simple_factor_or_function_or_parens(e){let t=this.factor(e);return!!(t.length<=1||"string"==typeof e&&e.match(/^\w+$/)||Array.isArray(e)&&"apply"===e[0]||t.match(/^\(.*\)$/)||t.match(/^⟨.*⟩$/))||"number"==typeof e&&(e>=0&&!e.toString().includes("e"))}factor(e){if("string"==typeof e)return this.symbolConvert(e);if("number"==typeof e){if(e===1/0)return this.output_unicode?"∞":"infinity";if(e===-1/0)return this.output_unicode?"-∞":"-infinity";if(Number.isNaN(e))return"NaN";{let t=e.toString(),r=t.indexOf("e");if(-1===r)return null!==this.padToDigits?t=padNumberStringToDigits(t,this.padToDigits):null!==this.padToDecimals&&(t=padNumberStringToDecimals(t,this.padToDecimals)),t;let n=t.substring(0,r),i=t.substring(r+1);if(null!==this.padToDigits)n=padNumberStringToDigits(n,this.padToDigits);else if(null!==this.padToDecimals){let r=Number(i);if(r>0)return t=e.toLocaleString("fullwide",{useGrouping:!1}),padNumberStringToDecimals(t,this.padToDecimals);n=padNumberStringToDecimals(n,this.padToDecimals+r)}return"+"===i[0]?n+" * 10^"+i.substring(1):n+" * 10^("+i+")"}}if(!Array.isArray(e))return"";let t=e[0],r=e.slice(1);if("^"===t){if(Number.isInteger(r[0])&&Number.isInteger(r[1])){let e;return e=r[0]<0?"("+r[0].toString()+")":r[0].toString(),r[1]<0?e+"^("+r[1].toString()+")":e+"^"+r[1].toString()}let e=this.factor(r[0]),t=r[0];for(;"prime"===t[0];)t=t[1];this.simple_factor_or_function_or_parens(t)||"_"===t[0]&&"string"==typeof t[1]||(e="("+e.toString()+")");let n=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||(n="("+n.toString()+")"),e+"^"+n}if("_"===t)return this.operators[t](r.map(function(e,t){let r=this.factor(e);return this.simple_factor_or_function_or_parens(e)?r:"("+r+")"}.bind(this)));if("prime"===t){let e=r[0],t=1;for(;"prime"===e[0];)t+=1,e=e[1];let n=this.factor(e);this.simple_factor_or_function_or_parens(e)||"_"===e[0]&&"string"==typeof e[1]||(n="("+n+")");for(let e=0;e1&&(s=s+"^"+a),s=s+this.symbolConvert(o)+"/";let u=1;Array.isArray(i)&&(u=i.length-1);for(let t=1;t<=u;t++){let r=i[t],n=1,a="";Array.isArray(r)?(a=r[1],n=r[2]):a=r,s=s+e+this.symbolConvert(a),n>1&&(s=s+"^"+n)}return s}if("apply"===t){if("abs"===r[0])return"|"+this.statement(r[1])+"|";if("factorial"===r[0]){let e=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||"_"===r[1][0]&&"string"==typeof r[1][1]?e+"!":"("+e+")!"}let e=r[0];if("^"===e[0]&&(e=e[1]),"_"===e[0]&&(e=e[1]),"int"===e){let e,t=this.factor(r[0]),n=r[1];if(Array.isArray(n)&&"*"===n[0]){let t=[],r=["*"];for(let e=1;e0&&(e+=" "+t.map((e=>"d"+this.factor(e[1]))).join(" "))}return e||(e=this.term(r[1])),t+" "+e}let t=this.factor(r[0]),n=this.statement(r[1]);return"tuple"!==r[1][0]&&(n="("+n+")"),t+n}if("angle"===t){let e=r.every((e=>{if("string"==typeof e&&1===e.length)return!0;if(!Array.isArray(e))return!1;let t=e[0];return"_"===t||"^"===t||"prime"===t}));return this.operators[t](r.map(function(e,t){return this.statement(e)}.bind(this)),e)}return"+"===t&&2===e.length?"+ "+this.factor(e[1]):"("+this.statement(e)+")"}factorWithParenthesesIfNegatedOrExplicitPlus(e){var t=this.factor(e);return t.match(/^-/)||t.match(/^\+/)?"("+t+")":t}termWithPlusIfNotNegated(e){let t=this.term(e);return t.match(/^-/)?t.match(/^-[^ ]/)?"- "+t.slice(1):t:"+ "+t}}var astToText$1=new astToText$2;function subscripts_to_strings(e,t=!1){var r=get_tree(e);if(!Array.isArray(r))return r;let n=r[0],i=r.slice(1);return"_"===n&&(t||i.every((e=>["number","string"].includes(typeof e))))?astToText$1.convert(r):[n].concat(i.map((e=>subscripts_to_strings(e,t))))}function strings_to_subscripts(e){var t=get_tree(e);if("string"==typeof t){let e=t.match(/^([0-9a-zA-Z]+)_([a-zA-Z]+|[0-9]+)$/);if(e){let t=Number(e[1]);isNaN(t)&&(t=e[1]);let r=Number(e[2]);return isNaN(r)&&(r=e[2]),["_",t,r]}return t}if(!Array.isArray(t))return t;let r=t[0],n=t.slice(1);return[r].concat(n.map(strings_to_subscripts))}var normalization=Object.freeze({__proto__:null,normalize_function_names:normalize_function_names,normalize_applied_functions:normalize_applied_functions,log_subscript_to_two_arg_log:log_subscript_to_two_arg_log,substitute_abs:substitute_abs,default_order:default_order,constants_to_floats:constants_to_floats,normalize_angle_linesegment_arg_order:normalize_angle_linesegment_arg_order,tuples_to_vectors:tuples_to_vectors,to_intervals:to_intervals,altvectors_to_vectors:altvectors_to_vectors,subscripts_to_strings:subscripts_to_strings,strings_to_subscripts:strings_to_subscripts}),astToText=new astToText$2;function generate_random_integer(e,t,r){return e=math$1.ceil(e),t=math$1.floor(t),math$1.floor(r()*(t-e+1))+e}const equals$5=function({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,relative_tolerance:a=1e-12,absolute_tolerance:o=0,tolerance_for_zero:s=1e-15,allowed_error_in_numbers:u=0,include_error_in_number_exponents:c=!1,allowed_error_is_absolute:l=!1,rng:f}){if(Array.isArray(e.tree)&&Array.isArray(t.tree)){let p=e.tree[0],m=e.tree.slice(1),d=t.tree[0],h=t.tree.slice(1);if("tuple"===p||"vector"===p||"altvector"===p||"list"===p||"array"===p||"matrix"===p||"interval"===p){if(d!==p)return!1;if(h.length!==m.length)return!1;for(let e=0;e","<","ge","le"].includes(p)){if(2!==h.length)return!1;if(">"===p?(p="<",m=[m[1],m[0]]):"ge"===p&&(p="le",m=[m[1],m[0]]),">"===d?(d="<",h=[h[1],h[0]]):"ge"===d&&(d="le",h=[h[1],h[0]]),p!==d)return!1;let e=["+",m[0],["-",m[1]]],t=["+",h[0],["-",h[1]]],y="="!==p;return component_equals({expr:n.fromAst(e),other:i.fromAst(t),randomBindings:r,expr_context:n,other_context:i,allow_proportional:!0,require_positive_proportion:y,relative_tolerance:a,absolute_tolerance:o,tolerance_for_zero:s,allowed_error_in_numbers:u,include_error_in_number_exponents:c,allowed_error_is_absolute:l,rng:f})}}return component_equals({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,relative_tolerance:a,absolute_tolerance:o,tolerance_for_zero:s,allowed_error_in_numbers:u,include_error_in_number_exponents:c,allowed_error_is_absolute:l,rng:f})},component_equals=function({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,allow_proportional:a=!1,require_positive_proportion:o=!1,relative_tolerance:s,absolute_tolerance:u,tolerance_for_zero:c,allowed_error_in_numbers:l,include_error_in_number_exponents:f,allowed_error_is_absolute:p,rng:m}){var d=1e-20*Number.MAX_VALUE,h=0,y=10;e=e.normalize_function_names(),t=t.normalize_function_names(),e=e.log_subscript_to_two_arg_log(),t=t.log_subscript_to_two_arg_log(),e=e.subscripts_to_strings(),t=t.subscripts_to_strings(),e=e.normalize_applied_functions(),t=t.normalize_applied_functions();let g=rename_functions_with_exponents(e.tree),v=rename_functions_with_exponents(t.tree);e=n.fromAst(rename_vecs(g)),t=i.fromAst(rename_vecs(v));var x=[...new Set([...e.variables(),...t.variables()])];math$1.define_pi&&(x=x.filter((function(e){return"pi"!==e}))),math$1.define_i&&(x=x.filter((function(e){return"i"!==e}))),math$1.define_e&&(x=x.filter((function(e){return"e"!==e})));var b=[];for(let e=0;e1===e.length||e.includes("_")||e.includes("^"))),w=_.filter((e=>x.includes(e)));if(_=_.filter((e=>!x.includes(e))),w.length>0){let r=e.tree,a=t.tree,o="x1";for(;[..._,...x].includes(o);)o+="x1";let s="x2";for(;[..._,...x].includes(s);)s+="x2";for(let e of w){let t=e+e;for(;[..._,...x].includes(t);)t+=e;let n=[[["apply",e,o],["apply",t,o],{variables:{[o]:!0}}]];r=applyAllTransformations(r,n),a=applyAllTransformations(a,n),_.push(t)}e=n.fromAst(r),t=i.fromAst(a)}try{var N=e.f(),$=t.f()}catch(r){return e.equalsViaSyntax(t,{allow_blanks:!0})}let A,M,S;if(l>0){let t=replace_numbers_with_parameters({expr:e,variables:x,include_exponents:f});A=n.fromAst(t.expr_with_params),M=t.parameters;let r=Object.keys(M);if(r.length>0){let e=A.derivative(r[0]);if(p||(e=e.multiply(M[r[0]])),r.length>1)for(let t of r.slice(1)){let r=A.derivative(t);p||(r=r.multiply(M[t])),e=e.add(r)}let t=e.multiply(l);try{S=t.f()}catch(e){}}}var E=1,T=[10,1,100,.1,1e3,.01],O=0;let C=0,k=!0,D=0;for(let e=0;e<1e3;e++){try{var I=B(T[O],m)}catch(e){continue}if(!1===I.always_zero&&(k=!1),!I.equal&&!I.out_of_bounds&&!I.always_zero&&!1!==I.sufficient_finite_values&&(D++,D>100))return!1;if(I.equal){if(I.always_zero){if(!k)continue;if(C+=1,C>5&&(O+=1,C=0),O>=T.length)return!0;continue}return!0}}return!1;function B(e,t){var n,i=r(t,x,e);for(let e=0;eh)||!(0===m||m>h))return{out_of_bounds:!0,always_zero:!1};var g=Math.min(p,m),v=Math.max(p,m),w=1;let A=0;if(S){try{A=math$1.abs(S(n))}catch(e){return{equal_at_start:!1,always_zero:!1}}if(!Number.isFinite(A))return{equal_at_start:!1,always_zero:!1}}if(A+=g*s,A=Math.min(A,.1*g),A+=0!==A||0!==l&&0!==f?u:c,!(0===v||math$1.abs(math$1.subtract(l,f))0))return{equal_at_start:!1,always_zero:!1}}var T=0===v,O=0;for(let e=0;e<100;e++){var C,k=r(t,x,E/100,i);for(let e=0;e=y)return{equal:!0,always_zero:T}}}return{sufficient_finite_values:!1,always_zero:T}}};function replace_numbers_with_parameters({expr:e,variables:t,include_exponents:r=!1}){let n={},i=0;function a(){i++;let e="par"+i;for(;t.includes(e);)i++,e="par"+i;return e}return{expr_with_params:function e(t){if("number"==typeof t){if(0===t)return t;{let e=a();return n[e]=t,e}}if("string"==typeof t){if("pi"===t){if(math$1.define_pi){let e=a();return n[e]=math$1.PI,e}}else if("e"===t&&math$1.define_e){let e=a();return n[e]=math$1.e,e}return t}if(!Array.isArray(t))return t;let i=t[0],o=t.slice(1);return"^"!==i||r?[i,...o.map(e)]:[i,e(o[0]),o[1]]}((e=e.evaluate_numbers({max_digits:1/0})).tree),parameters:n}}function rename_functions_with_exponents(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("apply"===t){let e=r[0];return Array.isArray(e)&&"^"===e[0]&&e.slice(1).every((e=>["number","string"].includes(typeof e)))&&(e=astToText.convert(e)),["apply",e,r[1]]}return[t,...r.map(rename_functions_with_exponents)]}function rename_vecs(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);return"vec"===t&&1===r.length?"__vec_"+astToText.convert(r[0]):[t,...r.map(rename_vecs)]}function randomComplexBindings(e,t,r,n){var i={};return void 0===n?t.forEach((function(t){i[t]=math$1.complex(2*e()*r-r,2*e()*r-r)})):t.forEach((function(t){i[t]=math$1.complex(n[t].re+2*e()*r-r,n[t].im+2*e()*r-r)})),i}const equals$4=function(e,t,{relative_tolerance:r=1e-12,absolute_tolerance:n=0,tolerance_for_zero:i=1e-15,allowed_error_in_numbers:a=0,include_error_in_number_exponents:o=!1,allowed_error_is_absolute:s=!1,allow_blanks:u=!1}={}){if(!u&&(e.variables().includes("＿")||t.variables().includes("＿")))return!1;let c=seedrandom$1("complex_seed");return e=e.remove_scaling_units(),t=t.remove_scaling_units(),!(!e.isAnalytic({allow_abs:!0,allow_arg:!0,allow_relation:!0})||!t.isAnalytic({allow_abs:!0,allow_arg:!0,allow_relation:!0}))&&equals$5({expr:e,other:t,randomBindings:randomComplexBindings,expr_context:e.context,other_context:t.context,relative_tolerance:r,absolute_tolerance:n,tolerance_for_zero:i,allowed_error_in_numbers:a,include_error_in_number_exponents:o,allowed_error_is_absolute:s,rng:c})};function randomRealBindings(e,t,r,n){var i={};return void 0===n?t.forEach((function(t){i[t]=2*e()*r-r})):t.forEach((function(t){i[t]=n[t]+2*e()*r-r})),i}const equals$3=function(e,t,{relative_tolerance:r=1e-12,absolute_tolerance:n=0,tolerance_for_zero:i=1e-15,allowed_error_in_numbers:a=0,include_error_in_number_exponents:o=!1,allowed_error_is_absolute:s=!1}={}){if(!e.isAnalytic()||!t.isAnalytic())return!1;let u=seedrandom("real_seed");return equals$5({expr:e,other:t,randomBindings:randomRealBindings,expr_context:e.context,other_content:t.context,relative_tolerance:r,absolute_tolerance:n,tolerance_for_zero:i,allowed_error_in_numbers:a,include_error_in_number_exponents:o,allowed_error_is_absolute:s,rng:u})},equals$2=function(e,t,{allowed_error_in_numbers:r=0,include_error_in_number_exponents:n=!1,allowed_error_is_absolute:i=!1,allow_blanks:a=!1}={}){if(!a&&(e.variables().includes("＿")||t.variables().includes("＿")))return!1;let o=e.normalize_function_names().normalize_applied_functions().normalize_angle_linesegment_arg_order(),s=t.normalize_function_names().normalize_applied_functions().normalize_angle_linesegment_arg_order();return equal(o.tree,s.tree,{allowed_error_in_numbers:r,include_error_in_number_exponents:n,allowed_error_is_absolute:i})},equals$1=function(e,t,{min_elements_match:r=3,match_partial:n=!1}={}){if(!is_discrete_infinite_set(e))return!1;if(is_discrete_infinite_set(t)){var i=[];let r=e.context.get_assumptions(e);if(void 0!==r&&i.push(r),r=t.context.get_assumptions(t),void 0!==r&&i.push(r),i=0===i.length?void 0:1===i.length?i[0]:clean_assumptions(["and"].concat(i)),n){let r=contained_in(e.tree,t.tree,i,n);if(!1===r)return 0;let a=contained_in(t.tree,e.tree,i,n);return!1===a?0:!0===r?!0===a?1:a:!0===a?r:Math.min(r,a)}return contained_in(e.tree,t.tree,i,n)&&contained_in(t.tree,e.tree,i,n)}{let n=t.tree;if("list"!==n[0])return!1;let i=n.length-2;if("ldots"!==n[i+1][0])return!1;if(icontained_in(e,t,r)))}var i=e[1],a=e[2],o=e[3],s=e[4];if(!Array.isArray(o)||"-"!==o[0]||o[1]!==1/0||s!==1/0)return!1;i=simplify(["/",i,a],r,1/0);var u=t.slice(1),c=[];for(let e=0;ee[0])))];let f=0;for(let e of l){let t=c.map((function(t,r){let n=e/t[0];return Number.isInteger(n)?[t[0],n,r]:void 0})).filter((e=>e)),a=[];for(let n of t){let t=n[0],o=n[1],s=n[2],u=c[s][2],l=c[s][3];for(let n=0;nf&&(f=t)}}return!!(n&&f>0)&&f}function sequence_from_discrete_infinite(e,t){var r=e.tree.slice(1);if(r.length>1)return;let n=r[0][1],i=r[0][2],a=evaluate_numbers(r[0][3]),o=r[0][4];if(!Number.isInteger(a)||o!==1/0)return;let s=[];for(let e=0;e0))throw Error(`Have not implemented equality check with ${n} sign errors.`);if(n>1){let e=r;r=function(t,r){return equalSpecifiedSignErrors(t,r,{equalityFunction:e,n_sign_errors:n-1})}}var i,a,o=e.tree,s=[[o]],u=0;e.tree=["-",o];var c=r(e,t);if(e.tree=o,c)return!0;for(;i=s[u++];)if(i=i[0],Array.isArray(i))for(a=1;a"];function isAnalytic(e,{allow_abs:t=!1,allow_arg:r=!1,allow_relation:n=!1}={}){var i=normalize_applied_functions(normalize_function_names(e)),a=operators$3(i=subscripts_to_strings(i));for(let e=0;e+")},"-":function(e){return"-"+e.join("-")+""},"*":function(e){return e.join('\\cdot*')},"/":function(e){return astToGuppy$1.dfrac(e[0],e[1])},"^":function(e){return astToGuppy$1.power(e[0],e[1])},sin:function(e){return astToGuppy$1.trig("sin",e[0])},cos:function(e){return astToGuppy$1.trig("cos",e[0])},tan:function(e){return astToGuppy$1.trig("tan",e[0])},arcsin:function(e){return astToGuppy$1.trig("arcsin",e[0])},arccos:function(e){return astToGuppy$1.trig("arccos",e[0])},arctan:function(e){return astToGuppy$1.trig("arctan",e[0])},arccsc:function(e){return astToGuppy$1.trig("arccsc",e[0])},arcsec:function(e){return astToGuppy$1.trig("arcsec",e[0])},arccot:function(e){return astToGuppy$1.trig("arccot",e[0])},csc:function(e){return astToGuppy$1.trig("csc",e[0])},sec:function(e){return astToGuppy$1.trig("sec",e[0])},cot:function(e){return astToGuppy$1.trig("cot",e[0])},log:function(e){return astToGuppy$1.trig("log",e[0])},exp:function(e){return astToGuppy$1.trig("exp",e[0])},ln:function(e){return astToGuppy$1.trig("ln",e[0])},sqrt:function(e){return astToGuppy$1.sqrt(e[0])},abs:function(e){return astToGuppy$1.abs(e[0])}}}static dfrac(e,t){return'\\dfrac{}{}\\frac{}{}()/()'+e+''+t+""}static trig(e,t){return'\\'+e+'\\left(\\right) '+e+'()'+t+""}static sqrt(e){return'\\sqrt{}sqrt()'+e+""}static power(e,t){return'{}^{}()^()'+e+''+t+""}static abs(e){return'\\left|\\right|abs()'+e+""}static paren(e){return'\\left(\\right)()'+e+""}static isFunctionSymbol(e){return-1!==["sin","cos","tan","csc","sec","cot","arcsin","arccos","arctan","arccsc","arcsec","arccot","log","ln","exp","sqrt","abs","this.factorial"].indexOf(e)}static isGreekLetterSymbol(e){return-1!==["pi","theta","theta","Theta","alpha","nu","beta","xi","Xi","gamma","Gamma","delta","Delta","pi","Pi","epsilon","epsilon","rho","rho","zeta","sigma","Sigma","eta","tau","upsilon","Upsilon","iota","phi","phi","Phi","kappa","chi","lambda","Lambda","psi","Psi","omega","Omega"].indexOf(e)}factorWithParenthesesIfNegated(e){var t=this.factor(e);return t.toString().match(/^-/)?astToGuppy$1.paren(t.toString()):t}factor(e){if("string"==typeof e)return astToGuppy$1.isGreekLetterSymbol(e)?'\\'+e+' $'+e+"":""+e+"";if("number"==typeof e)return""+e+"";if(!Array.isArray(e))return"";var t=e[0],r=e.slice(1);return"apply"===t&&(t=e[1],r=e.slice(2)),"abs"===t?this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this))):astToGuppy$1.isFunctionSymbol(t)?"this.factorial"!==t||1!==r[0].toString().length&&!r[0].toString().match(/^[0-9]*$/)?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):this.operators[t](r):"^"===t||"~"===t?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):astToGuppy$1.paren(this.expression(e))}term(e){if(!Array.isArray(e))return this.factor(e);var t=e[0],r=e.slice(1);return"*"===t?this.operators[t](r.map(function(e,t){var r=this.factorWithParenthesesIfNegated(e);return r.toString().match(/^[0-9]/)&&t>0?" * "+r:r}.bind(this))):"/"===t?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):this.factor(e)}expression(e){if(!Array.isArray(e))return this.term(e);var t=e[0],r=e.slice(1);return"+"===t||"-"===t?this.operators[t](r.map(function(e,t){return this.factorWithParenthesesIfNegated(e)}.bind(this))):this.term(e)}convert(e){return(""+this.expression(e)+"").replace(/<\/e>/g,"")}}const glslOperators={"+":function(e){var t=e[0];return e.slice(1).forEach((function(e){t=t+"+"+e})),t},"-":function(e){var t="-"+e[0];return e.slice(1).forEach((function(e){t=t+"-"+e})),t},"~":function(e){var t="vec2(0.0,0.0)";return e.forEach((function(e){t=t+"-"+e})),t},"*":function(e){var t=e[0];return e.slice(1).forEach((function(e){t="cmul("+t+","+e+")"})),t},"/":function(e){var t=e[0];return e.slice(1).forEach((function(e){t="cdiv("+t+","+e+")"})),t},sin:function(e){return"csin("+e[0]+")"},cos:function(e){return"ccos("+e[0]+")"},tan:function(e){return"ctan("+e[0]+")"},sinh:function(e){return"csinh("+e[0]+")"},cosh:function(e){return"ccosh("+e[0]+")"},arcsin:function(e){return"carcsin("+e[0]+")"},arccos:function(e){return"carccos("+e[0]+")"},arctan:function(e){return"carctan("+e[0]+")"},arccsc:function(e){return"carcsin(cdiv(vec2(1.0,0),"+e[0]+"))"},arcsec:function(e){return"carccos(cdiv(vec2(1.0,0),"+e[0]+"))"},arccot:function(e){return"carctan(cdiv(vec2(1.0,0),"+e[0]+"))"},csc:function(e){return"ccsc("+e[0]+")"},sec:function(e){return"csec("+e[0]+")"},cot:function(e){return"ccot("+e[0]+")"},exp:function(e){return"cexp("+e[0]+")"},conj:function(e){return"conjugate("+e[0]+")"},sqrt:function(e){return"cpower("+e[0]+",vec2(0.5,0.0))"},log:function(e){return"clog("+e[0]+")"},ln:function(e){return"clog("+e[0]+")"},"^":function(e){return"cpower("+e[0]+","+e[1]+")"},abs:function(e){return"cabs("+e[0]+")"},apply:function(e){return"vec2(NaN,NaN)"}};class astToGLSL$1{constructor(){}convert(e){if("boolean"==typeof e)throw Error("no support for boolean");if("string"==typeof e)return"e"===e?"vec2(2.71828182845905,0.0)":"pi"===e?"vec2(3.14159265358979,0.0)":"i"===e?"vec2(0.0,1.0)":String(e);if("number"==typeof e)return"vec2("+String(e)+",0.0)";if("real"in e&&"imaginary"in e)return e;if(!Array.isArray(e))throw Error("Invalid ast");var t=e[0],r=e.slice(1);if("apply"===t){if("string"!=typeof r[0])throw Error("Non string functions not implemented for conversion to GLSL");t=r[0],r=r.slice(1);return glslOperators[t](r.map(function(e,t){return this.convert(e)}.bind(this)))}if(t in glslOperators)return glslOperators[t](r.map(function(e,t){return this.convert(e)}.bind(this)));throw Error("Operator "+t+" not implemented for conversion to mathjs")}}var astToGuppy=new astToGuppy$1,astToGLSL=new astToGLSL$1;const tex=function(e,t){return new astToLatex$1(t).convert(e.tree)},toLatex=tex,toString=function(e,t){return new astToText$2(t).convert(e.tree)},toGLSL=function(e){return astToGLSL.convert(e.tree)},toXML=function(e){return astToGuppy.convert(e.tree)};var printing=Object.freeze({__proto__:null,tex:tex,toLatex:toLatex,toString:toString,toXML:toXML,toGLSL:toGLSL});const integrateNumerically=function(e,t,r,n){for(var i=0,a={},o=0;o<100;o++){var s=r+(n-r)*(o+.5)/100;a[t]=s,i+=e.evaluate(a)}return i*(n-r)/100};var integration=Object.freeze({__proto__:null,integrateNumerically:integrateNumerically});function expression_to_polynomial(e){var t=get_tree(e);if("string"==typeof t)return"pi"===t&&math$1.define_pi||"i"===t&&math$1.define_i||"e"===t&&math$1.define_e?t:["polynomial",t,[[1,1]]];if("number"==typeof t)return t;var r=evaluate_to_constant(t,{remove_units_first:!1});if(Number.isFinite(r))return simplify(t);if(!Array.isArray(t))return!1;if(!operators$3(t).every((e=>["+","-","*","^","/","_","prime"].includes(e))))return!1;var n=t[0],i=t.slice(1);if("+"===n){let e=i.map(expression_to_polynomial);return!!e.every((e=>!1!==e))&&e.reduce(((e,t)=>polynomial_add(e,t)))}if("-"===n){let e=expression_to_polynomial(i[0]);return!!e&&polynomial_neg(e)}if("*"===n){let e=i.map(expression_to_polynomial);return!!e.every((e=>!1!==e))&&e.reduce(((e,t)=>polynomial_mul(e,t)))}if("^"===n){let e=i[0],r=expression_to_polynomial(e);if(!1===r)return!1;let n=simplify(i[1]);if("number"!=typeof n||n<0||!Number.isInteger(n)){let r=evaluate_to_constant(n,{remove_units_first:!1});if(Number.isFinite(r)){let t=math$1.fraction(r);if(t.d<=100){e=t.s<0?["^",e,["/",-1,t.d]]:["^",e,["/",1,t.d]];var a=["polynomial",simplify(e),[]];return a[2].push([t.n,1]),a}}return["polynomial",t,[[1,1]]]}return 0===n?1:1===n?r:polynomial_pow(r,n)}if("/"===n){var o=i[1],s=evaluate_to_constant(o,{remove_units_first:!1});return Number.isFinite(s)?polynomial_mul(expression_to_polynomial(i[0]),["/",1,s]):["polynomial",t,[[1,1]]]}return["polynomial",t,[[1,1]]]}function polynomials_in_same_leading_variable(e,t){return e[1]!==t[1]&&(compare_function(e[1],t[1])<0?t=["polynomial",e[1],[[0,t]]]:e=["polynomial",t[1],[[0,e]]]),[e,t]}function polynomial_add(e,t){if("polynomial"!==e[0]){if("polynomial"!==t[0])return simplify(["+",e,t]);e=["polynomial",t[1],[[0,e]]]}else if("polynomial"!==t[0])t=["polynomial",e[1],[[0,t]]];else{let r=polynomials_in_same_leading_variable(e,t);e=r[0],t=r[1]}let r=["polynomial",e[1],[]],n=e[2],i=t[2],a=r[2],o=n.length,s=i.length,u=0,c=0;for(;u0;)1&t&&(r=polynomial_mul(r,e)),e=polynomial_mul(e,e),t>>=1;return r}function polynomial_to_expression(e){if(!Array.isArray(e)||"polynomial"!==e[0])return e;let t=e[1],r=e[2],n=[],i=r.length;for(var a=0;an[s][1])return!1}return i!==a&&o!==a}function mono_gcd(e,t){if(!Array.isArray(e)||!Array.isArray(t)||"monomial"!==e[0]||"monomial"!==t[0])return 1;let r=e[2],n=t[2],i=[],a=r.length,o=n.length,s=0,u=0;for(;s=0;){var n=[];n.push([e[2][t][1],r]),r=["polynomial",e[2][t][0],n],t-=1}return r}function max_div_init(e,t){if(0===e)return 0;let r=e,n=[];for(;Array.isArray(r)&&"polynomial"===r[0];){let e=r[1],t=r[2],i=t[t.length-1][0];r=t[t.length-1][1],n.push([e,i])}let i=["monomial",r,n],a=t.length;for(var o=0;o0?choice_lowest_degree(a):0}function update_hij_table(e,t,r){let n=t.length;t.push(r);let i=0,a=1,o=[];for(;a0?choice_lowest_degree(o):0}function choice_lowest_degree(e){let t=[],r=e.length;for(i=0;i2?i=i.concat(n[a].slice(1)):i.push(n[a]);n=i}return[r].concat(n)}const unflattenRight=function(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if((n=n.map((function(e,t){return unflattenRight(e)}))).length>2&&is_associative$1[r]){for(var i=[r,n[0],void 0],a=i,o=1;o2&&is_associative$1[r]){for(var i=[r,void 0,n[n.length-1]],a=i,o=n.length-2;o>0;o--)a[1]=[r,void 0,n[o]],a=a[1];return a[1]=n[0],i}return[r].concat(n)},allChildren=function(e){if(!Array.isArray(e))return[];var t=e[0],r=e.slice(1);return is_associative$1[t]?r.reduce((function(e,r){return Array.isArray(r)&&r[0]===t?e.concat(allChildren(r)):e.concat([r])}),[]):r};function get_all_units(){return{"%":{scale:e=>["/",e,100],only_scales:!0},$:{prefix:!0,scale:e=>e},deg:{scale:e=>["/",["*",e,"pi"],180],only_scales:!0}}}let all_units$1=get_all_units();function get_unit_of_tree(e){if("unit"===e[0])for(let t in all_units$1)if(all_units$1[t].prefix){if(e[1]===t)return t}else if(e[2]===t)return t;return null}function get_unit_value_of_tree(e){if("unit"===e[0])for(let t in all_units$1)if(all_units$1[t].prefix){if(e[1]===t)return[t,e[2]]}else if(e[2]===t)return[t,e[1]];return null}function remove_duplicate_negatives(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);return"-"===t&&"-"===r[0][0]?remove_duplicate_negatives(r[0][1]):(r=r.map(remove_duplicate_negatives),[t].concat(r))}function normalize_negatives_in_factors(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if(r=r.map(normalize_negatives_in_factors),"*"!==t&&"/"!==t)return[t].concat(r);for(var n=1,i=[],a=0;asort_key(e,t)))):s=[sort_key(a,t)],i.push([o,s]),i}if("unit"===r){let[r,n]=get_unit_value_of_tree(e);if(r){let e=sort_key(n,t);return e[1]+="_"+r,e}}var u=n.length,c=n.map(sort_key,t);return"*"===r?[4,"product",u,c]:"/"===r?[4,"quotient",u,c]:"+"===r?[5,"sum",u,c]:"-"===r?t.ignore_negatives?c[0]:[6,"minus",u,c]:[7,r,u,c]}function arrayCompare(e,t){if(Array.isArray(e)){if(Array.isArray(t)){let r=Math.min(e.length,t.length);for(let n=0;nt.length?1:0}return 1}return Array.isArray(t)||et?1:0}function compare_function(e,t,r={}){return arrayCompare(sort_key(e,r),sort_key(t,r))}function coeff_factors_from_term(e,t){if("string"==typeof e){let r=t.indexOf(e);-1===r&&(t.push(e),r=t.length-1);let n=[];return n[r]=1,{factor_contains:n,coeff:1}}if(Array.isArray(e)){let r=e[0],n=e.slice(1);if("*"===r){let e=[],r=[];for(let i of n)if("string"!=typeof i)if(Array.isArray(i)&&"^"===i[0]||"-"===i[0]){let n=coeff_factors_from_term(i,t);for(let e in n.factor_contains)void 0===r[e]&&(r[e]=0),r[e]+=n.factor_contains[e];1!==n.coeff&&e.push(n.coeff)}else e.push(i);else{let e=t.indexOf(i);-1===e&&(t.push(i),e=t.length-1),void 0===r[e]&&(r[e]=0),r[e]++}return e=0===e.length?1:1===e.length?e[0]:["*",...e],{factor_contains:r,coeff:e}}if("^"===r){let e=n[0],r=n[1],i=[];if("string"==typeof e&&Number.isFinite(r)){let n=t.indexOf(e);return-1===n&&(t.push(e),n=t.length-1),i[n]=r,{factor_contains:i,coeff:1}}}else{if("-"===r){let e=coeff_factors_from_term(n[0],t),r=-1;return"number"==typeof e.coeff?r*=e.coeff:r=["-",e.coeff],{factor_contains:e.factor_contains,coeff:r}}if("/"===r){let e=coeff_factors_from_term(n[0],t),r=["/",e.coeff,n[1]];return{factor_contains:e.factor_contains,coeff:r}}}}return{factor_contains:[],coeff:e}}function default_order(e,t){void 0===t&&(t={});var r=get_tree(e);return r=normalize_negatives(r=flatten$5(r)),normalize_negatives(function e(r){if(!Array.isArray(r))return r;var n=r[0],i=r.slice(1);if(i=i.map(e),"+"===n){let e=[],r=[],n=[];for(let t of i){let i=coeff_factors_from_term(t,e);r.push(i.factor_contains),n.push(i.coeff)}let a=[];for(let[t,n]of e.entries()){let e={varname:n,exponents_in_term:[]};for(let n=0;ne.varname[...t,-r.exponents_in_term[e]]),[]);r.push(sort_key(n[e],t)),o.push(r)}let s=[];for(let[e,t]of i.entries())s.push({term:t,sort_key:o[e]});s.sort(((e,t)=>arrayCompare(e.sort_key,t.sort_key))),i=s.map((e=>e.term))}else if("*"===n){let e=[],r=[];for(let t of i)["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t[0])?r.push(t):e.push(t);e.sort(((e,r)=>compare_function(e,r,t))),i=[...e,...r]}else if("="===n||"and"===n||"or"===n||"ne"===n||"union"===n||"intersect"===n)i.sort(((e,r)=>compare_function(e,r,t)));else if(">"===n||"ge"===n)i=i.reverse(),n=">"===n?"<":"le";else if("gts"===n){var a=i[0],o=i[1];if("tuple"!==a[0]||"tuple"!==o[0])throw new Error("Badly formed ast");n="lts",i=[a=["tuple"].concat(a.slice(1).reverse()),o=["tuple"].concat(o.slice(1).reverse())]}else 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toFixed$2(e,t){if(isNaN(e)||!isFinite(e))return String(e);var r=splitNumber(e),n="number"==typeof t?roundDigits(r,r.exponent+1+t):r,i=n.coefficients,a=n.exponent+1,o=a+(t||0);return i.length0?"."+i.join(""):"")+"e"+(a>=0?"+":"")+a}function toPrecision(e,t,r){if(isNaN(e)||!isFinite(e))return String(e);var n=r&&void 0!==r.lowerExp?r.lowerExp:-3,i=r&&void 0!==r.upperExp?r.upperExp:5,a=splitNumber(e),o=t?roundDigits(a,t):a;if(o.exponent=i)return toExponential$1(e,t);var s=o.coefficients,u=o.exponent;s.length0?u:0;return c<(s=zeros$1(-u).concat(s)).length-1&&s.splice(c+1,0,"."),o.sign+s.join("")}function roundDigits(e,t){for(var r={sign:e.sign,coefficients:e.coefficients,exponent:e.exponent},n=r.coefficients;t<=0;)n.unshift(0),r.exponent++,t++;if(n.length>t&&n.splice(t,n.length-t)[0]>=5){var i=t-1;for(n[i]++;10===n[i];)n.pop(),0===i&&(n.unshift(0),r.exponent++,i++),n[--i]++}return r}function zeros$1(e){for(var t=[],r=0;r0||!(e<0)&&1/e==1/0)^(t>0||!(t<0)&&1/t==1/0)?-e:e}function 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dArray.isArray(e)&&1===e.length?e[0]:e));if(2!==n.length)throw new Error("Only two dimensions matrix are supported");return n.forEach((function(e){if(!isNumber$1(e)||!isInteger$1(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(n)+")")})),u(r?this.clone():this,n[0],n[1],t)},i.prototype.reshape=function(e,t){if(!isArray$1(e))throw new TypeError("Array expected");if(2!==e.length)throw new Error("Sparse matrices can only be reshaped in two dimensions");e.forEach((function(t){if(!isNumber$1(t)||!isInteger$1(t)||t<=-2||0===t)throw new TypeError("Invalid size, must contain positive integers or -1 (size: "+format$1(e)+")")}));var r=this._size[0]*this._size[1];if(r!==(e=processSizesWildcard(e,r))[0]*e[1])throw new Error("Reshaping sparse matrix will result in the wrong number of elements");var n=t?this.clone():this;if(this._size[0]===e[0]&&this._size[1]===e[1])return n;for(var i=[],a=0;a=n&&b<=a&&h(e._values[x],b-n,y-o)}else{for(var _={},w=g;w 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n(e,t);var[i,a]="".concat(e,"e").split("e"),o=Math.ceil(Number("".concat(i,"e").concat(Number(a)+t)));return[i,a]="".concat(o,"e").split("e"),Number("".concat(i,"e").concat(Number(a)-t))}})})),createCeil=factory(name$40,dependencies$40,(e=>{var{typed:t,config:r,round:n,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}=e,u=createAlgorithm11({typed:t,equalScalar:a}),c=createAlgorithm12({typed:t,DenseMatrix:s}),l=createAlgorithm14({typed:t}),f=createCeilNumber({typed:t,config:r,round:n});return t("ceil",{number:f.signatures.number,"number,number":f.signatures["number,number"],Complex:function(e){return e.ceil()},"Complex, number":function(e,t){return e.ceil(t)},"Complex, BigNumber":function(e,t){return e.ceil(t.toNumber())},BigNumber:function(e){return nearlyEqual(e,n(e),r.epsilon)?n(e):e.ceil()},"BigNumber, BigNumber":function(e,t){return nearlyEqual(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),Decimal.ROUND_CEIL)},Fraction:function(e){return e.ceil()},"Fraction, number":function(e,t){return e.ceil(t)},"Fraction, BigNumber":function(e,t){return e.ceil(t.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},"Array, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(i(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return a(e,0)?o(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3$="cube",dependencies$3$=["typed"],createCube=factory(name$3$,dependencies$3$,(e=>{var{typed:t}=e;return t(name$3$,{number:cubeNumber,Complex:function(e){return e.mul(e).mul(e)},BigNumber:function(e){return e.times(e).times(e)},Fraction:function(e){return e.pow(3)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return 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number":function(e,t){return e.floor(t)},"Fraction, BigNumber":function(e,t){return e.floor(t.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},"Array, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(i(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return a(e,0)?o(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3W="algorithm01",dependencies$3W=["typed"],createAlgorithm01=factory(name$3W,dependencies$3W,(e=>{var{typed:t}=e;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,l=r._ptr,f=r._size,p=r._datatype;if(o.length!==f.length)throw new DimensionError(o.length,f.length);if(o[0]!==f[0]||o[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+f+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,d,h=o[0],y=o[1],g="string"==typeof s&&s===p?s:void 0,v=g?t.find(n,[g,g]):n,x=[];for(m=0;m{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A,M=a&&l?[]:void 0,S=[],E=[],T=a&&l?[]:void 0,O=a&&l?[]:void 0,C=[],k=[];for(w=0;w{var{typed:t,DenseMatrix:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=i;"string"==typeof l&&(f=l,n=t.convert(n,f),d=t.find(i,[f,f]));for(var h=[],y=[],g=[],v=0;v{var{typed:t}=e;return function(e,n,i){var a,o=e._data,s=e._size,u=e._datatype,c=n._data,l=n._size,f=n._datatype,p=[];if(s.length!==l.length)throw new DimensionError(s.length,l.length);for(var m=0;m0?r(d,0,p,p[0],o,c):[];return e.createDenseMatrix({data:h,size:p,datatype:a})};function r(e,t,n,i,a,o){var s=[];if(t===n.length-1)for(var u=0;u{var{typed:t,matrix:r,equalScalar:n,BigNumber:i,DenseMatrix:a}=e,o=createAlgorithm01({typed:t}),s=createAlgorithm04({typed:t,equalScalar:n}),u=createAlgorithm10({typed:t,DenseMatrix:a}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t});return t(name$3S,{"number, number":gcdNumber,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function gcd must be integer numbers");var r=new i(0);for(;!t.isZero();){var n=e.mod(t);e=t,t=n}return e.lt(r)?e.neg():e},"Fraction, Fraction":function(e,t){return e.gcd(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return u(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return l(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return l(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i{var{typed:t,equalScalar:r}=e;return function(e,n,i,a){var o=e._data,s=e._size,u=e._datatype,c=n._values,l=n._index,f=n._ptr,p=n._size,m=n._datatype;if(s.length!==p.length)throw new DimensionError(s.length,p.length);if(s[0]!==p[0]||s[1]!==p[1])throw new RangeError("Dimension mismatch. Matrix A ("+s+") must match Matrix B ("+p+")");if(!c)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var d,h=s[0],y=s[1],g=r,v=0,x=i;"string"==typeof u&&u===m&&(d=u,g=t.find(r,[d,d]),v=t.convert(0,d),x=t.find(i,[d,d]));for(var b=[],_=[],w=[],N=0;N{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._size,s=e._datatype,u=n._values,c=n._size,l=n._datatype;if(o.length!==c.length)throw new DimensionError(o.length,c.length);if(o[0]!==c[0]||o[1]!==c[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+c+")");var f,p=o[0],m=o[1],d=r,h=0,y=i;"string"==typeof s&&s===l&&(f=s,d=t.find(r,[f,f]),h=t.convert(0,f),y=t.find(i,[f,f]));for(var g=a&&u?[]:void 0,v=[],x=[],b=g?[]:void 0,_=[],w=[],N=0;N{var{typed:t,matrix:r,equalScalar:n}=e,i=createAlgorithm02({typed:t,equalScalar:n}),a=createAlgorithm06({typed:t,equalScalar:n}),o=createAlgorithm11({typed:t,equalScalar:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3P,{"number, number":lcmNumber,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function lcm must be integer numbers");if(e.isZero())return e;if(t.isZero())return t;var r=e.times(t);for(;!t.isZero();){var n=t;t=e.mod(n),e=n}return r.div(e).abs()},"Fraction, Fraction":function(e,t){return e.lcm(t)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return o(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return o(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return u(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return u(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i{var{typed:t,config:r,Complex:n}=e;return t(name$3O,{number:function(e){return e>=0||r.predictable?log10Number(e):new n(e,0).log().div(Math.LN10)},Complex:function(e){return new n(e).log().div(Math.LN10)},BigNumber:function(e){return!e.isNegative()||r.predictable?e.log():new n(e.toNumber(),0).log().div(Math.LN10)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3N="log2",dependencies$3N=["typed","config","Complex"],createLog2=factory(name$3N,dependencies$3N,(e=>{var{typed:t,config:r,Complex:n}=e;return t(name$3N,{number:function(e){return e>=0||r.predictable?log2Number(e):i(new n(e,0))},Complex:i,BigNumber:function(e){return!e.isNegative()||r.predictable?e.log(2):i(new n(e.toNumber(),0))},"Array | Matrix":function(e){return deepMap(e,this)}});function i(e){var t=Math.sqrt(e.re*e.re+e.im*e.im);return new n(Math.log2?Math.log2(t):Math.log(t)/Math.LN2,Math.atan2(e.im,e.re)/Math.LN2)}})),name$3M="algorithm03",dependencies$3M=["typed"],createAlgorithm03=factory(name$3M,dependencies$3M,(e=>{var{typed:t}=e;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,l=r._ptr,f=r._size,p=r._datatype;if(o.length!==f.length)throw new DimensionError(o.length,f.length);if(o[0]!==f[0]||o[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+f+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,d=o[0],h=o[1],y=0,g=n;"string"==typeof s&&s===p&&(m=s,y=t.convert(0,m),g=t.find(n,[m,m]));for(var v=[],x=0;x{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A=a&&l?[]:void 0,M=[],S=[],E=A?[]:void 0,T=A?[]:void 0,O=[],C=[];for(w=0;w{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm02({typed:t,equalScalar:n}),o=createAlgorithm03({typed:t}),s=createAlgorithm05({typed:t,equalScalar:n}),u=createAlgorithm11({typed:t,equalScalar:n}),c=createAlgorithm12({typed:t,DenseMatrix:i}),l=createAlgorithm13({typed:t}),f=createAlgorithm14({typed:t});return t(name$3K,{"number, number":modNumber,"BigNumber, BigNumber":function(e,t){if(t.isNeg())throw new Error("Cannot calculate mod for a negative divisor");return t.isZero()?e:e.mod(t)},"Fraction, Fraction":function(e,t){if(t.compare(0)<0)throw new Error("Cannot calculate mod for a negative divisor");return e.compare(0)>=0?e.mod(t):e.mod(t).add(t).mod(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return l(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return u(e,t,this,!1)},"DenseMatrix, any":function(e,t){return f(e,t,this,!1)},"any, SparseMatrix":function(e,t){return c(t,e,this,!0)},"any, DenseMatrix":function(e,t){return f(t,e,this,!0)},"Array, any":function(e,t){return f(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return f(r(t),e,this,!0).valueOf()}})})),name$3J="multiplyScalar",dependencies$3J=["typed"],createMultiplyScalar=factory(name$3J,dependencies$3J,(e=>{var{typed:t}=e;return t("multiplyScalar",{"number, number":multiplyNumber,"Complex, Complex":function(e,t){return e.mul(t)},"BigNumber, BigNumber":function(e,t){return e.times(t)},"Fraction, Fraction":function(e,t){return e.mul(t)},"number | Fraction | BigNumber | Complex, Unit":function(e,t){var r=t.clone();return r.value=null===r.value?r._normalize(e):this(r.value,e),r},"Unit, number | Fraction | BigNumber | Complex":function(e,t){var r=e.clone();return r.value=null===r.value?r._normalize(t):this(r.value,t),r},"Unit, Unit":function(e,t){return e.multiply(t)}})})),name$3I="multiply",dependencies$3I=["typed","matrix","addScalar","multiplyScalar","equalScalar","dot"],createMultiply=factory(name$3I,dependencies$3I,(e=>{var{typed:t,matrix:r,addScalar:n,multiplyScalar:i,equalScalar:a,dot:o}=e,s=createAlgorithm11({typed:t,equalScalar:a}),u=createAlgorithm14({typed:t});function c(e,t){switch(e.length){case 1:switch(t.length){case 1:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vectors must have the same length");break;case 2:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vector length ("+e[0]+") must match Matrix rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;case 2:switch(t.length){case 1:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix columns ("+e[1]+") must match Vector length ("+t[0]+")");break;case 2:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix A columns ("+e[1]+") must match Matrix B rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix A has "+e.length+" dimensions)")}}function l(e,r){if("dense"!==r.storage())throw new Error("Support for SparseMatrix not implemented");return function(e,r){var a,o=e._data,s=e._size,u=e._datatype,c=r._data,l=r._size,f=r._datatype,p=s[0],m=l[1],d=n,h=i;u&&f&&u===f&&"string"==typeof u&&(a=u,d=t.find(n,[a,a]),h=t.find(i,[a,a]));for(var y=[],g=0;gM)for(var E=0,T=0;T{var{typed:t,matrix:r,equalScalar:n,BigNumber:i}=e,a=createAlgorithm01({typed:t}),o=createAlgorithm02({typed:t,equalScalar:n}),s=createAlgorithm06({typed:t,equalScalar:n}),u=createAlgorithm11({typed:t,equalScalar:n}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t}),f="Complex number not supported in function nthRoot. Use nthRoots instead.";return t(name$3H,{number:nthRootNumber,"number, number":nthRootNumber,BigNumber:function(e){return p(e,new i(2))},Complex:function(e){throw new Error(f)},"Complex, number":function(e,t){throw new Error(f)},"BigNumber, BigNumber":p,"Array | Matrix":function(e){return this(e,2)},"SparseMatrix, SparseMatrix":function(e,t){if(1===t.density())return s(e,t,this);throw new Error("Root must be non-zero")},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){if(1===t.density())return a(e,t,this,!1);throw new Error("Root must be non-zero")},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){if(1===t.density())return u(t,e,this,!0);throw new Error("Root must be non-zero")},"number | BigNumber, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return this(r(e),t).valueOf()},"number | BigNumber, Array":function(e,t){return this(e,r(t)).valueOf()}});function p(e,t){var r=i.precision,n=i.clone({precision:r+2}),a=new i(0),o=new n(1),s=t.isNegative();if(s&&(t=t.neg()),t.isZero())throw new Error("Root must be non-zero");if(e.isNegative()&&!t.abs().mod(2).equals(1))throw new Error("Root must be odd when a is negative.");if(e.isZero())return s?new n(1/0):0;if(!e.isFinite())return s?a:e;var u=e.abs().pow(o.div(t));return u=e.isNeg()?u.neg():u,new i((s?o.div(u):u).toPrecision(r))}})),name$3G="sign",dependencies$3G=["typed","BigNumber","Fraction","complex"],createSign=factory(name$3G,dependencies$3G,(e=>{var{typed:t,BigNumber:r,complex:n,Fraction:i}=e;return t(name$3G,{number:signNumber,Complex:function(e){return 0===e.im?n(signNumber(e.re)):e.sign()},BigNumber:function(e){return new r(e.cmp(0))},Fraction:function(e){return new i(e.s,1)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){if(!e._isDerived()&&0!==e.units[0].unit.offset)throw new TypeError("sign is ambiguous for units with offset");return this(e.value)}})})),name$3F="sqrt",dependencies$3F=["config","typed","Complex"],createSqrt=factory(name$3F,dependencies$3F,(e=>{var{config:t,typed:r,Complex:n}=e;return r("sqrt",{number:i,Complex:function(e){return e.sqrt()},BigNumber:function(e){return!e.isNegative()||t.predictable?e.sqrt():i(e.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(.5)}});function i(e){return isNaN(e)?NaN:e>=0||t.predictable?Math.sqrt(e):new n(e,0).sqrt()}})),name$3E="square",dependencies$3E=["typed"],createSquare=factory(name$3E,dependencies$3E,(e=>{var{typed:t}=e;return t(name$3E,{number:squareNumber,Complex:function(e){return e.mul(e)},BigNumber:function(e){return e.times(e)},Fraction:function(e){return e.mul(e)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(2)}})})),name$3D="subtract",dependencies$3D=["typed","matrix","equalScalar","addScalar","unaryMinus","DenseMatrix"],createSubtract=factory(name$3D,dependencies$3D,(e=>{var{typed:t,matrix:r,equalScalar:n,addScalar:i,unaryMinus:a,DenseMatrix:o}=e,s=createAlgorithm01({typed:t}),u=createAlgorithm03({typed:t}),c=createAlgorithm05({typed:t,equalScalar:n}),l=createAlgorithm10({typed:t,DenseMatrix:o}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$3D,{"number, number":function(e,t){return e-t},"Complex, Complex":function(e,t){return e.sub(t)},"BigNumber, BigNumber":function(e,t){return e.minus(t)},"Fraction, Fraction":function(e,t){return e.sub(t)},"Unit, Unit":function(e,t){if(null===e.value)throw new Error("Parameter x contains a unit with undefined value");if(null===t.value)throw new Error("Parameter y contains a unit with undefined value");if(!e.equalBase(t))throw new Error("Units do not match");var r=e.clone();return r.value=this(r.value,t.value),r.fixPrefix=!1,r},"SparseMatrix, SparseMatrix":function(e,t){return checkEqualDimensions(e,t),c(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return checkEqualDimensions(e,t),u(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return checkEqualDimensions(e,t),s(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return checkEqualDimensions(e,t),f(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return l(e,a(t),i)},"DenseMatrix, any":function(e,t){return p(e,t,this)},"any, SparseMatrix":function(e,t){return l(t,e,this,!0)},"any, DenseMatrix":function(e,t){return p(t,e,this,!0)},"Array, any":function(e,t){return p(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return p(r(t),e,this,!0).valueOf()}})}));function checkEqualDimensions(e,t){var r=e.size(),n=t.size();if(r.length!==n.length)throw new DimensionError(r.length,n.length)}var name$3C="xgcd",dependencies$3C=["typed","config","matrix","BigNumber"],createXgcd=factory(name$3C,dependencies$3C,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t(name$3C,{"number, number":function(e,t){var i=xgcdNumber(e,t);return"Array"===r.matrix?i:n(i)},"BigNumber, BigNumber":function(e,t){var a,o,s,u,c=new i(0),l=new i(1),f=c,p=l,m=l,d=c;if(!e.isInt()||!t.isInt())throw new Error("Parameters in function xgcd must be integer numbers");for(;!t.isZero();)o=e.div(t).floor(),s=e.mod(t),a=f,f=p.minus(o.times(f)),p=a,a=m,m=d.minus(o.times(m)),d=a,e=t,t=s;u=e.lt(c)?[e.neg(),p.neg(),d.neg()]:[e,e.isZero()?0:p,d];return"Array"===r.matrix?u:n(u)}})})),name$3B="invmod",dependencies$3B=["typed","config","BigNumber","xgcd","equal","smaller","mod","add","isInteger"],createInvmod=factory(name$3B,dependencies$3B,(e=>{var{typed:t,config:r,BigNumber:n,xgcd:i,equal:a,smaller:o,mod:s,add:u,isInteger:c}=e;return t(name$3B,{"number, number":l,"BigNumber, BigNumber":l});function l(e,t){if(!c(e)||!c(t))throw new Error("Parameters in function invmod must be integer numbers");if(e=s(e,t),a(t,0))throw new Error("Divisor must be non zero");var r=i(e,t);r=r.valueOf();var[l,f]=r;return a(l,n(1))?(f=s(f,t),o(f,n(0))&&(f=u(f,t)),f):NaN}})),name$3A="algorithm09",dependencies$3A=["typed","equalScalar"],createAlgorithm09=factory(name$3A,dependencies$3A,(e=>{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A,M=a&&l?[]:void 0,S=[],E=[],T=M?[]:void 0,O=[];for(w=0;w{var{typed:t,matrix:r,equalScalar:n,multiplyScalar:i}=e,a=createAlgorithm02({typed:t,equalScalar:n}),o=createAlgorithm09({typed:t,equalScalar:n}),s=createAlgorithm11({typed:t,equalScalar:n}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3z,{"any, any":i,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,i,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,i,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,i,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,i)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,i,!1)},"DenseMatrix, any":function(e,t){return c(e,t,i,!1)},"any, SparseMatrix":function(e,t){return s(t,e,i,!0)},"any, DenseMatrix":function(e,t){return c(t,e,i,!0)},"Array, any":function(e,t){return c(r(e),t,i,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,i,!0).valueOf()}})}));function bitAndBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitAnd");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero()||t.eq(-1)||e.eq(t))return e;if(t.isZero()||e.eq(-1))return t;if(!e.isFinite()||!t.isFinite()){if(!e.isFinite()&&!t.isFinite())return e.isNegative()===t.isNegative()?e:new r(0);if(!e.isFinite())return t.isNegative()?e:e.isNegative()?new r(0):t;if(!t.isFinite())return e.isNegative()?t:t.isNegative()?new r(0):e}return bitwise(e,t,(function(e,t){return e&t}))}function bitNotBigNumber(e){if(e.isFinite()&&!e.isInteger())throw new Error("Integer expected in function bitNot");var t=e.constructor,r=t.precision;t.config({precision:1e9});var n=e.plus(new t(1));return n.s=-n.s||null,t.config({precision:r}),n}function bitOrBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitOr");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);var n=new r(-1);return e.isZero()||t.eq(n)||e.eq(t)?t:t.isZero()||e.eq(n)?e:e.isFinite()&&t.isFinite()?bitwise(e,t,(function(e,t){return e|t})):!e.isFinite()&&!e.isNegative()&&t.isNegative()||e.isNegative()&&!t.isNegative()&&!t.isFinite()?n:e.isNegative()&&t.isNegative()?e.isFinite()?e:t:e.isFinite()?t:e}function bitwise(e,t,r){var n,i,a,o,s,u=e.constructor,c=+(e.s<0),l=+(t.s<0);if(c){n=decCoefficientToBinaryString(bitNotBigNumber(e));for(var f=0;f0;)r(a[--m],o[--d])===h&&(y=y.plus(g)),g=g.times(v);for(;d>0;)r(s,o[--d])===h&&(y=y.plus(g)),g=g.times(v);return u.config({precision:x}),0===h&&(y.s=-y.s),y}function decCoefficientToBinaryString(e){for(var t=e.d,r=t[0]+"",n=1;n0)if(++s>c)for(s-=c;s--;)u+="0";else s1&&(null!==l[m+1]&&void 0!==l[m+1]||(l[m+1]=0),l[m+1]+=l[m]>>1,l[m]&=1)}return l.reverse()}function bitXor$1(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitXor");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero())return t;if(t.isZero())return e;if(e.eq(t))return new r(0);var n=new r(-1);return e.eq(n)?bitNotBigNumber(t):t.eq(n)?bitNotBigNumber(e):e.isFinite()&&t.isFinite()?bitwise(e,t,(function(e,t){return e^t})):e.isFinite()||t.isFinite()?new r(e.isNegative()===t.isNegative()?1/0:-1/0):n}function leftShiftBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function leftShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:e.isFinite()||t.isFinite()?t.lt(55)?e.times(Math.pow(2,t.toNumber())+""):e.times(new r(2).pow(t)):new r(NaN)}function rightArithShiftBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function rightArithShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:t.isFinite()?t.lt(55)?e.div(Math.pow(2,t.toNumber())+"").floor():e.div(new r(2).pow(t)).floor():e.isNegative()?new r(-1):e.isFinite()?new r(0):new r(NaN)}var name$3y="bitAnd",dependencies$3y=["typed","matrix","equalScalar"],createBitAnd=factory(name$3y,dependencies$3y,(e=>{var{typed:t,matrix:r,equalScalar:n}=e,i=createAlgorithm02({typed:t,equalScalar:n}),a=createAlgorithm06({typed:t,equalScalar:n}),o=createAlgorithm11({typed:t,equalScalar:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3y,{"number, number":bitAndNumber,"BigNumber, BigNumber":bitAndBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3x="bitNot",dependencies$3x=["typed"],createBitNot=factory(name$3x,dependencies$3x,(e=>{var{typed:t}=e;return t(name$3x,{number:bitNotNumber,BigNumber:bitNotBigNumber,"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3w="bitOr",dependencies$3w=["typed","matrix","equalScalar","DenseMatrix"],createBitOr=factory(name$3w,dependencies$3w,(e=>{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm01({typed:t}),o=createAlgorithm04({typed:t,equalScalar:n}),s=createAlgorithm10({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3w,{"number, number":bitOrNumber,"BigNumber, BigNumber":bitOrBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$3v="algorithm07",dependencies$3v=["typed","DenseMatrix"],createAlgorithm07=factory(name$3v,dependencies$3v,(e=>{var{typed:t,DenseMatrix:r}=e;return function(e,i,a){var o=e._size,s=e._datatype,u=i._size,c=i._datatype;if(o.length!==u.length)throw new DimensionError(o.length,u.length);if(o[0]!==u[0]||o[1]!==u[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+u+")");var l,f,p,m=o[0],d=o[1],h=0,y=a;"string"==typeof s&&s===c&&(l=s,h=t.convert(0,l),y=t.find(a,[l,l]));var g=[];for(f=0;f{var{typed:t,matrix:r,DenseMatrix:n}=e,i=createAlgorithm03({typed:t}),a=createAlgorithm07({typed:t,DenseMatrix:n}),o=createAlgorithm12({typed:t,DenseMatrix:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3u,{"number, number":bitXorNumber,"BigNumber, BigNumber":bitXor$1,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3t="arg",dependencies$3t=["typed"],createArg=factory(name$3t,dependencies$3t,(e=>{var{typed:t}=e;return t(name$3t,{number:function(e){return Math.atan2(0,e)},BigNumber:function(e){return e.constructor.atan2(0,e)},Complex:function(e){return e.arg()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3s="conj",dependencies$3s=["typed"],createConj=factory(name$3s,dependencies$3s,(e=>{var{typed:t}=e;return t(name$3s,{number:function(e){return e},BigNumber:function(e){return e},Complex:function(e){return e.conjugate()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3r="im",dependencies$3r=["typed"],createIm=factory(name$3r,dependencies$3r,(e=>{var{typed:t}=e;return t(name$3r,{number:function(e){return 0},BigNumber:function(e){return e.mul(0)},Fraction:function(e){return e.mul(0)},Complex:function(e){return e.im},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3q="re",dependencies$3q=["typed"],createRe=factory(name$3q,dependencies$3q,(e=>{var{typed:t}=e;return t(name$3q,{number:function(e){return e},BigNumber:function(e){return e},Fraction:function(e){return e},Complex:function(e){return e.re},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3p="not",dependencies$3p=["typed"],createNot=factory(name$3p,dependencies$3p,(e=>{var{typed:t}=e;return t(name$3p,{number:notNumber,Complex:function(e){return 0===e.re&&0===e.im},BigNumber:function(e){return e.isZero()||e.isNaN()},Unit:function(e){return null===e.value||this(e.value)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3o="or",dependencies$3o=["typed","matrix","equalScalar","DenseMatrix"],createOr=factory(name$3o,dependencies$3o,(e=>{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm05({typed:t,equalScalar:n}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3o,{"number, number":orNumber,"Complex, Complex":function(e,t){return 0!==e.re||0!==e.im||0!==t.re||0!==t.im},"BigNumber, BigNumber":function(e,t){return!e.isZero()&&!e.isNaN()||!t.isZero()&&!t.isNaN()},"Unit, Unit":function(e,t){return this(e.value||0,t.value||0)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$3n="xor",dependencies$3n=["typed","matrix","DenseMatrix"],createXor=factory(name$3n,dependencies$3n,(e=>{var{typed:t,matrix:r,DenseMatrix:n}=e,i=createAlgorithm03({typed:t}),a=createAlgorithm07({typed:t,DenseMatrix:n}),o=createAlgorithm12({typed:t,DenseMatrix:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3n,{"number, number":xorNumber,"Complex, Complex":function(e,t){return(0!==e.re||0!==e.im)!=(0!==t.re||0!==t.im)},"BigNumber, BigNumber":function(e,t){return(!e.isZero()&&!e.isNaN())!=(!t.isZero()&&!t.isNaN())},"Unit, Unit":function(e,t){return this(e.value||0,t.value||0)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3m="concat",dependencies$3m=["typed","matrix","isInteger"],createConcat=factory(name$3m,dependencies$3m,(e=>{var{typed:t,matrix:r,isInteger:n}=e;return t(name$3m,{"...Array | Matrix | number | BigNumber":function(e){var t,i,a=e.length,o=-1,s=!1,u=[];for(t=0;t0&&o>i)throw new IndexError(o,i+1)}else{var l=clone$3(c).valueOf(),f=arraySize(l);if(u[t]=l,i=o,o=f.length-1,t>0&&o!==i)throw new DimensionError(i+1,o+1)}}if(0===u.length)throw new SyntaxError("At least one matrix expected");for(var p=u.shift();u.length;)p=_concat(p,u.shift(),o,0);return s?r(p):p},"...string":function(e){return e.join("")}})}));function _concat(e,t,r,n){if(n{var{typed:t,Index:r,matrix:n,range:i}=e;return t(name$3l,{"Matrix, number":a,"Array, number":function(e,t){return a(n(clone$3(e)),t).valueOf()}});function a(e,t){if(2!==e.size().length)throw new Error("Only two dimensional matrix is supported");validateIndex(t,e.size()[1]);var n=i(0,e.size()[0]),a=new r(n,t);return e.subset(a)}})),name$3k="count",dependencies$3k=["typed","size","prod"],createCount=factory(name$3k,dependencies$3k,(e=>{var{typed:t,size:r,prod:n}=e;return t(name$3k,{string:function(e){return e.length},"Matrix | Array":function(e){return n(r(e))}})})),name$3j="cross",dependencies$3j=["typed","matrix","subtract","multiply"],createCross=factory(name$3j,dependencies$3j,(e=>{var{typed:t,matrix:r,subtract:n,multiply:i}=e;return t(name$3j,{"Matrix, Matrix":function(e,t){return r(a(e.toArray(),t.toArray()))},"Matrix, Array":function(e,t){return r(a(e.toArray(),t))},"Array, Matrix":function(e,t){return r(a(e,t.toArray()))},"Array, Array":a});function a(e,t){var r=Math.max(arraySize(e).length,arraySize(t).length);e=squeeze$1(e),t=squeeze$1(t);var a=arraySize(e),o=arraySize(t);if(1!==a.length||1!==o.length||3!==a[0]||3!==o[0])throw new RangeError("Vectors with length 3 expected (Size A = ["+a.join(", ")+"], B = ["+o.join(", ")+"])");var s=[n(i(e[1],t[2]),i(e[2],t[1])),n(i(e[2],t[0]),i(e[0],t[2])),n(i(e[0],t[1]),i(e[1],t[0]))];return r>1?[s]:s}})),name$3i="diag",dependencies$3i=["typed","matrix","DenseMatrix","SparseMatrix"],createDiag=factory(name$3i,dependencies$3i,(e=>{var{typed:t,matrix:r,DenseMatrix:n,SparseMatrix:i}=e;return t(name$3i,{Array:function(e){return a(e,0,arraySize(e),null)},"Array, number":function(e,t){return a(e,t,arraySize(e),null)},"Array, BigNumber":function(e,t){return a(e,t.toNumber(),arraySize(e),null)},"Array, string":function(e,t){return a(e,0,arraySize(e),t)},"Array, number, string":function(e,t,r){return a(e,t,arraySize(e),r)},"Array, BigNumber, string":function(e,t,r){return a(e,t.toNumber(),arraySize(e),r)},Matrix:function(e){return a(e,0,e.size(),e.storage())},"Matrix, number":function(e,t){return a(e,t,e.size(),e.storage())},"Matrix, BigNumber":function(e,t){return a(e,t.toNumber(),e.size(),e.storage())},"Matrix, string":function(e,t){return a(e,0,e.size(),t)},"Matrix, number, string":function(e,t,r){return a(e,t,e.size(),r)},"Matrix, BigNumber, string":function(e,t,r){return a(e,t.toNumber(),e.size(),r)}});function a(e,t,a,o){if(!isInteger$1(t))throw new TypeError("Second parameter in function diag must be an integer");var s=t>0?t:0,u=t<0?-t:0;switch(a.length){case 1:return function(e,t,r,a,o,s){var u=[a+o,a+s];if(r&&"sparse"!==r&&"dense"!==r)throw new TypeError("Unknown matrix type ".concat(r,'"'));var c="sparse"===r?i.diagonal(u,e,t):n.diagonal(u,e,t);return null!==r?c:c.valueOf()}(e,t,o,a[0],u,s);case 2:return function(e,t,n,i,a,o){if(isMatrix(e)){var s=e.diagonal(t);return null!==n?n!==s.storage()?r(s,n):s:s.valueOf()}for(var u=Math.min(i[0]-a,i[1]-o),c=[],l=0;l1&&void 0!==arguments[1]?arguments[1]:{};return r=null==r?Number.POSITIVE_INFINITY:r,t=null==t?JSON.stringify:t,function n(){"object"!=typeof n.cache&&(n.cache={values:new Map,lru:lruQueue(r||Number.POSITIVE_INFINITY)});for(var i=[],a=0;a{var{typed:t}=e;return t("filter",{"Array, function":_filterCallback,"Matrix, function":function(e,t){return e.create(_filterCallback(e.toArray(),t))},"Array, RegExp":filterRegExp,"Matrix, RegExp":function(e,t){return e.create(filterRegExp(e.toArray(),t))}})}));function _filterCallback(e,t){var r=maxArgumentCount(t);return filter$2(e,(function(e,n,i){return 1===r?t(e):2===r?t(e,[n]):t(e,[n],i)}))}var name$3g="flatten",dependencies$3g=["typed","matrix"],createFlatten=factory(name$3g,dependencies$3g,(e=>{var{typed:t,matrix:r}=e;return t(name$3g,{Array:function(e){return flatten$4(clone$3(e))},Matrix:function(e){var t=flatten$4(clone$3(e.toArray()));return r(t)}})})),name$3f="forEach",dependencies$3f=["typed"],createForEach=factory(name$3f,dependencies$3f,(e=>{var{typed:t}=e;return t(name$3f,{"Array, function":_forEach,"Matrix, function":function(e,t){return e.forEach(t)}})}));function _forEach(e,t){var r=maxArgumentCount(t);!function n(i,a){Array.isArray(i)?forEach$1(i,(function(e,t){n(e,a.concat(t))})):1===r?t(i):2===r?t(i,a):t(i,a,e)}(e,[])}var name$3e="getMatrixDataType",dependencies$3e=["typed"],createGetMatrixDataType=factory(name$3e,dependencies$3e,(e=>{var{typed:t}=e;return t(name$3e,{Array:function(e){return getArrayDataType(e,typeOf$1)},Matrix:function(e){return e.getDataType()}})})),name$3d="identity",dependencies$3d=["typed","config","matrix","BigNumber","DenseMatrix","SparseMatrix"],createIdentity=factory(name$3d,dependencies$3d,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i,DenseMatrix:a,SparseMatrix:o}=e;return t(name$3d,{"":function(){return"Matrix"===r.matrix?n([]):[]},string:function(e){return n(e)},"number | BigNumber":function(e){return u(e,e,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber, string":function(e,t){return u(e,e,t)},"number | BigNumber, number | BigNumber":function(e,t){return u(e,t,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber, number | BigNumber, 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l=resize$1([],c,u),f=e{var{typed:t,matrix:r,multiplyScalar:n}=e;return t(name$3c,{"Matrix, Matrix":function(e,t){return r(i(e.toArray(),t.toArray()))},"Matrix, Array":function(e,t){return r(i(e.toArray(),t))},"Array, Matrix":function(e,t){return r(i(e,t.toArray()))},"Array, Array":i});function i(e,t){if(1===arraySize(e).length&&(e=[e]),1===arraySize(t).length&&(t=[t]),arraySize(e).length>2||arraySize(t).length>2)throw new RangeError("Vectors with dimensions greater then 2 are not supported expected (Size x = "+JSON.stringify(e.length)+", y = "+JSON.stringify(t.length)+")");var r=[],i=[];return e.map((function(e){return t.map((function(t){return i=[],r.push(i),e.map((function(e){return t.map((function(t){return i.push(n(e,t))}))}))}))}))&&r}})),name$3b="map",dependencies$3b=["typed"],createMap=factory(name$3b,dependencies$3b,(e=>{var{typed:t}=e;return t(name$3b,{"Array, function":_map$1,"Matrix, function":function(e,t){return e.map(t)}})}));function _map$1(e,t){var r=maxArgumentCount(t);return function n(i,a){if(Array.isArray(i))return i.map((function(e,t){return n(e,a.concat(t))}));try{return 1===r?t(i):2===r?t(i,a):t(i,a,e)}catch(t){if(t instanceof TypeError&&"data"in t&&"wrongType"===t.data.category){var o="map attempted to call '".concat(t.data.fn,"(").concat(i),s=JSON.stringify(a);throw 2===r?o+=","+s:1!==r&&(o+=",".concat(s,",").concat(e)),o+=")' but argument ".concat(t.data.index+1," of type "),o+="".concat(t.data.actual," does not match expected type "),o+=t.data.expected.join(" or "),new TypeError(o)}throw t}}(e,[])}var name$3a="diff",dependencies$3a=["typed","matrix","subtract","number"],createDiff=factory(name$3a,dependencies$3a,(e=>{var{typed:t,matrix:r,subtract:n,number:i}=e;return t(name$3a,{"Array | Matrix":function(e){return isMatrix(e)?r(o(e.toArray())):o(e)},"Array | Matrix, number":function(e,t){if(!isInteger$1(t))throw new RangeError("Dimension must be a whole number");return isMatrix(e)?r(a(e.toArray(),t)):a(e,t)},"Array | Matrix, BigNumber":function(e,t){return this(e,i(t))}});function a(e,t){if(isMatrix(e)&&(e=e.toArray()),!Array.isArray(e))throw RangeError("Array/Matrix does not have that many dimensions");if(t>0){var r=[];return e.forEach((e=>{r.push(a(e,t-1))})),r}if(0===t)return o(e);throw RangeError("Cannot have negative dimension")}function o(e){var t=[],r=e.length;if(r<2)return e;for(var n=1;n{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t("ones",{"":function(){return"Array"===r.matrix?a([]):a([],"default")},"...number | BigNumber | string":function(e){if("string"==typeof e[e.length-1]){var t=e.pop();return a(e,t)}return"Array"===r.matrix?a(e):a(e,"default")},Array:a,Matrix:function(e){var t=e.storage();return a(e.valueOf(),t)},"Array | Matrix, string":function(e,t){return a(e.valueOf(),t)}});function a(e,t){var r=function(e){var t=!1;return e.forEach((function(e,r,n){isBigNumber(e)&&(t=!0,n[r]=e.toNumber())})),t}(e),a=r?new i(1):1;if(function(e){e.forEach((function(e){if("number"!=typeof 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c(n?p(e,t,r):f(e,t,r))},"BigNumber, BigNumber":function(e,t){return c(m(e,t,new(0,e.constructor)(1)))},"BigNumber, BigNumber, BigNumber":function(e,t,r){return c(m(e,t,r))},"BigNumber, BigNumber, boolean":function(e,t,r){var n=e.constructor;return c(r?d(e,t,new n(1)):m(e,t,new n(1)))},"BigNumber, BigNumber, BigNumber, boolean":function(e,t,r,n){return c(n?d(e,t,r):m(e,t,r))}});function c(e){return"Matrix"===r.matrix?n?n(e):noMatrix():e}function l(e,t){var n=function(e){var t=e.split(":"),r=t.map((function(e){return Number(e)}));if(r.some((function(e){return isNaN(e)})))return null;switch(r.length){case 2:return{start:r[0],end:r[1],step:1};case 3:return{start:r[0],end:r[2],step:r[1]};default:return null}}(e);if(!n)throw new SyntaxError('String "'+e+'" is no valid range');return"BigNumber"===r.number?(void 0===i&&noBignumber(),c((t?d:m)(i(n.start),i(n.end),i(n.step)))):c((t?p:f)(n.start,n.end,n.step))}function f(e,t,r){var n=[],i=e;if(r>0)for(;a(i,t);)n.push(i),i+=r;else if(r<0)for(;s(i,t);)n.push(i),i+=r;return n}function p(e,t,r){var n=[],i=e;if(r>0)for(;o(i,t);)n.push(i),i+=r;else if(r<0)for(;u(i,t);)n.push(i),i+=r;return n}function m(e,t,r){var n=i(0),o=[],u=e;if(r.gt(n))for(;a(u,t);)o.push(u),u=u.plus(r);else if(r.lt(n))for(;s(u,t);)o.push(u),u=u.plus(r);return o}function d(e,t,r){var n=i(0),a=[],s=e;if(r.gt(n))for(;o(s,t);)a.push(s),s=s.plus(r);else if(r.lt(n))for(;u(s,t);)a.push(s),s=s.plus(r);return a}})),name$37="reshape",dependencies$37=["typed","isInteger","matrix"],createReshape=factory(name$37,dependencies$37,(e=>{var{typed:t,isInteger:r}=e;return t(name$37,{"Matrix, Array":function(e,t){return e.reshape(t)},"Array, Array":function(e,t){return t.forEach((function(e){if(!r(e))throw new TypeError("Invalid size for dimension: "+e)})),reshape$1(e,t)}})}));function ArgumentsError(e,t,r,n){if(!(this instanceof ArgumentsError))throw new SyntaxError("Constructor must be called with the new operator");this.fn=e,this.count=t,this.min=r,this.max=n,this.message="Wrong number of arguments in function "+e+" ("+t+" provided, "+r+(null!=n?"-"+n:"")+" expected)",this.stack=(new Error).stack}ArgumentsError.prototype=new Error,ArgumentsError.prototype.constructor=Error,ArgumentsError.prototype.name="ArgumentsError",ArgumentsError.prototype.isArgumentsError=!0;var name$36="resize",dependencies$36=["config","matrix"],createResize=factory(name$36,dependencies$36,(e=>{var{config:t,matrix:r}=e;return function(e,n,i){if(2!==arguments.length&&3!==arguments.length)throw new ArgumentsError("resize",arguments.length,2,3);if(isMatrix(n)&&(n=n.valueOf()),isBigNumber(n[0])&&(n=n.map((function(e){return isBigNumber(e)?e.toNumber():e}))),isMatrix(e))return e.resize(n,i,!0);if("string"==typeof e)return function(e,t,r){if(void 0!==r){if("string"!=typeof r||1!==r.length)throw new TypeError("Single character expected as defaultValue")}else r=" ";if(1!==t.length)throw new DimensionError(t.length,1);var n=t[0];if("number"!=typeof n||!isInteger$1(n))throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(t)+")");if(e.length>n)return e.substring(0,n);if(e.length{var{typed:t,multiply:r,rotationMatrix:n}=e;return t(name$35,{"Array , number | BigNumber | Complex | Unit":function(e,t){return i(e,2),r(n(t),e).toArray()},"Matrix , number | BigNumber | Complex | Unit":function(e,t){return i(e,2),r(n(t),e)},"Array, number | BigNumber | Complex | Unit, Array | Matrix":function(e,t,a){return i(e,3),r(n(t,a),e)},"Matrix, number | BigNumber | Complex | Unit, Array | Matrix":function(e,t,a){return i(e,3),r(n(t,a),e)}});function i(e,t){var r=Array.isArray(e)?arraySize(e):e.size();if(r.length>2)throw new RangeError("Vector must be of dimensions 1x".concat(t));if(2===r.length&&1!==r[1])throw new RangeError("Vector must be of dimensions 1x".concat(t));if(r[0]!==t)throw new RangeError("Vector must be of dimensions 1x".concat(t))}})),name$34="rotationMatrix",dependencies$34=["typed","config","multiplyScalar","addScalar","unaryMinus","norm","matrix","BigNumber","DenseMatrix","SparseMatrix","cos","sin"],createRotationMatrix=factory(name$34,dependencies$34,(e=>{var{typed:t,config:r,multiplyScalar:n,addScalar:i,unaryMinus:a,norm:o,BigNumber:s,matrix:u,DenseMatrix:c,SparseMatrix:l,cos:f,sin:p}=e;return t(name$34,{"":function(){return"Matrix"===r.matrix?u([]):[]},string:function(e){return u(e)},"number | BigNumber | Complex | Unit":function(e){return m(e,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber | Complex | Unit, string":function(e,t){return m(e,t)},"number | BigNumber | Complex | Unit, Array":function(e,t){var r=u(t);return d(r),g(e,r,void 0)},"number | BigNumber | Complex | Unit, Matrix":function(e,t){d(t);var n=t.storage()||("Matrix"===r.matrix?"dense":void 0);return g(e,t,n)},"number | BigNumber | Complex | Unit, Array, string":function(e,t,r){var n=u(t);return d(n),g(e,n,r)},"number | BigNumber | Complex | Unit, Matrix, string":function(e,t,r){return d(t),g(e,t,r)}});function m(e,t){var r=isBigNumber(e)?new s(-1):-1,i=f(e),a=p(e);return y([[i,n(r,a)],[a,i]],t)}function d(e){var t=e.size();if(t.length<1||3!==t[0])throw new RangeError("Vector must be of dimensions 1x3")}function h(e){return e.reduce(((e,t)=>n(e,t)))}function y(e,t){if(t){if("sparse"===t)return new l(e);if("dense"===t)return new c(e);throw new TypeError('Unknown matrix type "'.concat(t,'"'))}return e}function g(e,t,r){var n=o(t);if(0===n)throw new RangeError("Rotation around zero vector");var u=isBigNumber(e)?s:null,c=u?new u(1):1,l=u?new u(-1):-1,m=u?new u(t.get([0])/n):t.get([0])/n,d=u?new u(t.get([1])/n):t.get([1])/n,g=u?new u(t.get([2])/n):t.get([2])/n,v=f(e),x=i(c,a(v)),b=p(e);return y([[i(v,h([m,m,x])),i(h([m,d,x]),h([l,g,b])),i(h([m,g,x]),h([d,b]))],[i(h([m,d,x]),h([g,b])),i(v,h([d,d,x])),i(h([d,g,x]),h([l,m,b]))],[i(h([m,g,x]),h([l,d,b])),i(h([d,g,x]),h([m,b])),i(v,h([g,g,x]))]],r)}})),name$33="row",dependencies$33=["typed","Index","matrix","range"],createRow=factory(name$33,dependencies$33,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e;return t(name$33,{"Matrix, number":a,"Array, number":function(e,t){return a(n(clone$3(e)),t).valueOf()}});function a(e,t){if(2!==e.size().length)throw new Error("Only two dimensional matrix is supported");validateIndex(t,e.size()[0]);var n=i(0,e.size()[1]),a=new r(t,n);return e.subset(a)}})),name$32="size",dependencies$32=["typed","config","?matrix"],createSize=factory(name$32,dependencies$32,(e=>{var{typed:t,config:r,matrix:n}=e;return t(name$32,{Matrix:function(e){return e.create(e.size())},Array:arraySize,string:function(e){return"Array"===r.matrix?[e.length]:n([e.length])},"number | Complex | BigNumber | Unit | boolean | null":function(e){return"Array"===r.matrix?[]:n?n([]):noMatrix()}})})),name$31="squeeze",dependencies$31=["typed","matrix"],createSqueeze=factory(name$31,dependencies$31,(e=>{var{typed:t,matrix:r}=e;return t(name$31,{Array:function(e){return squeeze$1(clone$3(e))},Matrix:function(e){var t=squeeze$1(e.toArray());return Array.isArray(t)?r(t):t},any:function(e){return clone$3(e)}})})),name$30="subset",dependencies$30=["typed","matrix"],createSubset=factory(name$30,dependencies$30,(e=>{var{typed:t,matrix:r}=e;return t(name$30,{"Array, Index":function(e,t){var n=r(e).subset(t);return t.isScalar()?n:n.valueOf()},"Matrix, Index":function(e,t){return e.subset(t)},"Object, Index":_getObjectProperty,"string, Index":_getSubstring,"Array, Index, any":function(e,t,n){return r(clone$3(e)).subset(t,n,void 0).valueOf()},"Array, Index, any, any":function(e,t,n,i){return r(clone$3(e)).subset(t,n,i).valueOf()},"Matrix, Index, any":function(e,t,r){return e.clone().subset(t,r)},"Matrix, Index, any, any":function(e,t,r,n){return e.clone().subset(t,r,n)},"string, Index, string":_setSubstring,"string, Index, string, string":_setSubstring,"Object, Index, any":_setObjectProperty})}));function _getSubstring(e,t){if(!isIndex(t))throw new TypeError("Index expected");if(1!==t.size().length)throw new DimensionError(t.size().length,1);var r=e.length;validateIndex(t.min()[0],r),validateIndex(t.max()[0],r);var n=t.dimension(0),i="";return n.forEach((function(t){i+=e.charAt(t)})),i}function _setSubstring(e,t,r,n){if(!t||!0!==t.isIndex)throw new TypeError("Index expected");if(1!==t.size().length)throw new DimensionError(t.size().length,1);if(void 0!==n){if("string"!=typeof n||1!==n.length)throw new TypeError("Single character expected as defaultValue")}else n=" ";var i=t.dimension(0);if(i.size()[0]!==r.length)throw new DimensionError(i.size()[0],r.length);var a=e.length;validateIndex(t.min()[0]),validateIndex(t.max()[0]);for(var o=[],s=0;sa)for(var u=a-1,c=o.length;u{var{typed:t,matrix:r}=e;return t("transpose",{Array:function(e){return this(r(e)).valueOf()},Matrix:function(e){var t,r=e.size();switch(r.length){case 1:t=e.clone();break;case 2:var n=r[0],i=r[1];if(0===i)throw new RangeError("Cannot transpose a 2D matrix with no columns (size: "+format$1(r)+")");switch(e.storage()){case"dense":t=function(e,t,r){for(var n,i=e._data,a=[],o=0;o{var{typed:t,transpose:r,conj:n}=e;return t(name$2_,{any:function(e){return n(r(e))}})})),name$2Z="zeros",dependencies$2Z=["typed","config","matrix","BigNumber"],createZeros=factory(name$2Z,dependencies$2Z,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t(name$2Z,{"":function(){return"Array"===r.matrix?a([]):a([],"default")},"...number | BigNumber | string":function(e){if("string"==typeof e[e.length-1]){var t=e.pop();return a(e,t)}return"Array"===r.matrix?a(e):a(e,"default")},Array:a,Matrix:function(e){var t=e.storage();return a(e.valueOf(),t)},"Array | Matrix, string":function(e,t){return a(e.valueOf(),t)}});function a(e,t){var r=function(e){var t=!1;return e.forEach((function(e,r,n){isBigNumber(e)&&(t=!0,n[r]=e.toNumber())})),t}(e),a=r?new i(0):0;if(function(e){e.forEach((function(e){if("number"!=typeof e||!isInteger$1(e)||e<0)throw new Error("Parameters in function zeros must be positive integers")}))}(e),t){var o=n(t);return e.length>0?o.resize(e,a):o}var s=[];return e.length>0?resize$1(s,e,a):s}})),name$2Y="fft",dependencies$2Y=["typed","matrix","addScalar","multiplyScalar","divideScalar","exp","tau","i"],createFft=factory(name$2Y,dependencies$2Y,(e=>{var{typed:t,matrix:r,addScalar:n,multiplyScalar:i,divideScalar:a,exp:o,tau:s,i:u}=e;return t(name$2Y,{Array:c,Matrix:function(e){return e.create(c(e.toArray()))}});function c(e){var t=arraySize(e);return 1===t.length?f(e,t[0]):l(e.map((e=>c(e,t.slice(1)))),0)}function l(e,t){var r=arraySize(e);if(0!==t)return new Array(r[0]).fill(0).map(((r,n)=>l(e[n],t-1)));if(1===r.length)return f(e);function n(e){var t=arraySize(e);return new Array(t[1]).fill(0).map(((r,n)=>new Array(t[0]).fill(0).map(((t,r)=>e[r][n]))))}return n(l(n(e),1))}function f(e){var t=e.length;if(1===t)return[e[0]];if(t%2==0){for(var r=[...f(e.filter(((e,t)=>t%2==0))),...f(e.filter(((e,t)=>t%2==1)))],c=0;c{var{typed:t,fft:r,dotDivide:n,conj:i}=e;return t(name$2X,{"Array | Matrix":function(e){var t=isMatrix(e)?e.size():arraySize(e);return n(i(r(i(e))),t.reduce(((e,t)=>e*t),1))}})})),name$2W="erf",dependencies$2W=["typed"],createErf=factory(name$2W,dependencies$2W,(e=>{var{typed:t}=e;return t("name",{number:function(e){var t=Math.abs(e);return t>=MAX_NUM?sign$3(e):t<=THRESH?sign$3(e)*function(e){var t,r=e*e,n=P[0][4]*r,i=r;for(t=0;t<3;t+=1)n=(n+P[0][t])*r,i=(i+Q[0][t])*r;return e*(n+P[0][3])/(i+Q[0][3])}(t):t<=4?sign$3(e)*(1-function(e){var t,r=P[1][8]*e,n=e;for(t=0;t<7;t+=1)r=(r+P[1][t])*e,n=(n+Q[1][t])*e;var i=(r+P[1][7])/(n+Q[1][7]),a=parseInt(16*e)/16,o=(e-a)*(e+a);return Math.exp(-a*a)*Math.exp(-o)*i}(t)):sign$3(e)*(1-function(e){var t,r=1/(e*e),n=P[2][5]*r,i=r;for(t=0;t<4;t+=1)n=(n+P[2][t])*r,i=(i+Q[2][t])*r;var a=r*(n+P[2][4])/(i+Q[2][4]);a=(SQRPI-a)/e,r=parseInt(16*e)/16;var o=(e-r)*(e+r);return Math.exp(-r*r)*Math.exp(-o)*a}(t))},"Array | Matrix":function(e){return 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s=null;if(e.lt("3317044064679887385961981"))s=[2,3,5,7,11,13,17,19,23,29,31,37,41].filter((t=>t{var{number:t,bignumber:r,fraction:n}=e,i={string:!0,number:!0,BigNumber:!0,Fraction:!0},a={number:e=>t(e),BigNumber:r?e=>r(e):noBignumber,Fraction:n?e=>n(e):noFraction};return function(e,t){var r=typeOf$1(e);if(!(r in i))throw new TypeError("Cannot convert "+e+' of type "'+r+'"; valid input types are '+Object.keys(i).join(", "));if(!(t in a))throw new TypeError("Cannot convert "+e+' to type "'+t+'"; valid output types are '+Object.keys(a).join(", "));return t===r?e:a[t](e)}})),name$2L="divideScalar",dependencies$2L=["typed","numeric"],createDivideScalar=factory(name$2L,dependencies$2L,(e=>{var{typed:t,numeric:r}=e;return t(name$2L,{"number, number":function(e,t){return e/t},"Complex, Complex":function(e,t){return e.div(t)},"BigNumber, BigNumber":function(e,t){return e.div(t)},"Fraction, Fraction":function(e,t){return e.div(t)},"Unit, number | Fraction | BigNumber":function(e,t){var n=e.clone(),i=r(1,typeOf$1(t));return n.value=this(null===n.value?n._normalize(i):n.value,t),n},"number | Fraction | BigNumber, Unit":function(e,t){var n=t.clone();n=n.pow(-1);var i=r(1,typeOf$1(e));return n.value=this(e,null===t.value?t._normalize(i):t.value),n},"Unit, Unit":function(e,t){return e.divide(t)}})})),name$2K="pow",dependencies$2K=["typed","config","identity","multiply","matrix","inv","fraction","number","Complex"],createPow=factory(name$2K,dependencies$2K,(e=>{var{typed:t,config:r,identity:n,multiply:i,matrix:a,inv:o,number:s,fraction:u,Complex:c}=e;return t(name$2K,{"number, number":l,"Complex, Complex":function(e,t){return e.pow(t)},"BigNumber, BigNumber":function(e,t){return t.isInteger()||e>=0||r.predictable?e.pow(t):new c(e.toNumber(),0).pow(t.toNumber(),0)},"Fraction, Fraction":function(e,t){var n=e.pow(t);if(null!=n)return n;if(r.predictable)throw new Error("Result of pow is non-rational and cannot be expressed as a fraction");return l(e.valueOf(),t.valueOf())},"Array, number":f,"Array, BigNumber":function(e,t){return f(e,t.toNumber())},"Matrix, number":p,"Matrix, BigNumber":function(e,t){return p(e,t.toNumber())},"Unit, number | BigNumber":function(e,t){return e.pow(t)}});function l(e,t){if(r.predictable&&!isInteger$1(t)&&e<0)try{var n=u(t),i=s(n);if((t===i||Math.abs((t-i)/t)<1e-14)&&n.d%2==1)return(n.n%2==0?1:-1)*Math.pow(-e,t)}catch(e){}return r.predictable&&(e<-1&&t===1/0||e>-1&&e<0&&t===-1/0)?NaN:isInteger$1(t)||e>=0||r.predictable?powNumber(e,t):e*e<1&&t===1/0||e*e>1&&t===-1/0?0:new c(e,0).pow(t,0)}function f(e,t){if(!isInteger$1(t))throw new TypeError("For A^b, b must be an integer (value is "+t+")");var r=arraySize(e);if(2!==r.length)throw new Error("For A^b, A must be 2 dimensional (A has "+r.length+" dimensions)");if(r[0]!==r[1])throw new Error("For A^b, A must be square (size is "+r[0]+"x"+r[1]+")");if(t<0)try{return f(o(e),-t)}catch(e){if("Cannot calculate inverse, determinant is zero"===e.message)throw new TypeError("For A^b, when A is not invertible, b must be a positive integer (value is "+t+")");throw e}for(var a=n(r[0]).valueOf(),s=e;t>=1;)1==(1&t)&&(a=i(s,a)),t>>=1,s=i(s,s);return a}function p(e,t){return a(f(e.valueOf(),t))}})),NO_INT="Number of decimals in function round must be an integer",name$2J="round",dependencies$2J=["typed","matrix","equalScalar","zeros","BigNumber","DenseMatrix"],createRound=factory(name$2J,dependencies$2J,(e=>{var{typed:t,matrix:r,equalScalar:n,zeros:i,BigNumber:a,DenseMatrix:o}=e,s=createAlgorithm11({typed:t,equalScalar:n}),u=createAlgorithm12({typed:t,DenseMatrix:o}),c=createAlgorithm14({typed:t});return t(name$2J,{number:roundNumber,"number, number":roundNumber,"number, BigNumber":function(e,t){if(!t.isInteger())throw new TypeError(NO_INT);return new a(e).toDecimalPlaces(t.toNumber())},Complex:function(e){return e.round()},"Complex, number":function(e,t){if(t%1)throw new TypeError(NO_INT);return e.round(t)},"Complex, 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n(e,0)?i(t.size(),t.storage()):c(t,e,this,!0)},"number | Complex | BigNumber | Fraction, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$2I="log",dependencies$2I=["config","typed","divideScalar","Complex"],createLog=factory(name$2I,dependencies$2I,(e=>{var{typed:t,config:r,divideScalar:n,Complex:i}=e;return t(name$2I,{number:function(e){return e>=0||r.predictable?logNumber(e):new i(e,0).log()},Complex:function(e){return e.log()},BigNumber:function(e){return!e.isNegative()||r.predictable?e.ln():new i(e.toNumber(),0).log()},"Array | Matrix":function(e){return deepMap(e,this)},"any, any":function(e,t){return n(this(e),this(t))}})})),name$2H="log1p",dependencies$2H=["typed","config","divideScalar","log","Complex"],createLog1p=factory(name$2H,dependencies$2H,(e=>{var{typed:t,config:r,divideScalar:n,log:i,Complex:a}=e;return t(name$2H,{number:function(e){return e>=-1||r.predictable?log1p$1(e):o(new a(e,0))},Complex:o,BigNumber:function(e){var t=e.plus(1);return!t.isNegative()||r.predictable?t.ln():o(new a(e.toNumber(),0))},"Array | Matrix":function(e){return deepMap(e,this)},"any, any":function(e,t){return n(this(e),i(t))}});function o(e){var t=e.re+1;return new a(Math.log(Math.sqrt(t*t+e.im*e.im)),Math.atan2(e.im,t))}})),name$2G="nthRoots",dependencies$2G=["config","typed","divideScalar","Complex"],createNthRoots=factory(name$2G,dependencies$2G,(e=>{var{typed:t,config:r,divideScalar:n,Complex:i}=e,a=[function(e){return new i(e,0)},function(e){return new i(0,e)},function(e){return new i(-e,0)},function(e){return new i(0,-e)}];function o(e,t){if(t<0)throw new Error("Root must be greater than zero");if(0===t)throw new Error("Root must be non-zero");if(t%1!=0)throw new Error("Root must be an integer");if(0===e||0===e.abs())return[new i(0,0)];var r,n="number"==typeof e;(n||0===e.re||0===e.im)&&(r=n?2*+(e<0):0===e.im?2*+(e.re<0):2*+(e.im<0)+1);for(var 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f(t,e,this,!0)},"Array, any":function(e,t){return f(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return f(n(t),e,this,!0).valueOf()}})})),name$2E="dotDivide",dependencies$2E=["typed","matrix","equalScalar","divideScalar","DenseMatrix"],createDotDivide=factory(name$2E,dependencies$2E,(e=>{var{typed:t,matrix:r,equalScalar:n,divideScalar:i,DenseMatrix:a}=e,o=createAlgorithm02({typed:t,equalScalar:n}),s=createAlgorithm03({typed:t}),u=createAlgorithm07({typed:t,DenseMatrix:a}),c=createAlgorithm11({typed:t,equalScalar:n}),l=createAlgorithm12({typed:t,DenseMatrix:a}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$2E,{"any, any":i,"SparseMatrix, SparseMatrix":function(e,t){return u(e,t,i,!1)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,i,!0)},"DenseMatrix, SparseMatrix":function(e,t){return s(e,t,i,!1)},"DenseMatrix, DenseMatrix":function(e,t){return f(e,t,i)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, 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Matrix columns must match vector length.");for(var c=0;c{var{typed:t,matrix:r,divideScalar:n,multiplyScalar:i,subtract:a,equalScalar:o,DenseMatrix:s}=e,u=createSolveValidation({DenseMatrix:s});return t(name$2D,{"SparseMatrix, Array | Matrix":function(e,t){return function(e,t){for(var r=(t=u(e,t,!0))._data,c=e._size[0],l=e._size[1],f=e._values,p=e._index,m=e._ptr,d=[],h=0;hh&&(v.push(f[w]),x.push(N))}if(o(g,0))throw new Error("Linear system cannot be solved since matrix is singular");for(var $=n(y,g),A=0,M=x.length;A{var{typed:t,matrix:r,divideScalar:n,multiplyScalar:i,subtract:a,equalScalar:o,DenseMatrix:s}=e,u=createSolveValidation({DenseMatrix:s});return t(name$2C,{"SparseMatrix, Array | Matrix":function(e,t){return function(e,t){for(var r=(t=u(e,t,!0))._data,c=e._size[0],l=e._size[1],f=e._values,p=e._index,m=e._ptr,d=[],h=l-1;h>=0;h--){var y=r[h][0]||0;if(o(y,0))d[h]=[0];else{for(var g=0,v=[],x=[],b=m[h],_=m[h+1]-1;_>=b;_--){var w=p[_];w===h?g=f[_]:w=0;m--){var d=r[m][0]||0,h=void 0;if(o(d,0))h=0;else{var y=p[m][m];if(o(y,0))throw new Error("Linear system cannot be solved since matrix is singular");h=n(d,y);for(var g=m-1;g>=0;g--)r[g]=[a(r[g][0]||0,i(h,p[g][m]))]}f[m]=[h]}return new s({data:f,size:[c,1]})}})),name$2B="lsolveAll",dependencies$2B=["typed","matrix","divideScalar","multiplyScalar","subtract","equalScalar","DenseMatrix"],createLsolveAll=factory(name$2B,dependencies$2B,(e=>{var{typed:t,matrix:r,divideScalar:n,multiplyScalar:i,subtract:a,equalScalar:o,DenseMatrix:s}=e,u=createSolveValidation({DenseMatrix:s});return t(name$2B,{"SparseMatrix, Array | Matrix":function(e,t){return function(e,t){for(var r=[u(e,t,!0)._data.map((e=>e[0]))],c=e._size[0],l=e._size[1],f=e._values,p=e._index,m=e._ptr,d=0;dd&&(v.push(f[N]),x.push($))}if(o(w,0))if(o(g[d],0)){if(0===y){var A=[...g];A[d]=1;for(var M=0,S=x.length;Mnew s({data:e.map((e=>[e])),size:[c,1]})))}(e,t)},"DenseMatrix, Array | Matrix":function(e,t){return c(e,t)},"Array, Array | Matrix":function(e,t){return c(r(e),t).map((e=>e.valueOf()))}});function c(e,t){for(var r=[u(e,t,!0)._data.map((e=>e[0]))],c=e._data,l=e._size[0],f=e._size[1],p=0;pnew s({data:e.map((e=>[e])),size:[l,1]})))}})),name$2A="usolveAll",dependencies$2A=["typed","matrix","divideScalar","multiplyScalar","subtract","equalScalar","DenseMatrix"],createUsolveAll=factory(name$2A,dependencies$2A,(e=>{var{typed:t,matrix:r,divideScalar:n,multiplyScalar:i,subtract:a,equalScalar:o,DenseMatrix:s}=e,u=createSolveValidation({DenseMatrix:s});return t(name$2A,{"SparseMatrix, Array | Matrix":function(e,t){return function(e,t){for(var r=[u(e,t,!0)._data.map((e=>e[0]))],c=e._size[0],l=e._size[1],f=e._values,p=e._index,m=e._ptr,d=l-1;d>=0;d--)for(var h=r.length,y=0;y=b;w--){var N=p[w];N===d?_=f[w]:Nnew s({data:e.map((e=>[e])),size:[c,1]})))}(e,t)},"DenseMatrix, Array | Matrix":function(e,t){return c(e,t)},"Array, Array | Matrix":function(e,t){return c(r(e),t).map((e=>e.valueOf()))}});function c(e,t){for(var r=[u(e,t,!0)._data.map((e=>e[0]))],c=e._data,l=e._size[0],f=e._size[1]-1;f>=0;f--)for(var p=r.length,m=0;m=0;y--)h[y]=a(h[y],c[y][f]);r.push(h)}}else{if(0===m)return[];r.splice(m,1),m-=1,p-=1}else{d[f]=n(d[f],c[f][f]);for(var g=f-1;g>=0;g--)d[g]=a(d[g],i(d[f],c[g][f]))}}return r.map((e=>new s({data:e.map((e=>[e])),size:[l,1]})))}})),name$2z="algorithm08",dependencies$2z=["typed","equalScalar"],createAlgorithm08=factory(name$2z,dependencies$2z,(e=>{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");if(!a||!l)throw new Error("Cannot perform operation on Pattern Sparse Matrices");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));for(var _,w,N,$,A=[],M=[],S=[],E=[],T=[],O=0;O{var{typed:t,matrix:r,equalScalar:n,zeros:i,DenseMatrix:a}=e,o=createAlgorithm01({typed:t}),s=createAlgorithm02({typed:t,equalScalar:n}),u=createAlgorithm08({typed:t,equalScalar:n}),c=createAlgorithm10({typed:t,DenseMatrix:a}),l=createAlgorithm11({typed:t,equalScalar:n}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$2y,{"number, number":leftShiftNumber,"BigNumber, BigNumber":leftShiftBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return u(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return s(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return f(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return n(t,0)?e.clone():l(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return n(t,0)?e.clone():p(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return n(e,0)?i(t.size(),t.storage()):c(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return n(e,0)?i(t.size(),t.storage()):p(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return this(r(e),t).valueOf()},"number | BigNumber, Array":function(e,t){return this(e,r(t)).valueOf()}})})),name$2x="rightArithShift",dependencies$2x=["typed","matrix","equalScalar","zeros","DenseMatrix"],createRightArithShift=factory(name$2x,dependencies$2x,(e=>{var{typed:t,matrix:r,equalScalar:n,zeros:i,DenseMatrix:a}=e,o=createAlgorithm01({typed:t}),s=createAlgorithm02({typed:t,equalScalar:n}),u=createAlgorithm08({typed:t,equalScalar:n}),c=createAlgorithm10({typed:t,DenseMatrix:a}),l=createAlgorithm11({typed:t,equalScalar:n}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$2x,{"number, number":rightArithShiftNumber,"BigNumber, BigNumber":rightArithShiftBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return u(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return s(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return f(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return 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o,s=typeOf$1(e),u=typeOf$1(t);if(!("number"!==s&&"BigNumber"!==s&&"Fraction"!==s||"number"!==u&&"BigNumber"!==u&&"Fraction"!==u))return"0"!==(o=r(e,t)).toString()?o>0?1:-1:naturalSort(s,u);if("Array"===s||"Matrix"===s||"Array"===u||"Matrix"===u)return 0!==(o=i(this,e,t))?o:naturalSort(s,u);if(s!==u)return naturalSort(s,u);if("Complex"===s)return compareComplexNumbers(e,t);if("Unit"===s)return e.equalBase(t)?this(e.value,t.value):a(this,e.formatUnits(),t.formatUnits());if("boolean"===s)return n(e,t);if("string"===s)return naturalSort(e,t);if("Object"===s)return function(e,t,r){var n=Object.keys(t),i=Object.keys(r);n.sort(naturalSort),i.sort(naturalSort);var o=a(e,n,i);if(0!==o)return o;for(var s=0;sr.length?1:t.lengtht.re?1:e.ret.im?1:e.im{var{typed:t,matrix:r}=e,n=createAlgorithm13({typed:t}),i=createAlgorithm14({typed:t});return t(name$2s,{"any, any":compareText$1,"DenseMatrix, DenseMatrix":function(e,t){return n(e,t,compareText$1)},"Array, Array":function(e,t){return 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name$2q="equalText",dependencies$2q=["typed","compareText","isZero"],createEqualText=factory(name$2q,dependencies$2q,(e=>{var{typed:t,compareText:r,isZero:n}=e;return t(name$2q,{"any, any":function(e,t){return n(r(e,t))}})})),name$2p="smaller",dependencies$2p=["typed","config","matrix","DenseMatrix"],createSmaller=factory(name$2p,dependencies$2p,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2p,{"boolean, boolean":function(e,t){return e{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2o,{"boolean, boolean":function(e,t){return e<=t},"number, number":function(e,t){return e<=t||nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.lte(t)||nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return 1!==e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2n="larger",dependencies$2n=["typed","config","matrix","DenseMatrix"],createLarger=factory(name$2n,dependencies$2n,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2n,{"boolean, boolean":function(e,t){return e>t},"number, number":function(e,t){return e>t&&!nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.gt(t)&&!nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return 1===e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2m="largerEq",dependencies$2m=["typed","config","matrix","DenseMatrix"],createLargerEq=factory(name$2m,dependencies$2m,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2m,{"boolean, boolean":function(e,t){return e>=t},"number, number":function(e,t){return e>=t||nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.gte(t)||nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return-1!==e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2l="deepEqual",dependencies$2l=["typed","equal"],createDeepEqual=factory(name$2l,dependencies$2l,(e=>{var{typed:t,equal:r}=e;return t(name$2l,{"any, any":function(e,t){return n(e.valueOf(),t.valueOf())}});function n(e,t){if(Array.isArray(e)){if(Array.isArray(t)){var i=e.length;if(i!==t.length)return!1;for(var a=0;a{var{typed:t,config:r,equalScalar:n,matrix:i,DenseMatrix:a}=e,o=createAlgorithm03({typed:t}),s=createAlgorithm07({typed:t,DenseMatrix:a}),u=createAlgorithm12({typed:t,DenseMatrix:a}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t});return t("unequal",{"any, any":function(e,t){return null===e?null!==t:null===t?null!==e:void 0===e?void 0!==t:void 0===t?void 0!==e:f(e,t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,f)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,f,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,f,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,f)},"Array, Array":function(e,t){return this(i(e),i(t)).valueOf()},"Array, Matrix":function(e,t){return this(i(e),t)},"Matrix, Array":function(e,t){return this(e,i(t))},"SparseMatrix, any":function(e,t){return u(e,t,f,!1)},"DenseMatrix, any":function(e,t){return l(e,t,f,!1)},"any, SparseMatrix":function(e,t){return u(t,e,f,!0)},"any, DenseMatrix":function(e,t){return l(t,e,f,!0)},"Array, any":function(e,t){return l(i(e),t,f,!1).valueOf()},"any, Array":function(e,t){return l(i(t),e,f,!0).valueOf()}});function f(e,t){return!n(e,t)}}));factory(name$2k,["typed","equalScalar"],(e=>{var{typed:t,equalScalar:r}=e;return t(name$2k,{"any, any":function(e,t){return null===e?null!==t:null===t?null!==e:void 0===e?void 0!==t:void 0===t?void 0!==e:!r(e,t)}})}));var name$2j="partitionSelect",dependencies$2j=["typed","isNumeric","isNaN","compare"],createPartitionSelect=factory(name$2j,dependencies$2j,(e=>{var{typed:t,isNumeric:r,isNaN:n,compare:i}=e,a=i,o=(e,t)=>-i(e,t);return t(name$2j,{"Array | Matrix, number":function(e,t){return s(e,t,a)},"Array | Matrix, number, string":function(e,t,r){if("asc"===r)return s(e,t,a);if("desc"===r)return s(e,t,o);throw new Error('Compare string must be "asc" or "desc"')},"Array | Matrix, number, function":s});function s(e,t,r){if(!isInteger$1(t)||t<0)throw new Error("k must be a non-negative integer");if(isMatrix(e)){if(e.size().length>1)throw new Error("Only one dimensional matrices supported");return u(e.valueOf(),t,r)}if(Array.isArray(e))return u(e,t,r)}function u(e,t,i){if(t>=e.length)throw new Error("k out of bounds");for(var a=0;a=0){var f=e[c];e[c]=e[u],e[u]=f,--c}else++u;i(e[u],l)>0&&--u,t<=u?s=u:o=u+1}return e[t]}})),name$2i="sort",dependencies$2i=["typed","matrix","compare","compareNatural"],createSort=factory(name$2i,dependencies$2i,(e=>{var{typed:t,matrix:r,compare:n,compareNatural:i}=e,a=n,o=(e,t)=>-n(e,t);return t(name$2i,{Array:function(e){return u(e),e.sort(a)},Matrix:function(e){return c(e),r(e.toArray().sort(a),e.storage())},"Array, function":function(e,t){return u(e),e.sort(t)},"Matrix, function":function(e,t){return c(e),r(e.toArray().sort(t),e.storage())},"Array, string":function(e,t){return u(e),e.sort(s(t))},"Matrix, string":function(e,t){return c(e),r(e.toArray().sort(s(t)),e.storage())}});function s(e){if("asc"===e)return a;if("desc"===e)return o;if("natural"===e)return i;throw new Error('String "asc", "desc", or "natural" expected')}function u(e){if(1!==arraySize(e).length)throw new Error("One dimensional array expected")}function c(e){if(1!==e.size().length)throw new Error("One dimensional matrix expected")}})),name$2h="max",dependencies$2h=["typed","config","numeric","larger"],createMax=factory(name$2h,dependencies$2h,(e=>{var{typed:t,config:r,numeric:n,larger:i}=e;return t(name$2h,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return reduce$2(e,t.valueOf(),a)},"...":function(e){if(containsCollections(e))throw new TypeError("Scalar values expected in function max");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw improveErrorMessage(e,"max",t)}}function o(e){var t;if(deepForEach(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw improveErrorMessage(t,"max",e)}})),void 0===t)throw new Error("Cannot calculate max of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),name$2g="min",dependencies$2g=["typed","config","numeric","smaller"],createMin=factory(name$2g,dependencies$2g,(e=>{var{typed:t,config:r,numeric:n,smaller:i}=e;return t(name$2g,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return reduce$2(e,t.valueOf(),a)},"...":function(e){if(containsCollections(e))throw new TypeError("Scalar values expected in function min");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw improveErrorMessage(e,"min",t)}}function o(e){var t;if(deepForEach(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw improveErrorMessage(t,"min",e)}})),void 0===t)throw new Error("Cannot calculate min of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),name$2f="ImmutableDenseMatrix",dependencies$2f=["smaller","DenseMatrix"],createImmutableDenseMatrixClass=factory(name$2f,dependencies$2f,(e=>{var{smaller:t,DenseMatrix:r}=e;function n(e,t){if(!(this instanceof n))throw new SyntaxError("Constructor must be called with the new operator");if(t&&!isString$1(t))throw new Error("Invalid datatype: "+t);if(isMatrix(e)||isArray$1(e)){var i=new r(e,t);this._data=i._data,this._size=i._size,this._datatype=i._datatype,this._min=null,this._max=null}else if(e&&isArray$1(e.data)&&isArray$1(e.size))this._data=e.data,this._size=e.size,this._datatype=e.datatype,this._min=void 0!==e.min?e.min:null,this._max=void 0!==e.max?e.max:null;else{if(e)throw new TypeError("Unsupported type of data ("+typeOf$1(e)+")");this._data=[],this._size=[0],this._datatype=t,this._min=null,this._max=null}}return n.prototype=new r,n.prototype.type="ImmutableDenseMatrix",n.prototype.isImmutableDenseMatrix=!0,n.prototype.subset=function(e){switch(arguments.length){case 1:var t=r.prototype.subset.call(this,e);return isMatrix(t)?new n({data:t._data,size:t._size,datatype:t._datatype}):t;case 2:case 3:throw new Error("Cannot invoke set subset on an Immutable Matrix instance");default:throw new SyntaxError("Wrong number of arguments")}},n.prototype.set=function(){throw new Error("Cannot invoke set on an Immutable Matrix instance")},n.prototype.resize=function(){throw new Error("Cannot invoke resize on an Immutable Matrix instance")},n.prototype.reshape=function(){throw new Error("Cannot invoke reshape on an Immutable Matrix instance")},n.prototype.clone=function(){return new n({data:clone$3(this._data),size:clone$3(this._size),datatype:this._datatype})},n.prototype.toJSON=function(){return{mathjs:"ImmutableDenseMatrix",data:this._data,size:this._size,datatype:this._datatype}},n.fromJSON=function(e){return new n(e)},n.prototype.swapRows=function(){throw new Error("Cannot invoke swapRows on an Immutable Matrix instance")},n.prototype.min=function(){if(null===this._min){var e=null;this.forEach((function(r){(null===e||t(r,e))&&(e=r)})),this._min=null!==e?e:void 0}return this._min},n.prototype.max=function(){if(null===this._max){var e=null;this.forEach((function(r){(null===e||t(e,r))&&(e=r)})),this._max=null!==e?e:void 0}return this._max},n}),{isClass:!0}),name$2e="Index",dependencies$2e=["ImmutableDenseMatrix"],createIndexClass=factory(name$2e,dependencies$2e,(e=>{var{ImmutableDenseMatrix:t}=e;function r(e){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");this._dimensions=[],this._isScalar=!0;for(var t=0,i=arguments.length;t{var{smaller:t,larger:r}=e,n=1/Math.log((1+Math.sqrt(5))/2);function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._minimum=null,this._size=0}function a(e,t,r){t.left.right=t.right,t.right.left=t.left,r.degree--,r.child===t&&(r.child=t.right),0===r.degree&&(r.child=null),t.left=e,t.right=e.right,e.right=t,t.right.left=t,t.parent=null,t.mark=!1}function o(e,t){var r=t.parent;r&&(t.mark?(a(e,t,r),o(r)):t.mark=!0)}i.prototype.type="FibonacciHeap",i.prototype.isFibonacciHeap=!0,i.prototype.insert=function(e,r){var n={key:e,value:r,degree:0};if(this._minimum){var i=this._minimum;n.left=i,n.right=i.right,i.right=n,n.right.left=n,t(e,i.key)&&(this._minimum=n)}else n.left=n,n.right=n,this._minimum=n;return this._size++,n},i.prototype.size=function(){return this._size},i.prototype.clear=function(){this._minimum=null,this._size=0},i.prototype.isEmpty=function(){return 0===this._size},i.prototype.extractMinimum=function(){var e=this._minimum;if(null===e)return e;for(var i=this._minimum,a=e.degree,o=e.child;a>0;){var u=o.right;o.left.right=o.right,o.right.left=o.left,o.left=i,o.right=i.right,i.right=o,o.right.left=o,o.parent=null,o=u,a--}return e.left.right=e.right,e.right.left=e.left,i=e===e.right?null:function(e,i){var a,o=Math.floor(Math.log(i)*n)+1,u=new Array(o),c=0,l=e;if(l)for(c++,l=l.right;l!==e;)c++,l=l.right;for(;c>0;){for(var f=l.degree,p=l.right;a=u[f];){if(r(l.key,a.key)){var m=a;a=l,l=m}s(a,l),u[f]=null,f++}u[f]=l,l=p,c--}e=null;for(var d=0;d{var{addScalar:t,equalScalar:r,FibonacciHeap:n}=e;function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._values=[],this._heap=new n}return i.prototype.type="Spa",i.prototype.isSpa=!0,i.prototype.set=function(e,t){if(this._values[e])this._values[e].value=t;else{var r=this._heap.insert(e,t);this._values[e]=r}},i.prototype.get=function(e){var t=this._values[e];return t?t.value:0},i.prototype.accumulate=function(e,r){var n=this._values[e];n?n.value=t(n.value,r):(n=this._heap.insert(e,r),this._values[e]=n)},i.prototype.forEach=function(e,t,n){var i=this._heap,a=this._values,o=[],s=i.extractMinimum();for(s&&o.push(s);s&&s.key<=t;)s.key>=e&&(r(s.value,0)||n(s.key,s.value,this)),(s=i.extractMinimum())&&o.push(s);for(var u=0;u{var t,r,n,{on:i,config:a,addScalar:o,subtract:s,multiplyScalar:u,divideScalar:c,pow:l,abs:f,fix:p,round:m,equal:d,isNumeric:h,format:y,number:g,Complex:v,BigNumber:x,Fraction:b}=e,_=g;function w(e,t){if(!(this instanceof w))throw new Error("Constructor must be called with the new operator");if(null!=e&&!h(e)&&!isComplex(e))throw new TypeError("First parameter in Unit constructor must be number, BigNumber, Fraction, Complex, or undefined");if(void 0!==t&&("string"!=typeof t||""===t))throw new TypeError("Second parameter in Unit constructor must be a string");if(void 0!==t){var r=w.parse(t);this.units=r.units,this.dimensions=r.dimensions}else{this.units=[{unit:z,prefix:k.NONE,power:0}],this.dimensions=[];for(var n=0;n="0"&&e<="9"}function A(){r++,n=t.charAt(r)}function M(e){r=e,n=t.charAt(r)}function S(){var e="",t=r;if("+"===n?A():"-"===n&&(e+=n,A()),!function(e){return e>="0"&&e<="9"||"."===e}(n))return M(t),null;if("."===n){if(e+=n,A(),!$(n))return M(t),null}else{for(;$(n);)e+=n,A();"."===n&&(e+=n,A())}for(;$(n);)e+=n,A();if("E"===n||"e"===n){var i="",a=r;if(i+=n,A(),"+"!==n&&"-"!==n||(i+=n,A()),!$(n))return M(a),e;for(e+=i;$(n);)e+=n,A()}return e}function E(){for(var e="";$(n)||w.isValidAlpha(n);)e+=n,A();var t=e.charAt(0);return w.isValidAlpha(t)?e:null}function T(e){return n===e?(A(),e):null}w.prototype.type="Unit",w.prototype.isUnit=!0,w.parse=function(e,i){if(i=i||{},r=-1,n="","string"!=typeof(t=e))throw new TypeError("Invalid argument in Unit.parse, string expected");var o=new w;o.units=[];var s=1,u=!1;A(),N();var c=S(),l=null;if(c){if("BigNumber"===a.number)l=new x(c);else if("Fraction"===a.number)try{l=new b(c)}catch(e){l=parseFloat(c)}else l=parseFloat(c);N(),T("*")?(s=1,u=!0):T("/")&&(s=-1,u=!0)}for(var f=[],p=1;;){for(N();"("===n;)f.push(s),p*=s,s=1,A(),N();var m=void 0;if(!n)break;var d=n;if(null===(m=E()))throw new SyntaxError('Unexpected "'+d+'" in "'+t+'" at index '+r.toString());var h=O(m);if(null===h)throw new SyntaxError('Unit "'+m+'" not found.');var y=s*p;if(N(),T("^")){N();var g=S();if(null===g)throw new SyntaxError('In "'+e+'", "^" must be followed by a floating-point number');y*=g}o.units.push({unit:h.unit,prefix:h.prefix,power:y});for(var v=0;v1||Math.abs(this.units[0].power-1)>1e-15)},w.prototype._normalize=function(e){if(null==e||0===this.units.length)return e;for(var t=e,r=w._getNumberConverter(typeOf$1(e)),n=0;n{if(hasOwnProperty$2(R,e)){var t=R[e];return{unit:t,prefix:t.prefixes[""]}}for(var r in R)if(hasOwnProperty$2(R,r)&&endsWith(e,r)){var n=R[r],i=e.length-r.length,a=e.substring(0,i),o=hasOwnProperty$2(n.prefixes,a)?n.prefixes[a]:void 0;if(void 0!==o)return{unit:n,prefix:o}}return null}),{hasher:e=>e[0],limit:100});function C(e){return e.equalBase(I.NONE)&&null!==e.value&&!a.predictable?e.value:e}w.isValuelessUnit=function(e){return null!==O(e)},w.prototype.hasBase=function(e){if("string"==typeof e&&(e=I[e]),!e)return!1;for(var t=0;t1e-12)return!1;return!0},w.prototype.equalBase=function(e){for(var t=0;t1e-12)return!1;return!0},w.prototype.equals=function(e){return this.equalBase(e)&&d(this.value,e.value)},w.prototype.multiply=function(e){for(var t=this.clone(),r=0;r1e-12&&(hasOwnProperty$2(F,s)?n.push({unit:F[s].unit,prefix:F[s].prefix,power:r.dimensions[o]||0}):a=!0)}n.length1e-12){if(!hasOwnProperty$2(L.si,n))throw new Error("Cannot express custom unit "+n+" in SI units");t.push({unit:L.si[n].unit,prefix:L.si[n].prefix,power:e.dimensions[r]||0})}}return e.units=t,e.fixPrefix=!0,e.skipAutomaticSimplification=!0,e},w.prototype.formatUnits=function(){for(var e="",t="",r=0,n=0,i=0;i0?(r++,e+=" "+this.units[i].prefix.name+this.units[i].unit.name,Math.abs(this.units[i].power-1)>1e-15&&(e+="^"+this.units[i].power)):this.units[i].power<0&&n++;if(n>0)for(var a=0;a0?(t+=" "+this.units[a].prefix.name+this.units[a].unit.name,Math.abs(this.units[a].power+1)>1e-15&&(t+="^"+-this.units[a].power)):(t+=" "+this.units[a].prefix.name+this.units[a].unit.name,t+="^"+this.units[a].power));e=e.substr(1),t=t.substr(1),r>1&&n>0&&(e="("+e+")"),n>1&&r>0&&(t="("+t+")");var o=e;return r>0&&n>0&&(o+=" / "),o+=t},w.prototype.format=function(e){var t=this.skipAutomaticSimplification||null===this.value?this.clone():this.simplify(),r=!1;for(var n in void 0!==t.value&&null!==t.value&&isComplex(t.value)&&(r=Math.abs(t.value.re)<1e-14),t.units)hasOwnProperty$2(t.units,n)&&t.units[n].unit&&("VA"===t.units[n].unit.name&&r?t.units[n].unit=R.VAR:"VAR"!==t.units[n].unit.name||r||(t.units[n].unit=R.VA));1!==t.units.length||t.fixPrefix||Math.abs(t.units[0].power-Math.round(t.units[0].power))<1e-14&&(t.units[0].prefix=t._bestPrefix());var i=t._denormalize(t.value),a=null!==t.value?y(i,e||{}):"",o=t.formatUnits();return t.value&&isComplex(t.value)&&(a="("+a+")"),o.length>0&&a.length>0&&(a+=" "),a+=o},w.prototype._bestPrefix=function(){if(1!==this.units.length)throw new Error("Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!");if(Math.abs(this.units[0].power-Math.round(this.units[0].power))>=1e-14)throw new Error("Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!");var e=null!==this.value?f(this.value):0,t=f(this.units[0].unit.value),r=this.units[0].prefix;if(0===e)return r;var n=this.units[0].power,i=Math.log(e/Math.pow(r.value*t,n))/Math.LN10-1.2;if(i>-2.200001&&i<1.800001)return r;i=Math.abs(i);var a=this.units[0].unit.prefixes;for(var o in a)if(hasOwnProperty$2(a,o)){var s=a[o];if(s.scientific){var u=Math.abs(Math.log(e/Math.pow(s.value*t,n))/Math.LN10-1.2);(u0))},R={meter:{name:"meter",base:I.LENGTH,prefixes:k.LONG,value:1,offset:0},inch:{name:"inch",base:I.LENGTH,prefixes:k.NONE,value:.0254,offset:0},foot:{name:"foot",base:I.LENGTH,prefixes:k.NONE,value:.3048,offset:0},yard:{name:"yard",base:I.LENGTH,prefixes:k.NONE,value:.9144,offset:0},mile:{name:"mile",base:I.LENGTH,prefixes:k.NONE,value:1609.344,offset:0},link:{name:"link",base:I.LENGTH,prefixes:k.NONE,value:.201168,offset:0},rod:{name:"rod",base:I.LENGTH,prefixes:k.NONE,value:5.0292,offset:0},chain:{name:"chain",base:I.LENGTH,prefixes:k.NONE,value:20.1168,offset:0},angstrom:{name:"angstrom",base:I.LENGTH,prefixes:k.NONE,value:1e-10,offset:0},m:{name:"m",base:I.LENGTH,prefixes:k.SHORT,value:1,offset:0},in:{name:"in",base:I.LENGTH,prefixes:k.NONE,value:.0254,offset:0},ft:{name:"ft",base:I.LENGTH,prefixes:k.NONE,value:.3048,offset:0},yd:{name:"yd",base:I.LENGTH,prefixes:k.NONE,value:.9144,offset:0},mi:{name:"mi",base:I.LENGTH,prefixes:k.NONE,value:1609.344,offset:0},li:{name:"li",base:I.LENGTH,prefixes:k.NONE,value:.201168,offset:0},rd:{name:"rd",base:I.LENGTH,prefixes:k.NONE,value:5.02921,offset:0},ch:{name:"ch",base:I.LENGTH,prefixes:k.NONE,value:20.1168,offset:0},mil:{name:"mil",base:I.LENGTH,prefixes:k.NONE,value:254e-7,offset:0},m2:{name:"m2",base:I.SURFACE,prefixes:k.SQUARED,value:1,offset:0},sqin:{name:"sqin",base:I.SURFACE,prefixes:k.NONE,value:64516e-8,offset:0},sqft:{name:"sqft",base:I.SURFACE,prefixes:k.NONE,value:.09290304,offset:0},sqyd:{name:"sqyd",base:I.SURFACE,prefixes:k.NONE,value:.83612736,offset:0},sqmi:{name:"sqmi",base:I.SURFACE,prefixes:k.NONE,value:2589988.110336,offset:0},sqrd:{name:"sqrd",base:I.SURFACE,prefixes:k.NONE,value:25.29295,offset:0},sqch:{name:"sqch",base:I.SURFACE,prefixes:k.NONE,value:404.6873,offset:0},sqmil:{name:"sqmil",base:I.SURFACE,prefixes:k.NONE,value:6.4516e-10,offset:0},acre:{name:"acre",base:I.SURFACE,prefixes:k.NONE,value:4046.86,offset:0},hectare:{name:"hectare",base:I.SURFACE,prefixes:k.NONE,value:1e4,offset:0},m3:{name:"m3",base:I.VOLUME,prefixes:k.CUBIC,value:1,offset:0},L:{name:"L",base:I.VOLUME,prefixes:k.SHORT,value:.001,offset:0},l:{name:"l",base:I.VOLUME,prefixes:k.SHORT,value:.001,offset:0},litre:{name:"litre",base:I.VOLUME,prefixes:k.LONG,value:.001,offset:0},cuin:{name:"cuin",base:I.VOLUME,prefixes:k.NONE,value:16387064e-12,offset:0},cuft:{name:"cuft",base:I.VOLUME,prefixes:k.NONE,value:.028316846592,offset:0},cuyd:{name:"cuyd",base:I.VOLUME,prefixes:k.NONE,value:.764554857984,offset:0},teaspoon:{name:"teaspoon",base:I.VOLUME,prefixes:k.NONE,value:5e-6,offset:0},tablespoon:{name:"tablespoon",base:I.VOLUME,prefixes:k.NONE,value:15e-6,offset:0},drop:{name:"drop",base:I.VOLUME,prefixes:k.NONE,value:5e-8,offset:0},gtt:{name:"gtt",base:I.VOLUME,prefixes:k.NONE,value:5e-8,offset:0},minim:{name:"minim",base:I.VOLUME,prefixes:k.NONE,value:6.161152e-8,offset:0},fluiddram:{name:"fluiddram",base:I.VOLUME,prefixes:k.NONE,value:36966911e-13,offset:0},fluidounce:{name:"fluidounce",base:I.VOLUME,prefixes:k.NONE,value:2957353e-11,offset:0},gill:{name:"gill",base:I.VOLUME,prefixes:k.NONE,value:.0001182941,offset:0},cc:{name:"cc",base:I.VOLUME,prefixes:k.NONE,value:1e-6,offset:0},cup:{name:"cup",base:I.VOLUME,prefixes:k.NONE,value:.0002365882,offset:0},pint:{name:"pint",base:I.VOLUME,prefixes:k.NONE,value:.0004731765,offset:0},quart:{name:"quart",base:I.VOLUME,prefixes:k.NONE,value:.0009463529,offset:0},gallon:{name:"gallon",base:I.VOLUME,prefixes:k.NONE,value:.003785412,offset:0},beerbarrel:{name:"beerbarrel",base:I.VOLUME,prefixes:k.NONE,value:.1173478,offset:0},oilbarrel:{name:"oilbarrel",base:I.VOLUME,prefixes:k.NONE,value:.1589873,offset:0},hogshead:{name:"hogshead",base:I.VOLUME,prefixes:k.NONE,value:.238481,offset:0},fldr:{name:"fldr",base:I.VOLUME,prefixes:k.NONE,value:36966911e-13,offset:0},floz:{name:"floz",base:I.VOLUME,prefixes:k.NONE,value:2957353e-11,offset:0},gi:{name:"gi",base:I.VOLUME,prefixes:k.NONE,value:.0001182941,offset:0},cp:{name:"cp",base:I.VOLUME,prefixes:k.NONE,value:.0002365882,offset:0},pt:{name:"pt",base:I.VOLUME,prefixes:k.NONE,value:.0004731765,offset:0},qt:{name:"qt",base:I.VOLUME,prefixes:k.NONE,value:.0009463529,offset:0},gal:{name:"gal",base:I.VOLUME,prefixes:k.NONE,value:.003785412,offset:0},bbl:{name:"bbl",base:I.VOLUME,prefixes:k.NONE,value:.1173478,offset:0},obl:{name:"obl",base:I.VOLUME,prefixes:k.NONE,value:.1589873,offset:0},g:{name:"g",base:I.MASS,prefixes:k.SHORT,value:.001,offset:0},gram:{name:"gram",base:I.MASS,prefixes:k.LONG,value:.001,offset:0},ton:{name:"ton",base:I.MASS,prefixes:k.SHORT,value:907.18474,offset:0},t:{name:"t",base:I.MASS,prefixes:k.SHORT,value:1e3,offset:0},tonne:{name:"tonne",base:I.MASS,prefixes:k.LONG,value:1e3,offset:0},grain:{name:"grain",base:I.MASS,prefixes:k.NONE,value:6479891e-11,offset:0},dram:{name:"dram",base:I.MASS,prefixes:k.NONE,value:.0017718451953125,offset:0},ounce:{name:"ounce",base:I.MASS,prefixes:k.NONE,value:.028349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"expr"');if(keywords.has(e))throw new Error('Illegal function name, "'+e+'" is a reserved keyword');this.name=e,this.params=t.map((function(e){return e&&e.name||e})),this.types=t.map((function(e){return e&&e.type||"any"})),this.expr=r}function i(e,t){var r=getPrecedence(e,t),n=getPrecedence(e.expr,t);return"all"===t||null!==n&&n<=r}return n.prototype=new r,n.prototype.type="FunctionAssignmentNode",n.prototype.isFunctionAssignmentNode=!0,n.prototype._compile=function(e,r){var n=Object.create(r);forEach$1(this.params,(function(e){n[e]=!0}));var i=this.expr._compile(e,n),a=this.name,o=this.params,s=join(this.types,","),u=a+"("+join(this.params,", ")+")";return function(e,r,n){var c={};c[s]=function(){for(var t=Object.create(r),a=0;a'+escape$1(this.params[n])+"");var a=this.expr.toHTML(e);return i(this,t)&&(a='('+a+')'),''+escape$1(this.name)+'('+r.join(',')+')='+a},n.prototype._toTex=function(e){var t=e&&e.parenthesis?e.parenthesis:"keep",r=this.expr.toTex(e);return i(this,t)&&(r="\\left(".concat(r,"\\right)")),"\\mathrm{"+this.name+"}\\left("+this.params.map(toSymbol).join(",")+"\\right):="+r},n}),{isClass:!0,isNode:!0}),name$1m="IndexNode",dependencies$1m=["Node","size"],createIndexNode=factory(name$1m,dependencies$1m,(e=>{var{Node:t,size:r}=e;function n(e,t){if(!(this instanceof n))throw new SyntaxError("Constructor must be called with the new operator");if(this.dimensions=e,this.dotNotation=t||!1,!Array.isArray(e)||!e.every(isNode))throw new TypeError('Array containing Nodes expected for parameter "dimensions"');if(this.dotNotation&&!this.isObjectProperty())throw new Error("dotNotation only applicable for object properties")}return n.prototype=new t,n.prototype.type="IndexNode",n.prototype.isIndexNode=!0,n.prototype._compile=function(e,t){var n=map$2(this.dimensions,(function(n,i){if(n.filter((e=>e.isSymbolNode&&"end"===e.name)).length>0){var a=Object.create(t);a.end=!0;var o=n._compile(e,a);return function(e,t,n){if(!isMatrix(n)&&!isArray$1(n)&&!isString$1(n))throw new TypeError('Cannot resolve "end": context must be a Matrix, Array, or string but is '+typeOf$1(n));var a=r(n).valueOf(),s=Object.create(t);return s.end=a[i],o(e,s,n)}}return n._compile(e,t)})),i=getSafeProperty(e,"index");return function(e,t,r){var a=map$2(n,(function(n){return n(e,t,r)}));return i(...a)}},n.prototype.forEach=function(e){for(var t=0;t.'+escape$1(this.getObjectProperty())+"":'['+t.join(',')+']'},n.prototype._toTex=function(e){var t=this.dimensions.map((function(t){return t.toTex(e)}));return this.dotNotation?"."+this.getObjectProperty():"_{"+t.join(",")+"}"},n}),{isClass:!0,isNode:!0}),name$1l="ObjectNode",dependencies$1l=["Node"],createObjectNode=factory(name$1l,dependencies$1l,(e=>{var{Node:t}=e;function r(e){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");if(this.properties=e||{},e&&("object"!=typeof e||!Object.keys(e).every((function(t){return isNode(e[t])}))))throw new TypeError("Object containing Nodes expected")}return r.prototype=new t,r.prototype.type="ObjectNode",r.prototype.isObjectNode=!0,r.prototype._compile=function(e,t){var r={};for(var n in this.properties)if(hasOwnProperty$2(this.properties,n)){var i=stringify(n),a=JSON.parse(i);if(!isSafeProperty(this.properties,a))throw new Error('No access to property "'+a+'"');r[a]=this.properties[n]._compile(e,t)}return function(e,t,n){var i={};for(var a in r)hasOwnProperty$2(r,a)&&(i[a]=r[a](e,t,n));return i}},r.prototype.forEach=function(e){for(var t in this.properties)hasOwnProperty$2(this.properties,t)&&e(this.properties[t],"properties["+stringify(t)+"]",this)},r.prototype.map=function(e){var t={};for(var n in this.properties)hasOwnProperty$2(this.properties,n)&&(t[n]=this._ifNode(e(this.properties[n],"properties["+stringify(n)+"]",this)));return new r(t)},r.prototype.clone=function(){var e={};for(var t in this.properties)hasOwnProperty$2(this.properties,t)&&(e[t]=this.properties[t]);return new r(e)},r.prototype._toString=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push(stringify(r)+": "+this.properties[r].toString(e));return"{"+t.join(", ")+"}"},r.prototype.toJSON=function(){return{mathjs:"ObjectNode",properties:this.properties}},r.fromJSON=function(e){return new r(e.properties)},r.prototype.toHTML=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push(''+escape$1(r)+':'+this.properties[r].toHTML(e));return'{'+t.join(',')+'}'},r.prototype._toTex=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push("\\mathbf{"+r+":} & "+this.properties[r].toTex(e)+"\\\\");return"\\left\\{\\begin{array}{ll}".concat(t.join("\n"),"\\end{array}\\right\\}")},r}),{isClass:!0,isNode:!0}),name$1k="OperatorNode",dependencies$1k=["Node"],createOperatorNode=factory(name$1k,dependencies$1k,(e=>{var{Node:t}=e;function r(e,t,n,i,a){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");if("string"!=typeof e)throw new TypeError('string expected for parameter "op"');if("string"!=typeof t)throw new TypeError('string expected for parameter "fn"');if(!Array.isArray(n)||!n.every(isNode))throw new TypeError('Array containing Nodes expected for parameter "args"');this.implicit=!0===i,this.isPercentage=!0===a,this.op=e,this.fn=t,this.args=n||[]}function n(e,t,r,n,i){var a,o=getPrecedence(e,t),s=getAssociativity(e,t);if("all"===t||n.length>2&&"OperatorNode:add"!==e.getIdentifier()&&"OperatorNode:multiply"!==e.getIdentifier())return n.map((function(e){switch(e.getContent().type){case"ArrayNode":case"ConstantNode":case"SymbolNode":case"ParenthesisNode":return!1;default:return!0}}));switch(n.length){case 0:a=[];break;case 1:var u=getPrecedence(n[0],t);if(i&&null!==u){var c,l;if("keep"===t?(c=n[0].getIdentifier(),l=e.getIdentifier()):(c=n[0].getContent().getIdentifier(),l=e.getContent().getIdentifier()),!1===properties[o][l].latexLeftParens){a=[!1];break}if(!1===properties[u][c].latexParens){a=[!1];break}}if(null===u){a=[!1];break}if(u<=o){a=[!0];break}a=[!1];break;case 2:var f,p,m=getPrecedence(n[0],t),d=isAssociativeWith(e,n[0],t);f=null!==m&&(m===o&&"right"===s&&!d||m=2&&"OperatorNode:multiply"===e.getIdentifier()&&e.implicit&&"auto"===t&&"hide"===r&&(a=n.map((function(e,t){var r="ParenthesisNode"===e.getIdentifier();return!(!a[t]&&!r)}))),a}return r.prototype=new t,r.prototype.type="OperatorNode",r.prototype.isOperatorNode=!0,r.prototype._compile=function(e,t){if("string"!=typeof this.fn||!isSafeMethod(e,this.fn))throw e[this.fn]?new Error('No access to function "'+this.fn+'"'):new Error("Function "+this.fn+' missing in provided namespace "math"');var r=getSafeProperty(e,this.fn),n=map$2(this.args,(function(r){return r._compile(e,t)}));if(1===n.length){var i=n[0];return function(e,t,n){return r(i(e,t,n))}}if(2===n.length){var a=n[0],o=n[1];return function(e,t,n){return r(a(e,t,n),o(e,t,n))}}return function(e,t,i){return r.apply(null,map$2(n,(function(r){return r(e,t,i)})))}},r.prototype.forEach=function(e){for(var t=0;t2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())){var f=i.map((function(t,r){return t=t.toString(e),a[r]&&(t="("+t+")"),t}));return this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?f.join(" "):f.join(" "+this.op+" ")}return this.fn+"("+this.args.join(", ")+")"},r.prototype.toJSON=function(){return{mathjs:"OperatorNode",op:this.op,fn:this.fn,args:this.args,implicit:this.implicit,isPercentage:this.isPercentage}},r.fromJSON=function(e){return new r(e.op,e.fn,e.args,e.implicit,e.isPercentage)},r.prototype.toHTML=function(e){var t=e&&e.parenthesis?e.parenthesis:"keep",r=e&&e.implicit?e.implicit:"hide",i=this.args,a=n(this,t,r,i,!1);if(1===i.length){var o=getAssociativity(this,t),s=i[0].toHTML(e);return a[0]&&(s='('+s+')'),"right"===o?''+escape$1(this.op)+""+s:s+''+escape$1(this.op)+""}if(2===i.length){var u=i[0].toHTML(e),c=i[1].toHTML(e);return a[0]&&(u='('+u+')'),a[1]&&(c='('+c+')'),this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?u+''+c:u+''+escape$1(this.op)+""+c}var l=i.map((function(t,r){return t=t.toHTML(e),a[r]&&(t='('+t+')'),t}));return i.length>2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())?this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?l.join(''):l.join(''+escape$1(this.op)+""):''+escape$1(this.fn)+'('+l.join(',')+')'},r.prototype._toTex=function(e){var t=e&&e.parenthesis?e.parenthesis:"keep",r=e&&e.implicit?e.implicit:"hide",i=this.args,a=n(this,t,r,i,!0),o=latexOperators[this.fn];if(o=void 0===o?this.op:o,1===i.length){var s=getAssociativity(this,t),u=i[0].toTex(e);return a[0]&&(u="\\left(".concat(u,"\\right)")),"right"===s?o+u:u+o}if(2===i.length){var c=i[0],l=c.toTex(e);a[0]&&(l="\\left(".concat(l,"\\right)"));var f,p=i[1].toTex(e);switch(a[1]&&(p="\\left(".concat(p,"\\right)")),f="keep"===t?c.getIdentifier():c.getContent().getIdentifier(),this.getIdentifier()){case"OperatorNode:divide":return o+"{"+l+"}{"+p+"}";case"OperatorNode:pow":switch(l="{"+l+"}",p="{"+p+"}",f){case"ConditionalNode":case"OperatorNode:divide":l="\\left(".concat(l,"\\right)")}break;case"OperatorNode:multiply":if(this.implicit&&"hide"===r)return l+"~"+p}return l+o+p}if(i.length>2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())){var m=i.map((function(t,r){return t=t.toTex(e),a[r]&&(t="\\left(".concat(t,"\\right)")),t}));return"OperatorNode:multiply"===this.getIdentifier()&&this.implicit?m.join("~"):m.join(o)}return"\\mathrm{"+this.fn+"}\\left("+i.map((function(t){return t.toTex(e)})).join(",")+"\\right)"},r.prototype.getIdentifier=function(){return this.type+":"+this.fn},r}),{isClass:!0,isNode:!0}),name$1j="ParenthesisNode",dependencies$1j=["Node"],createParenthesisNode=factory(name$1j,dependencies$1j,(e=>{var{Node:t}=e;function r(e){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");if(!isNode(e))throw new TypeError('Node expected for parameter "content"');this.content=e}return r.prototype=new t,r.prototype.type="ParenthesisNode",r.prototype.isParenthesisNode=!0,r.prototype._compile=function(e,t){return this.content._compile(e,t)},r.prototype.getContent=function(){return this.content.getContent()},r.prototype.forEach=function(e){e(this.content,"content",this)},r.prototype.map=function(e){return new r(e(this.content,"content",this))},r.prototype.clone=function(){return new r(this.content)},r.prototype._toString=function(e){return!e||e&&!e.parenthesis||e&&"keep"===e.parenthesis?"("+this.content.toString(e)+")":this.content.toString(e)},r.prototype.toJSON=function(){return{mathjs:"ParenthesisNode",content:this.content}},r.fromJSON=function(e){return new r(e.content)},r.prototype.toHTML=function(e){return!e||e&&!e.parenthesis||e&&"keep"===e.parenthesis?'('+this.content.toHTML(e)+')':this.content.toHTML(e)},r.prototype._toTex=function(e){return!e||e&&!e.parenthesis||e&&"keep"===e.parenthesis?"\\left(".concat(this.content.toTex(e),"\\right)"):this.content.toTex(e)},r}),{isClass:!0,isNode:!0}),name$1i="RangeNode",dependencies$1i=["Node"],createRangeNode=factory(name$1i,dependencies$1i,(e=>{var{Node:t}=e;function r(e,t,n){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");if(!isNode(e))throw new TypeError("Node expected");if(!isNode(t))throw new TypeError("Node expected");if(n&&!isNode(n))throw new TypeError("Node expected");if(arguments.length>3)throw new Error("Too many arguments");this.start=e,this.end=t,this.step=n||null}function n(e,t){var r=getPrecedence(e,t),n={},i=getPrecedence(e.start,t);if(n.start=null!==i&&i<=r||"all"===t,e.step){var a=getPrecedence(e.step,t);n.step=null!==a&&a<=r||"all"===t}var o=getPrecedence(e.end,t);return n.end=null!==o&&o<=r||"all"===t,n}return r.prototype=new t,r.prototype.type="RangeNode",r.prototype.isRangeNode=!0,r.prototype.needsEnd=function(){return this.filter((function(e){return isSymbolNode(e)&&"end"===e.name})).length>0},r.prototype._compile=function(e,t){var r=e.range,n=this.start._compile(e,t),i=this.end._compile(e,t);if(this.step){var a=this.step._compile(e,t);return function(e,t,o){return r(n(e,t,o),i(e,t,o),a(e,t,o))}}return function(e,t,a){return r(n(e,t,a),i(e,t,a))}},r.prototype.forEach=function(e){e(this.start,"start",this),e(this.end,"end",this),this.step&&e(this.step,"step",this)},r.prototype.map=function(e){return new r(this._ifNode(e(this.start,"start",this)),this._ifNode(e(this.end,"end",this)),this.step&&this._ifNode(e(this.step,"step",this)))},r.prototype.clone=function(){return new r(this.start,this.end,this.step&&this.step)},r.prototype._toString=function(e){var t,r=n(this,e&&e.parenthesis?e.parenthesis:"keep"),i=this.start.toString(e);if(r.start&&(i="("+i+")"),t=i,this.step){var a=this.step.toString(e);r.step&&(a="("+a+")"),t+=":"+a}var o=this.end.toString(e);return r.end&&(o="("+o+")"),t+=":"+o},r.prototype.toJSON=function(){return{mathjs:"RangeNode",start:this.start,end:this.end,step:this.step}},r.fromJSON=function(e){return new r(e.start,e.end,e.step)},r.prototype.toHTML=function(e){var t,r=n(this,e&&e.parenthesis?e.parenthesis:"keep"),i=this.start.toHTML(e);if(r.start&&(i='('+i+')'),t=i,this.step){var a=this.step.toHTML(e);r.step&&(a='('+a+')'),t+=':'+a}var o=this.end.toHTML(e);return r.end&&(o='('+o+')'),t+=':'+o},r.prototype._toTex=function(e){var t=n(this,e&&e.parenthesis?e.parenthesis:"keep"),r=this.start.toTex(e);if(t.start&&(r="\\left(".concat(r,"\\right)")),this.step){var i=this.step.toTex(e);t.step&&(i="\\left(".concat(i,"\\right)")),r+=":"+i}var a=this.end.toTex(e);return t.end&&(a="\\left(".concat(a,"\\right)")),r+=":"+a},r}),{isClass:!0,isNode:!0}),name$1h="RelationalNode",dependencies$1h=["Node"],createRelationalNode=factory(name$1h,dependencies$1h,(e=>{var{Node:t}=e;function r(e,t){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");if(!Array.isArray(e))throw new TypeError("Parameter conditionals must be an array");if(!Array.isArray(t))throw new TypeError("Parameter params must be an array");if(e.length!==t.length-1)throw new TypeError("Parameter params must contain exactly one more element than parameter conditionals");this.conditionals=e,this.params=t}return r.prototype=new t,r.prototype.type="RelationalNode",r.prototype.isRelationalNode=!0,r.prototype._compile=function(e,t){var r=this,n=this.params.map((r=>r._compile(e,t)));return function(t,i,a){for(var o,s=n[0](t,i,a),u=0;ue(t,"params["+r+"]",this)),this)},r.prototype.map=function(e){return new r(this.conditionals.slice(),this.params.map(((t,r)=>this._ifNode(e(t,"params["+r+"]",this))),this))},r.prototype.clone=function(){return new r(this.conditionals,this.params)},r.prototype._toString=function(e){for(var t=e&&e.parenthesis?e.parenthesis:"keep",r=getPrecedence(this,t),n=this.params.map((function(n,i){var a=getPrecedence(n,t);return"all"===t||null!==a&&a<=r?"("+n.toString(e)+")":n.toString(e)})),i={equal:"==",unequal:"!=",smaller:"<",larger:">",smallerEq:"<=",largerEq:">="},a=n[0],o=0;o('+n.toHTML(e)+')':n.toHTML(e)})),i={equal:"==",unequal:"!=",smaller:"<",larger:">",smallerEq:"<=",largerEq:">="},a=n[0],o=0;o'+escape$1(i[this.conditionals[o]])+""+n[o+1];return a},r.prototype._toTex=function(e){for(var t=e&&e.parenthesis?e.parenthesis:"keep",r=getPrecedence(this,t),n=this.params.map((function(n,i){var a=getPrecedence(n,t);return"all"===t||null!==a&&a<=r?"\\left("+n.toTex(e)+"\right)":n.toTex(e)})),i=n[0],a=0;a{var{math:t,Unit:r,Node:n}=e;function i(e){return!!r&&r.isValuelessUnit(e)}function a(e){if(!(this instanceof a))throw new SyntaxError("Constructor must be called with the new operator");if("string"!=typeof e)throw new TypeError('String expected for parameter "name"');this.name=e}return a.prototype=new n,a.prototype.type="SymbolNode",a.prototype.isSymbolNode=!0,a.prototype._compile=function(e,t){var n=this.name;if(!0===t[n])return function(e,t,r){return t[n]};if(n in e)return function(t,r,i){return t.has(n)?t.get(n):getSafeProperty(e,n)};var o=i(n);return function(e,t,i){return e.has(n)?e.get(n):o?new r(null,n):a.onUndefinedSymbol(n)}},a.prototype.forEach=function(e){},a.prototype.map=function(e){return this.clone()},a.onUndefinedSymbol=function(e){throw new Error("Undefined symbol "+e)},a.prototype.clone=function(){return new a(this.name)},a.prototype._toString=function(e){return this.name},a.prototype.toHTML=function(e){var 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Matrix A is decomposed in three matrices (L, U, P) where P * A = L * U",examples:["lup([[2, 1], [1, 4]])","lup(matrix([[2, 1], [1, 4]]))","lup(sparse([[2, 1], [1, 4]]))"],seealso:["lusolve","lsolve","usolve","matrix","sparse","slu","qr"]},lusolveDocs={name:"lusolve",category:"Algebra",syntax:["x=lusolve(A, b)","x=lusolve(lu, b)"],description:"Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lusolve(a, b)"],seealso:["lup","slu","lsolve","usolve","matrix","sparse"]},qrDocs={name:"qr",category:"Algebra",syntax:["qr(A)"],description:"Calculates the Matrix QR decomposition. Matrix `A` is decomposed in two matrices (`Q`, `R`) where `Q` is an orthogonal matrix and `R` is an upper triangular matrix.",examples:["qr([[1, -1, 4], [1, 4, -2], [1, 4, 2], [1, -1, 0]])"],seealso:["lup","slu","matrix"]},rationalizeDocs={name:"rationalize",category:"Algebra",syntax:["rationalize(expr)","rationalize(expr, scope)","rationalize(expr, scope, detailed)"],description:"Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.",examples:['rationalize("2x/y - y/(x+1)")','rationalize("2x/y - y/(x+1)", true)'],seealso:["simplify"]},resolveDocs={name:"resolve",category:"Algebra",syntax:["resolve(node, scope)"],description:"Recursively substitute variables in an expression tree.",examples:['resolve(parse("1 + x"), { x: 7 })','resolve(parse("size(text)"), { text: "Hello World" })','resolve(parse("x + y"), { x: parse("3z") })','resolve(parse("3x"), { x: parse("y+z"), z: parse("w^y") })'],seealso:["simplify","evaluate"],mayThrow:["ReferenceError"]},simplifyDocs={name:"simplify",category:"Algebra",syntax:["simplify(expr)","simplify(expr, rules)"],description:"Simplify an expression tree.",examples:['simplify("3 + 2 / 4")','simplify("2x + x")','f = parse("x * (x + 2 + x)")',"simplified = simplify(f)","simplified.evaluate({x: 2})"],seealso:["simplifyCore","derivative","evaluate","parse","rationalize","resolve"]},simplifyCoreDocs={name:"simplifyCore",category:"Algebra",syntax:["simplifyCore(node)"],description:"Perform simple one-pass simplifications on an expression tree.",examples:['simplifyCore(parse("0*x"))','simplifyCore(parse("(x+0)*2"))'],seealso:["simplify","evaluate"]},sluDocs={name:"slu",category:"Algebra",syntax:["slu(A, order, threshold)"],description:"Calculate the Matrix LU decomposition with full pivoting. Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U",examples:["slu(sparse([4.5, 0, 3.2, 0; 3.1, 2.9, 0, 0.9; 0, 1.7, 3, 0; 3.5, 0.4, 0, 1]), 1, 0.001)"],seealso:["lusolve","lsolve","usolve","matrix","sparse","lup","qr"]},symbolicEqualDocs={name:"symbolicEqual",category:"Algebra",syntax:["symbolicEqual(expr1, expr2)","symbolicEqual(expr1, expr2, options)"],description:"Returns true if the difference of the expressions simplifies to 0",examples:['symbolicEqual("x*y","y*x")','symbolicEqual("abs(x^2)", "x^2")','symbolicEqual("abs(x)", "x", {context: {abs: {trivial: true}}})'],seealso:["simplify","evaluate"]},usolveDocs={name:"usolve",category:"Algebra",syntax:["x=usolve(U, b)"],description:"Finds one solution of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.",examples:["x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])"],seealso:["usolveAll","lup","lusolve","lsolve","matrix","sparse"]},usolveAllDocs={name:"usolveAll",category:"Algebra",syntax:["x=usolve(U, b)"],description:"Finds all solutions of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.",examples:["x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])"],seealso:["usolve","lup","lusolve","lsolve","matrix","sparse"]},absDocs={name:"abs",category:"Arithmetic",syntax:["abs(x)"],description:"Compute the absolute value.",examples:["abs(3.5)","abs(-4.2)"],seealso:["sign"]},addDocs={name:"add",category:"Operators",syntax:["x + y","add(x, y)"],description:"Add two values.",examples:["a = 2.1 + 3.6","a - 3.6","3 + 2i","3 cm + 2 inch",'"2.3" + "4"'],seealso:["subtract"]},cbrtDocs={name:"cbrt",category:"Arithmetic",syntax:["cbrt(x)","cbrt(x, allRoots)"],description:"Compute the cubic root value. If x = y * y * y, then y is the cubic root of x. When `x` is a number or complex number, an optional second argument `allRoots` can be provided to return all three cubic roots. If not provided, the principal root is returned",examples:["cbrt(64)","cube(4)","cbrt(-8)","cbrt(2 + 3i)","cbrt(8i)","cbrt(8i, true)","cbrt(27 m^3)"],seealso:["square","sqrt","cube","multiply"]},ceilDocs={name:"ceil",category:"Arithmetic",syntax:["ceil(x)"],description:"Round a value towards plus infinity. If x is complex, both real and imaginary part are rounded towards plus infinity.",examples:["ceil(3.2)","ceil(3.8)","ceil(-4.2)"],seealso:["floor","fix","round"]},cubeDocs={name:"cube",category:"Arithmetic",syntax:["cube(x)"],description:"Compute the cube of a value. The cube of x is x * x * x.",examples:["cube(2)","2^3","2 * 2 * 2"],seealso:["multiply","square","pow"]},divideDocs={name:"divide",category:"Operators",syntax:["x / y","divide(x, y)"],description:"Divide two values.",examples:["a = 2 / 3","a * 3","4.5 / 2","3 + 4 / 2","(3 + 4) / 2","18 km / 4.5"],seealso:["multiply"]},dotDivideDocs={name:"dotDivide",category:"Operators",syntax:["x ./ y","dotDivide(x, y)"],description:"Divide two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a ./ b"],seealso:["multiply","dotMultiply","divide"]},dotMultiplyDocs={name:"dotMultiply",category:"Operators",syntax:["x .* y","dotMultiply(x, y)"],description:"Multiply two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a .* b"],seealso:["multiply","divide","dotDivide"]},dotPowDocs={name:"dotPow",category:"Operators",syntax:["x .^ y","dotPow(x, y)"],description:"Calculates the power of x to y element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","a .^ 2"],seealso:["pow"]},expDocs={name:"exp",category:"Arithmetic",syntax:["exp(x)"],description:"Calculate the exponent of a value.",examples:["exp(1.3)","e ^ 1.3","log(exp(1.3))","x = 2.4","(exp(i*x) == cos(x) + i*sin(x)) # Euler's formula"],seealso:["expm","expm1","pow","log"]},expmDocs={name:"expm",category:"Arithmetic",syntax:["exp(x)"],description:"Compute the matrix exponential, expm(A) = e^A. The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation.",examples:["expm([[0,2],[0,0]])"],seealso:["exp"]},expm1Docs={name:"expm1",category:"Arithmetic",syntax:["expm1(x)"],description:"Calculate the value of subtracting 1 from the exponential value.",examples:["expm1(2)","pow(e, 2) - 1","log(expm1(2) + 1)"],seealso:["exp","pow","log"]},fixDocs={name:"fix",category:"Arithmetic",syntax:["fix(x)"],description:"Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.",examples:["fix(3.2)","fix(3.8)","fix(-4.2)","fix(-4.8)"],seealso:["ceil","floor","round"]},floorDocs={name:"floor",category:"Arithmetic",syntax:["floor(x)"],description:"Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.",examples:["floor(3.2)","floor(3.8)","floor(-4.2)"],seealso:["ceil","fix","round"]},gcdDocs={name:"gcd",category:"Arithmetic",syntax:["gcd(a, b)","gcd(a, b, c, ...)"],description:"Compute the greatest common divisor.",examples:["gcd(8, 12)","gcd(-4, 6)","gcd(25, 15, -10)"],seealso:["lcm","xgcd"]},hypotDocs={name:"hypot",category:"Arithmetic",syntax:["hypot(a, b, c, ...)","hypot([a, b, c, ...])"],description:"Calculate the hypotenusa of a list with values. ",examples:["hypot(3, 4)","sqrt(3^2 + 4^2)","hypot(-2)","hypot([3, 4, 5])"],seealso:["abs","norm"]},invmodDocs={name:"invmod",category:"Arithmetic",syntax:["invmod(a, b)"],description:"Calculate the (modular) multiplicative inverse of a modulo b. Solution to the equation ax ≣ 1 (mod b)",examples:["invmod(8, 12)=NaN","invmod(7, 13)=2","math.invmod(15151, 15122)=10429"],seealso:["gcd","xgcd"]},lcmDocs={name:"lcm",category:"Arithmetic",syntax:["lcm(x, y)"],description:"Compute the least common multiple.",examples:["lcm(4, 6)","lcm(6, 21)","lcm(6, 21, 5)"],seealso:["gcd"]},logDocs={name:"log",category:"Arithmetic",syntax:["log(x)","log(x, base)"],description:"Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]},log10Docs={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]},log1pDocs={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]},log2Docs={name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]},modDocs={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]},multiplyDocs={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]},normDocs={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']},nthRootDocs={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]},nthRootsDocs={name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]},powDocs={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)","math.pow([[1, 2], [4, 3]], 2)","math.pow([[1, 2], [4, 3]], -1)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]},roundDocs={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)"],seealso:["ceil","floor","fix"]},signDocs={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]},sqrtDocs={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]},sqrtmDocs={name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[1, 2], [3, 4]])"],seealso:["sqrt","abs","square","multiply"]},squareDocs={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]},subtractDocs={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]},unaryMinusDocs={name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]},unaryPlusDocs={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]},xgcdDocs={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]},bitAndDocs={name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitNotDocs={name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitOrDocs={name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]},bitXorDocs={name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]},leftShiftDocs={name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]},rightArithShiftDocs={name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]},rightLogShiftDocs={name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]},bellNumbersDocs={name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]},catalanDocs={name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]},compositionDocs={name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]},stirlingS2Docs={name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]},argDocs={name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]},conjDocs={name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]},imDocs={name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]},reDocs={name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]},evaluateDocs={name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(" + 4 + ")")'],seealso:[]},helpDocs={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]},distanceDocs={name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]},intersectDocs={name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])"],seealso:[]},andDocs={name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]},notDocs={name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]},orDocs={name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]},xorDocs={name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]},columnDocs={name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row","matrixFromColumns"]},concatDocs={name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},countDocs={name:"count",category:"Matrix",syntax:["count(x)"],description:"Count the number of elements of a matrix, array or string.",examples:["a = [1, 2; 3, 4; 5, 6]","count(a)","size(a)",'count("hello world")'],seealso:["size"]},crossDocs={name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0], [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4], [5, 6, 7])"],seealso:["multiply","dot"]},ctransposeDocs={name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},detDocs={name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diagDocs={name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diffDocs={name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["diff([1, 2, 4, 7, 0])","diff([1, 2, 4, 7, 0], 0)","diff(matrix([1, 2, 4, 7, 0]))","diff([[1, 2], [3, 4]])","diff([[1, 2], [3, 4]], 0)","diff([[1, 2], [3, 4]], 1)","diff([[1, 2], [3, 4]], bignumber(1))","diff(matrix([[1, 2], [3, 4]]), 1)","diff([[1, 2], matrix([3, 4])], 1)"],seealso:["subtract","partitionSelect"]},dotDocs={name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]},eigsDocs={name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and eigenvectors of a real symmetric matrix",examples:["eigs([[5, 2.3], [2.3, 1]])"],seealso:["inv"]},filterDocs={name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]},flattenDocs={name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]},forEachDocs={name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["numberOfPets = {}","addPet(n) = numberOfPets[n] = (numberOfPets[n] ? numberOfPets[n]:0 ) + 1;",'forEach(["Dog","Cat","Cat"], addPet)',"numberOfPets"],seealso:["map","sort","filter"]},getMatrixDataTypeDocs={name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeOf"]},identityDocs={name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},invDocs={name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]},pinvDocs={name:"pinv",category:"Matrix",syntax:["pinv(x)"],description:"Calculate the Moore–Penrose inverse of a matrix",examples:["pinv([1, 2; 3, 4])","pinv([[1, 0], [0, 1], [0, 1]])","pinv(4)"],seealso:["inv"]},kronDocs={name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]},mapDocs={name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]},matrixFromColumnsDocs={name:"matrixFromColumns",category:"Matrix",syntax:["math.matrixFromColumns(...arr)","math.matrixFromColumns(row1, row2)","math.matrixFromColumns(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual columns.",examples:["matrixFromColumns([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromRows","matrixFromFunction","zeros"]},matrixFromFunctionDocs={name:"matrixFromFunction",category:"Matrix",syntax:["math.matrixFromFunction(size, fn)","math.matrixFromFunction(size, fn, format)","math.matrixFromFunction(size, fn, format, datatype)","math.matrixFromFunction(size, format, fn)","math.matrixFromFunction(size, format, datatype, fn)"],description:"Create a matrix by evaluating a generating function at each index.",examples:["f(I) = I[1] - I[2]","matrixFromFunction([3,3], f)","g(I) = I[1] - I[2] == 1 ? 4 : 0",'matrixFromFunction([100, 100], "sparse", g)',"matrixFromFunction([5], random)"],seealso:["matrix","matrixFromRows","matrixFromColumns","zeros"]},matrixFromRowsDocs={name:"matrixFromRows",category:"Matrix",syntax:["math.matrixFromRows(...arr)","math.matrixFromRows(row1, row2)","math.matrixFromRows(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual rows.",examples:["matrixFromRows([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromColumns","matrixFromFunction","zeros"]},onesDocs={name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]},partitionSelectDocs={name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1)'],seealso:["sort"]},rangeDocs={name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]},reshapeDocs={name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])"],seealso:["size","squeeze","resize"]},resizeDocs={name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]},rotateDocs={name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], math.pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]},rotationMatrixDocs={name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]},rowDocs={name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column","matrixFromRows"]},sizeDocs={name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","count","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]},sortDocs={name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"])',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]},squeezeDocs={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]},subsetDocs={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of the entries of a matrix or characters of a string. Indexes are one-based. There should be one index specification for each dimension of the target. Each specification can be a single index, a list of indices, or a range in colon notation `l:u`. In a range, both the lower bound l and upper bound u are included; and if a bound is omitted it defaults to the most extreme valid value. The cartesian product of the indices specified in each dimension determines the target of the operation.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]","f[[1,2], [1,3]] = [9, 10; 11, 12]","f"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]},traceDocs={name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]},transposeDocs={name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},zerosDocs={name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]},fftDocs={name:"fft",category:"Matrix",syntax:["fft(x)"],description:"Calculate N-dimensional fourier transform",examples:["fft([[1, 0], [1, 0]])"],seealso:["ifft"]},ifftDocs={name:"ifft",category:"Matrix",syntax:["ifft(x)"],description:"Calculate N-dimensional inverse fourier transform",examples:["ifft([[2, 2], [0, 0]])"],seealso:["fft"]},combinationsDocs={name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]},combinationsWithRepDocs={name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]},factorialDocs={name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]},gammaDocs={name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]},lgammaDocs={name:"lgamma",category:"Probability",syntax:["lgamma(n)"],description:"Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers.",examples:["lgamma(4)","lgamma(1/2)","lgamma(math.i)","lgamma(complex(1.1, 2))"],seealso:["gamma"]},kldivergenceDocs={name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]},multinomialDocs={name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]},permutationsDocs={name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]},pickRandomDocs={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]},randomDocs={name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]},randomIntDocs={name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]},compareDocs={name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]},compareNaturalDocs={name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]},compareTextDocs={name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]},deepEqualDocs={name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]},equalDocs={name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]},equalTextDocs={name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]},largerDocs={name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]},largerEqDocs={name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]},smallerDocs={name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]},smallerEqDocs={name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]},unequalDocs={name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]},setCartesianDocs={name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]},setDifferenceDocs={name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]},setDistinctDocs={name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]},setIntersectDocs={name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]},setIsSubsetDocs={name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]},setMultiplicityDocs={name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]},setPowersetDocs={name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]},setSizeDocs={name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]},setSymDifferenceDocs={name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]},setUnionDocs={name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]},erfDocs={name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]},madDocs={name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]},maxDocs={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]},meanDocs={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]},medianDocs={name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]},minDocs={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]},modeDocs={name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]},prodDocs={name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]},quantileSeqDocs={name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.",examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","variance"]},stdDocs={name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","prod","sum","variance"]},cumSumDocs={name:"cumsum",category:"Statistics",syntax:["cumsum(a, b, c, ...)","cumsum(A)"],description:"Compute the cumulative sum of all values.",examples:["cumsum(2, 3, 4, 1)","cumsum([2, 3, 4, 1])","cumsum([1, 2; 3, 4])","cumsum([1, 2; 3, 4], 1)","cumsum([1, 2; 3, 4], 2)"],seealso:["max","mean","median","min","prod","std","sum","variance"]},sumDocs={name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","variance"]},varianceDocs={name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, normalization)"],description:'Compute the variance of all values. Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["variance(2, 4, 6)","variance([2, 4, 6, 8])",'variance([2, 4, 6, 8], "uncorrected")','variance([2, 4, 6, 8], "biased")',"variance([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","min","prod","std","sum"]},acosDocs={name:"acos",category:"Trigonometry",syntax:["acos(x)"],description:"Compute the inverse cosine of a value in radians.",examples:["acos(0.5)","acos(cos(2.3))"],seealso:["cos","atan","asin"]},acoshDocs={name:"acosh",category:"Trigonometry",syntax:["acosh(x)"],description:"Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.",examples:["acosh(1.5)"],seealso:["cosh","asinh","atanh"]},acotDocs={name:"acot",category:"Trigonometry",syntax:["acot(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acot(0.5)","acot(cot(0.5))","acot(2)"],seealso:["cot","atan"]},acothDocs={name:"acoth",category:"Trigonometry",syntax:["acoth(x)"],description:"Calculate the hyperbolic arccotangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.",examples:["acoth(2)","acoth(0.5)"],seealso:["acsch","asech"]},acscDocs={name:"acsc",category:"Trigonometry",syntax:["acsc(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acsc(2)","acsc(csc(0.5))","acsc(0.5)"],seealso:["csc","asin","asec"]},acschDocs={name:"acsch",category:"Trigonometry",syntax:["acsch(x)"],description:"Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.",examples:["acsch(0.5)"],seealso:["asech","acoth"]},asecDocs={name:"asec",category:"Trigonometry",syntax:["asec(x)"],description:"Calculate the inverse secant of a value.",examples:["asec(0.5)","asec(sec(0.5))","asec(2)"],seealso:["acos","acot","acsc"]},asechDocs={name:"asech",category:"Trigonometry",syntax:["asech(x)"],description:"Calculate the inverse secant of a value.",examples:["asech(0.5)"],seealso:["acsch","acoth"]},asinDocs={name:"asin",category:"Trigonometry",syntax:["asin(x)"],description:"Compute the inverse sine of a value in radians.",examples:["asin(0.5)","asin(sin(0.5))"],seealso:["sin","acos","atan"]},asinhDocs={name:"asinh",category:"Trigonometry",syntax:["asinh(x)"],description:"Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.",examples:["asinh(0.5)"],seealso:["acosh","atanh"]},atanDocs={name:"atan",category:"Trigonometry",syntax:["atan(x)"],description:"Compute the inverse tangent of a value in radians.",examples:["atan(0.5)","atan(tan(0.5))"],seealso:["tan","acos","asin"]},atan2Docs={name:"atan2",category:"Trigonometry",syntax:["atan2(y, x)"],description:"Computes the principal value of the arc tangent of y/x in radians.",examples:["atan2(2, 2) / pi","angle = 60 deg in rad","x = cos(angle)","y = sin(angle)","atan2(y, x)"],seealso:["sin","cos","tan"]},atanhDocs={name:"atanh",category:"Trigonometry",syntax:["atanh(x)"],description:"Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.",examples:["atanh(0.5)"],seealso:["acosh","asinh"]},cosDocs={name:"cos",category:"Trigonometry",syntax:["cos(x)"],description:"Compute the cosine of x in radians.",examples:["cos(2)","cos(pi / 4) ^ 2","cos(180 deg)","cos(60 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["acos","sin","tan"]},coshDocs={name:"cosh",category:"Trigonometry",syntax:["cosh(x)"],description:"Compute the hyperbolic cosine of x in radians.",examples:["cosh(0.5)"],seealso:["sinh","tanh","coth"]},cotDocs={name:"cot",category:"Trigonometry",syntax:["cot(x)"],description:"Compute the cotangent of x in radians. Defined as 1/tan(x)",examples:["cot(2)","1 / tan(2)"],seealso:["sec","csc","tan"]},cothDocs={name:"coth",category:"Trigonometry",syntax:["coth(x)"],description:"Compute the hyperbolic cotangent of x in radians.",examples:["coth(2)","1 / tanh(2)"],seealso:["sech","csch","tanh"]},cscDocs={name:"csc",category:"Trigonometry",syntax:["csc(x)"],description:"Compute the cosecant of x in radians. Defined as 1/sin(x)",examples:["csc(2)","1 / sin(2)"],seealso:["sec","cot","sin"]},cschDocs={name:"csch",category:"Trigonometry",syntax:["csch(x)"],description:"Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)",examples:["csch(2)","1 / sinh(2)"],seealso:["sech","coth","sinh"]},secDocs={name:"sec",category:"Trigonometry",syntax:["sec(x)"],description:"Compute the secant of x in radians. Defined as 1/cos(x)",examples:["sec(2)","1 / cos(2)"],seealso:["cot","csc","cos"]},sechDocs={name:"sech",category:"Trigonometry",syntax:["sech(x)"],description:"Compute the hyperbolic secant of x in radians. Defined as 1/cosh(x)",examples:["sech(2)","1 / cosh(2)"],seealso:["coth","csch","cosh"]},sinDocs={name:"sin",category:"Trigonometry",syntax:["sin(x)"],description:"Compute the sine of x in radians.",examples:["sin(2)","sin(pi / 4) ^ 2","sin(90 deg)","sin(30 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["asin","cos","tan"]},sinhDocs={name:"sinh",category:"Trigonometry",syntax:["sinh(x)"],description:"Compute the hyperbolic sine of x in radians.",examples:["sinh(0.5)"],seealso:["cosh","tanh"]},tanDocs={name:"tan",category:"Trigonometry",syntax:["tan(x)"],description:"Compute the tangent of x in radians.",examples:["tan(0.5)","sin(0.5) / cos(0.5)","tan(pi / 4)","tan(45 deg)"],seealso:["atan","sin","cos"]},tanhDocs={name:"tanh",category:"Trigonometry",syntax:["tanh(x)"],description:"Compute the hyperbolic tangent of x in radians.",examples:["tanh(0.5)","sinh(0.5) / cosh(0.5)"],seealso:["sinh","cosh"]},toDocs={name:"to",category:"Units",syntax:["x to unit","to(x, unit)"],description:"Change the unit of a value.",examples:["5 inch to cm","3.2kg to g","16 bytes in bits"],seealso:[]},binDocs={name:"bin",category:"Utils",syntax:["bin(value)"],description:"Format a number as binary",examples:["bin(2)"],seealso:["oct","hex"]},cloneDocs={name:"clone",category:"Utils",syntax:["clone(x)"],description:"Clone a variable. Creates a copy of primitive variables,and a deep copy of matrices",examples:["clone(3.5)","clone(2 - 4i)","clone(45 deg)","clone([1, 2; 3, 4])",'clone("hello world")'],seealso:[]},formatDocs={name:"format",category:"Utils",syntax:["format(value)","format(value, precision)"],description:"Format a value of any type as string.",examples:["format(2.3)","format(3 - 4i)","format([])","format(pi, 3)"],seealso:["print"]},hasNumericValueDocs={name:"hasNumericValue",category:"Utils",syntax:["hasNumericValue(x)"],description:"Test whether a value is an numeric value. In case of a string, true is returned if the string contains a numeric value.",examples:["hasNumericValue(2)",'hasNumericValue("2")','isNumeric("2")',"hasNumericValue(0)","hasNumericValue(bignumber(500))","hasNumericValue(fraction(0.125))","hasNumericValue(2 + 3i)",'hasNumericValue([2.3, "foo", false])'],seealso:["isInteger","isZero","isNegative","isPositive","isNaN","isNumeric"]},hexDocs={name:"hex",category:"Utils",syntax:["hex(value)"],description:"Format a number as hexadecimal",examples:["hex(240)"],seealso:["bin","oct"]},isIntegerDocs={name:"isInteger",category:"Utils",syntax:["isInteger(x)"],description:"Test whether a value is an integer number.",examples:["isInteger(2)","isInteger(3.5)","isInteger([3, 0.5, -2])"],seealso:["isNegative","isNumeric","isPositive","isZero"]},isNaNDocs={name:"isNaN",category:"Utils",syntax:["isNaN(x)"],description:"Test whether a value is NaN (not a number)",examples:["isNaN(2)","isNaN(0 / 0)","isNaN(NaN)","isNaN(Infinity)"],seealso:["isNegative","isNumeric","isPositive","isZero"]},isNegativeDocs={name:"isNegative",category:"Utils",syntax:["isNegative(x)"],description:"Test whether a value is negative: smaller than zero.",examples:["isNegative(2)","isNegative(0)","isNegative(-4)","isNegative([3, 0.5, -2])"],seealso:["isInteger","isNumeric","isPositive","isZero"]},isNumericDocs={name:"isNumeric",category:"Utils",syntax:["isNumeric(x)"],description:"Test whether a value is a numeric value. Returns true when the input is a number, BigNumber, Fraction, or boolean.",examples:["isNumeric(2)",'isNumeric("2")','hasNumericValue("2")',"isNumeric(0)","isNumeric(bignumber(500))","isNumeric(fraction(0.125))","isNumeric(2 + 3i)",'isNumeric([2.3, "foo", false])'],seealso:["isInteger","isZero","isNegative","isPositive","isNaN","hasNumericValue"]},isPositiveDocs={name:"isPositive",category:"Utils",syntax:["isPositive(x)"],description:"Test whether a value is positive: larger than zero.",examples:["isPositive(2)","isPositive(0)","isPositive(-4)","isPositive([3, 0.5, -2])"],seealso:["isInteger","isNumeric","isNegative","isZero"]},isPrimeDocs={name:"isPrime",category:"Utils",syntax:["isPrime(x)"],description:"Test whether a value is prime: has no divisors other than itself and one.",examples:["isPrime(3)","isPrime(-2)","isPrime([2, 17, 100])"],seealso:["isInteger","isNumeric","isNegative","isZero"]},isZeroDocs={name:"isZero",category:"Utils",syntax:["isZero(x)"],description:"Test whether a value is zero.",examples:["isZero(2)","isZero(0)","isZero(-4)","isZero([3, 0, -2, 0])"],seealso:["isInteger","isNumeric","isNegative","isPositive"]},numericDocs={name:"numeric",category:"Utils",syntax:["numeric(x)"],description:"Convert a numeric input to a specific numeric type: number, BigNumber, or Fraction.",examples:['numeric("4")','numeric("4", "number")','numeric("4", "BigNumber")','numeric("4", "Fraction)','numeric(4, "Fraction")','numeric(fraction(2, 5), "number)'],seealso:["number","fraction","bignumber","string","format"]},octDocs={name:"oct",category:"Utils",syntax:["oct(value)"],description:"Format a number as octal",examples:["oct(56)"],seealso:["bin","hex"]},printDocs={name:"print",category:"Utils",syntax:["print(template, values)","print(template, values, precision)"],description:"Interpolate values into a string template.",examples:['print("Lucy is $age years old", {age: 5})','print("The value of pi is $pi", {pi: pi}, 3)','print("Hello, $user.name!", {user: {name: "John"}})','print("Values: $0, $1, $2", [6, 9, 4])'],seealso:["format"]},typeOfDocs={name:"typeOf",category:"Utils",syntax:["typeOf(x)"],description:"Get the type of a variable.",examples:["typeOf(3.5)","typeOf(2 - 4i)","typeOf(45 deg)",'typeOf("hello world")'],seealso:["getMatrixDataType"]},embeddedDocs={bignumber:bignumberDocs,boolean:booleanDocs,complex:complexDocs,createUnit:createUnitDocs,fraction:fractionDocs,index:indexDocs,matrix:matrixDocs,number:numberDocs,sparse:sparseDocs,splitUnit:splitUnitDocs,string:stringDocs,unit:unitDocs,e:eDocs,E:eDocs,false:falseDocs,i:iDocs,Infinity:InfinityDocs,LN2:LN2Docs,LN10:LN10Docs,LOG2E:LOG2EDocs,LOG10E:LOG10EDocs,NaN:NaNDocs,null:nullDocs,pi:piDocs,PI:piDocs,phi:phiDocs,SQRT1_2:SQRT12Docs,SQRT2:SQRT2Docs,tau:tauDocs,true:trueDocs,version:versionDocs,speedOfLight:{description:"Speed of light in vacuum",examples:["speedOfLight"]},gravitationConstant:{description:"Newtonian constant of gravitation",examples:["gravitationConstant"]},planckConstant:{description:"Planck constant",examples:["planckConstant"]},reducedPlanckConstant:{description:"Reduced Planck constant",examples:["reducedPlanckConstant"]},magneticConstant:{description:"Magnetic constant (vacuum permeability)",examples:["magneticConstant"]},electricConstant:{description:"Electric constant (vacuum permeability)",examples:["electricConstant"]},vacuumImpedance:{description:"Characteristic impedance of vacuum",examples:["vacuumImpedance"]},coulomb:{description:"Coulomb's constant",examples:["coulomb"]},elementaryCharge:{description:"Elementary charge",examples:["elementaryCharge"]},bohrMagneton:{description:"Borh magneton",examples:["bohrMagneton"]},conductanceQuantum:{description:"Conductance quantum",examples:["conductanceQuantum"]},inverseConductanceQuantum:{description:"Inverse conductance quantum",examples:["inverseConductanceQuantum"]},magneticFluxQuantum:{description:"Magnetic flux quantum",examples:["magneticFluxQuantum"]},nuclearMagneton:{description:"Nuclear magneton",examples:["nuclearMagneton"]},klitzing:{description:"Von Klitzing constant",examples:["klitzing"]},bohrRadius:{description:"Borh radius",examples:["bohrRadius"]},classicalElectronRadius:{description:"Classical electron radius",examples:["classicalElectronRadius"]},electronMass:{description:"Electron mass",examples:["electronMass"]},fermiCoupling:{description:"Fermi coupling constant",examples:["fermiCoupling"]},fineStructure:{description:"Fine-structure constant",examples:["fineStructure"]},hartreeEnergy:{description:"Hartree energy",examples:["hartreeEnergy"]},protonMass:{description:"Proton mass",examples:["protonMass"]},deuteronMass:{description:"Deuteron Mass",examples:["deuteronMass"]},neutronMass:{description:"Neutron mass",examples:["neutronMass"]},quantumOfCirculation:{description:"Quantum of circulation",examples:["quantumOfCirculation"]},rydberg:{description:"Rydberg 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u(e(h.object,y),e(h.index,y));if(isIndexNode(h))return new p(h.dimensions.map((t=>e(t,y))));if(isObjectNode(h)){var O={};for(var C in h.properties)O[C]=e(h.properties[C],y);return new m(O)}}return h}})),name$n="resolve",dependencies$n=["parse","ConstantNode","FunctionNode","OperatorNode","ParenthesisNode"],createResolve=factory(name$n,dependencies$n,(e=>{var{parse:t,ConstantNode:r,FunctionNode:n,OperatorNode:i,ParenthesisNode:a}=e;return function e(o,s){var u=arguments.length>2&&void 0!==arguments[2]?arguments[2]:new Set;if(!s)return o;if(isMap$1(s)||(s=createMap$1(s)),isSymbolNode(o)){if(u.has(o.name)){var c=Array.from(u).join(", ");throw new ReferenceError("recursive loop of variable definitions among {".concat(c,"}"))}var l=s.get(o.name);if(isNode(l)){var f=new Set(u);return f.add(o.name),e(l,s,f)}return"number"==typeof l?t(String(l)):void 0!==l?new r(l):o}if(isOperatorNode(o)){var p=o.args.map((function(t){return e(t,s,u)}));return new i(o.op,o.fn,p,o.implicit)}if(isParenthesisNode(o))return new a(e(o.content,s,u));if(isFunctionNode(o)){var m=o.args.map((function(t){return e(t,s,u)}));return new n(o.name,m)}return o.map((t=>e(t,s,u)))}})),name$m="symbolicEqual",dependencies$m=["parse","simplify","typed","OperatorNode"],createSymbolicEqual=factory(name$m,dependencies$m,(e=>{var{parse:t,simplify:r,typed:n,OperatorNode:i}=e;return n(name$m,{"string, string":function(e,r){return this(t(e),t(r),{})},"string, string, Object":function(e,r,n){return this(t(e),t(r),n)},"Node, string":function(e,r){return this(e,t(r),{})},"Node, string, Object":function(e,r,n){return this(e,t(r),n)},"string, Node":function(e,r){return this(t(e),r,{})},"string, Node, Object":function(e,r,n){return this(t(e),r,n)},"Node, Node":function(e,t){return this(e,t,{})},"Node, Node, Object":function(e,t,n){var a=new i("-","subtract",[e,t]),o=r(a,{},n);return isConstantNode(o)&&!o.value}})})),name$l="derivative",dependencies$l=["typed","config","parse","simplify","equal","isZero","numeric","ConstantNode","FunctionNode","OperatorNode","ParenthesisNode","SymbolNode"],createDerivative=factory(name$l,dependencies$l,(e=>{var{typed:t,config:r,parse:n,simplify:i,equal:a,isZero:o,numeric:s,ConstantNode:u,FunctionNode:c,OperatorNode:l,ParenthesisNode:f,SymbolNode:p}=e,m=t("derivative",{"Node, SymbolNode, Object":function(e,t,r){var n={};h(n,e,t.name);var a=y(e,n);return r.simplify?i(a):a},"Node, SymbolNode":function(e,t){return this(e,t,{simplify:!0})},"string, SymbolNode":function(e,t){return this(n(e),t)},"string, SymbolNode, Object":function(e,t,r){return this(n(e),t,r)},"string, string":function(e,t){return this(n(e),n(t))},"string, string, Object":function(e,t,r){return this(n(e),n(t),r)},"Node, string":function(e,t){return this(e,n(t))},"Node, string, Object":function(e,t,r){return this(e,n(t),r)}});m._simplify=!0,m.toTex=function(e){return d.apply(null,e.args)};var d=t("_derivTex",{"Node, SymbolNode":function(e,t){return isConstantNode(e)&&"string"===typeOf$1(e.value)?d(n(e.value).toString(),t.toString(),1):d(e.toTex(),t.toString(),1)},"Node, ConstantNode":function(e,t){if("string"===typeOf$1(t.value))return d(e,n(t.value));throw new Error("The second parameter to 'derivative' is a non-string constant")},"Node, SymbolNode, ConstantNode":function(e,t,r){return d(e.toString(),t.name,r.value)},"string, string, number":function(e,t,r){return(1===r?"{d\\over d"+t+"}":"{d^{"+r+"}\\over d"+t+"^{"+r+"}}")+"\\left[".concat(e,"\\right]")}}),h=t("constTag",{"Object, ConstantNode, string":function(e,t){return e[t]=!0,!0},"Object, SymbolNode, string":function(e,t,r){return t.name!==r&&(e[t]=!0,!0)},"Object, ParenthesisNode, string":function(e,t,r){return h(e,t.content,r)},"Object, FunctionAssignmentNode, string":function(e,t,r){return-1===t.params.indexOf(r)?(e[t]=!0,!0):h(e,t.expr,r)},"Object, FunctionNode | OperatorNode, 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0!==t[m]){if(isConstantNode(m)){if(o(m.value))return g(0);if(a(m.value,1))return y(p,t)}var d=new l("^","pow",[p.clone(),new l("-","subtract",[m,g(1)])]);return new l("*","multiply",[m.clone(),new l("*","multiply",[y(p,t),d])])}return new l("*","multiply",[new l("^","pow",[p.clone(),m.clone()]),new l("+","add",[new l("*","multiply",[y(p,t),new l("/","divide",[m.clone(),p.clone()])]),new l("*","multiply",[y(m,t),new c("log",[p.clone()])])])])}throw new Error('Operator "'+e.op+'" is not supported by derivative, or a wrong number of arguments is passed')}});function g(e,t){return new u(s(e,t||r.number))}return m})),name$k="rationalize",dependencies$k=["config","typed","equal","isZero","add","subtract","multiply","divide","pow","parse","simplifyCore","simplify","?bignumber","?fraction","mathWithTransform","matrix","AccessorNode","ArrayNode","ConstantNode","FunctionNode","IndexNode","ObjectNode","OperatorNode","SymbolNode","ParenthesisNode"],createRationalize=factory(name$k,dependencies$k,(e=>{var{config:t,typed:r,equal:n,isZero:i,add:a,subtract:o,multiply:s,divide:u,pow:c,parse:l,simplifyCore:f,simplify:p,fraction:m,bignumber:d,mathWithTransform:h,matrix:y,AccessorNode:g,ArrayNode:v,ConstantNode:x,FunctionNode:b,IndexNode:_,ObjectNode:w,OperatorNode:N,SymbolNode:$,ParenthesisNode:A}=e,M=createSimplifyConstant({typed:r,config:t,mathWithTransform:h,matrix:y,fraction:m,bignumber:d,AccessorNode:g,ArrayNode:v,ConstantNode:x,FunctionNode:b,IndexNode:_,ObjectNode:w,OperatorNode:N,SymbolNode:$});return r(name$k,{string:function(e){return this(l(e),{},!1)},"string, boolean":function(e,t){return this(l(e),{},t)},"string, Object":function(e,t){return this(l(e),t,!1)},"string, Object, boolean":function(e,t,r){return this(l(e),t,r)},Node:function(e){return this(e,{},!1)},"Node, boolean":function(e,t){return this(e,{},t)},"Node, Object":function(e,t){return this(e,t,!1)},"Node, Object, boolean":function(e,t,r){var n=function(){var e=[f,{l:"n+n",r:"2*n"},{l:"n+-n",r:"0"},M,{l:"n*(n1^-1)",r:"n/n1"},{l:"n*n1^-n2",r:"n/n1^n2"},{l:"n1^-1",r:"1/n1"},{l:"n*(n1/n2)",r:"(n*n1)/n2"},{l:"1*n",r:"n"}],t=[{l:"(-n1)/(-n2)",r:"n1/n2"},{l:"(-n1)*(-n2)",r:"n1*n2"},{l:"n1--n2",r:"n1+n2"},{l:"n1-n2",r:"n1+(-n2)"},{l:"(n1+n2)*n3",r:"(n1*n3 + n2*n3)"},{l:"n1*(n2+n3)",r:"(n1*n2+n1*n3)"},{l:"c1*n + c2*n",r:"(c1+c2)*n"},{l:"c1*n + n",r:"(c1+1)*n"},{l:"c1*n - c2*n",r:"(c1-c2)*n"},{l:"c1*n - n",r:"(c1-1)*n"},{l:"v/c",r:"(1/c)*v"},{l:"v/-c",r:"-(1/c)*v"},{l:"-v*-c",r:"c*v"},{l:"-v*c",r:"-c*v"},{l:"v*-c",r:"-c*v"},{l:"v*c",r:"c*v"},{l:"-(-n1*n2)",r:"(n1*n2)"},{l:"-(n1*n2)",r:"(-n1*n2)"},{l:"-(-n1+n2)",r:"(n1-n2)"},{l:"-(n1+n2)",r:"(-n1-n2)"},{l:"(n1^n2)^n3",r:"(n1^(n2*n3))"},{l:"-(-n1/n2)",r:"(n1/n2)"},{l:"-(n1/n2)",r:"(-n1/n2)"}],r=[{l:"(n1/n2 + n3/n4)",r:"((n1*n4 + n3*n2)/(n2*n4))"},{l:"(n1/n2 + n3)",r:"((n1 + n3*n2)/n2)"},{l:"(n1 + n2/n3)",r:"((n1*n3 + n2)/n3)"}],n=[{l:"(n1/(n2/n3))",r:"((n1*n3)/n2)"},{l:"(n1/n2/n3)",r:"(n1/(n2*n3))"}],i={};return i.firstRules=e.concat(t,n),i.distrDivRules=r,i.sucDivRules=n,i.firstRulesAgain=e.concat(t),i.finalRules=[f,{l:"n*-n",r:"-n^2"},{l:"n*n",r:"n^2"},M,{l:"n*-n^n1",r:"-n^(n1+1)"},{l:"n*n^n1",r:"n^(n1+1)"},{l:"n^n1*-n^n2",r:"-n^(n1+n2)"},{l:"n^n1*n^n2",r:"n^(n1+n2)"},{l:"n^n1*-n",r:"-n^(n1+1)"},{l:"n^n1*n",r:"n^(n1+1)"},{l:"n^n1/-n",r:"-n^(n1-1)"},{l:"n^n1/n",r:"n^(n1-1)"},{l:"n/-n^n1",r:"-n^(1-n1)"},{l:"n/n^n1",r:"n^(1-n1)"},{l:"n^n1/-n^n2",r:"n^(n1-n2)"},{l:"n^n1/n^n2",r:"n^(n1-n2)"},{l:"n1+(-n2*n3)",r:"n1-n2*n3"},{l:"v*(-c)",r:"-c*v"},{l:"n1+-n2",r:"n1-n2"},{l:"v*c",r:"c*v"},{l:"(n1^n2)^n3",r:"(n1^(n2*n3))"}],i}(),i=function(e,t,r,n){var i=[],a=p(e,n,t,{exactFractions:!1}),o="+-*"+((r=!!r)?"/":"");u(a);var s={};return s.expression=a,s.variables=i,s;function u(e){var t=e.type;if("FunctionNode"===t)throw new Error("There is an unsolved function call");if("OperatorNode"===t)if("^"===e.op){if("ConstantNode"!==e.args[1].type||!isInteger$1(parseFloat(e.args[1].value)))throw new Error("There is a non-integer exponent");u(e.args[0])}else{if(-1===o.indexOf(e.op))throw new Error("Operator "+e.op+" invalid in polynomial expression");for(var r=0;r=1){var u,c;e=S(e);var l,m=!0,d=!1;for(e=p(e,n.firstRules,{},o);c=m?n.distrDivRules:n.sucDivRules,m=!m,(l=(e=p(e,c,{},s)).toString())!==u;)d=!0,u=l;d&&(e=p(e,n.firstRulesAgain,{},o)),e=p(e,n.finalRules,{},o)}var h=[],y={};return"OperatorNode"===e.type&&e.isBinary()&&"/"===e.op?(1===a&&(e.args[0]=E(e.args[0],h),e.args[1]=E(e.args[1])),r&&(y.numerator=e.args[0],y.denominator=e.args[1])):(1===a&&(e=E(e,h)),r&&(y.numerator=e,y.denominator=null)),r?(y.coefficients=h,y.variables=i.variables,y.expression=e,y):e}});function S(e,t,r){var n=e.type,i=arguments.length>1;if("OperatorNode"===n&&e.isBinary()){var a,o=!1;if("^"===e.op&&("ParenthesisNode"!==e.args[0].type&&"OperatorNode"!==e.args[0].type||"ConstantNode"!==e.args[1].type||(o=(a=parseFloat(e.args[1].value))>=2&&isInteger$1(a))),o){if(a>2){var s=e.args[0],u=new N("^","pow",[e.args[0].cloneDeep(),new x(a-1)]);e=new N("*","multiply",[s,u])}else e=new N("*","multiply",[e.args[0],e.args[0].cloneDeep()]);i&&("content"===r?t.content=e:t.args[r]=e)}}if("ParenthesisNode"===n)S(e.content,e,"content");else if("ConstantNode"!==n&&"SymbolNode"!==n)for(var c=0;cn&&(t[c]=0),t[c]+=o.cte*("+"===o.oper?1:-1),void(n=Math.max(c,n))}o.cte=c,""===o.fire&&(t[0]+=o.cte*("+"===o.oper?1:-1))}}(e,null,r);for(var a,o=!0,s=n=t.length-1;s>=0;s--)if(0!==t[s]){var u=new x(o?t[s]:Math.abs(t[s])),c=t[s]<0?"-":"+";if(s>0){var l=new $(i);if(s>1){var f=new x(s);l=new N("^","pow",[l,f])}u=-1===t[s]&&o?new N("-","unaryMinus",[l]):1===Math.abs(t[s])?l:new N("*","multiply",[u,l])}a=o?u:"+"===c?new N("+","add",[a,u]):new N("-","subtract",[a,u]),o=!1}return o?new x(0):a}})),name$j="reviver",dependencies$j=["classes"],createReviver=factory(name$j,dependencies$j,(e=>{var{classes:t}=e;return function(e,r){var n=t[r&&r.mathjs];return n&&"function"==typeof n.fromJSON?n.fromJSON(r):r}})),name$i="replacer",dependencies$i=[],createReplacer=factory(name$i,dependencies$i,(()=>function(e,t){return"number"!=typeof t||isFinite(t)&&!isNaN(t)?t:{mathjs:"number",value:String(t)}})),version$2="10.6.4",createTrue=factory("true",[],(()=>!0)),createFalse=factory("false",[],(()=>!1)),createNull=factory("null",[],(()=>null)),createInfinity=recreateFactory("Infinity",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1/0):1/0})),createNaN=recreateFactory("NaN",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(NaN):NaN})),createPi=recreateFactory("pi",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberPi(r):pi$1})),createTau=recreateFactory("tau",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberTau(r):tau$1})),createE=recreateFactory("e",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberE(r):e$1})),createPhi=recreateFactory("phi",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberPhi(r):phi$1})),createLN2=recreateFactory("LN2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(2).ln():Math.LN2})),createLN10=recreateFactory("LN10",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(10).ln():Math.LN10})),createLOG2E=recreateFactory("LOG2E",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1).div(new r(2).ln()):Math.LOG2E})),createLOG10E=recreateFactory("LOG10E",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1).div(new r(10).ln()):Math.LOG10E})),createSQRT1_2=recreateFactory("SQRT1_2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r("0.5").sqrt():Math.SQRT1_2})),createSQRT2=recreateFactory("SQRT2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(2).sqrt():Math.SQRT2})),createI=recreateFactory("i",["Complex"],(e=>{var{Complex:t}=e;return t.I})),createUppercasePi=factory("PI",["pi"],(e=>{var{pi:t}=e;return t})),createUppercaseE=factory("E",["e"],(e=>{var{e:t}=e;return t})),createVersion=factory("version",[],(()=>version$2));function recreateFactory(e,t,r){return factory(e,t,r,{recreateOnConfigChange:!0})}var createSpeedOfLight=unitFactory("speedOfLight","299792458","m s^-1"),createGravitationConstant=unitFactory("gravitationConstant","6.67430e-11","m^3 kg^-1 s^-2"),createPlanckConstant=unitFactory("planckConstant","6.62607015e-34","J s"),createReducedPlanckConstant=unitFactory("reducedPlanckConstant","1.0545718176461565e-34","J s"),createMagneticConstant=unitFactory("magneticConstant","1.25663706212e-6","N A^-2"),createElectricConstant=unitFactory("electricConstant","8.8541878128e-12","F m^-1"),createVacuumImpedance=unitFactory("vacuumImpedance","376.730313667","ohm"),createCoulomb=unitFactory("coulomb","8.987551792261171e9","N m^2 C^-2"),createElementaryCharge=unitFactory("elementaryCharge","1.602176634e-19","C"),createBohrMagneton=unitFactory("bohrMagneton","9.2740100783e-24","J T^-1"),createConductanceQuantum=unitFactory("conductanceQuantum","7.748091729863649e-5","S"),createInverseConductanceQuantum=unitFactory("inverseConductanceQuantum","12906.403729652257","ohm"),createMagneticFluxQuantum=unitFactory("magneticFluxQuantum","2.0678338484619295e-15","Wb"),createNuclearMagneton=unitFactory("nuclearMagneton","5.0507837461e-27","J T^-1"),createKlitzing=unitFactory("klitzing","25812.807459304513","ohm"),createBohrRadius=unitFactory("bohrRadius","5.29177210903e-11","m"),createClassicalElectronRadius=unitFactory("classicalElectronRadius","2.8179403262e-15","m"),createElectronMass=unitFactory("electronMass","9.1093837015e-31","kg"),createFermiCoupling=unitFactory("fermiCoupling","1.1663787e-5","GeV^-2"),createFineStructure=numberFactory("fineStructure",.0072973525693),createHartreeEnergy=unitFactory("hartreeEnergy","4.3597447222071e-18","J"),createProtonMass=unitFactory("protonMass","1.67262192369e-27","kg"),createDeuteronMass=unitFactory("deuteronMass","3.3435830926e-27","kg"),createNeutronMass=unitFactory("neutronMass","1.6749271613e-27","kg"),createQuantumOfCirculation=unitFactory("quantumOfCirculation","3.6369475516e-4","m^2 s^-1"),createRydberg=unitFactory("rydberg","10973731.568160","m^-1"),createThomsonCrossSection=unitFactory("thomsonCrossSection","6.6524587321e-29","m^2"),createWeakMixingAngle=numberFactory("weakMixingAngle",.2229),createEfimovFactor=numberFactory("efimovFactor",22.7),createAtomicMass=unitFactory("atomicMass","1.66053906660e-27","kg"),createAvogadro=unitFactory("avogadro","6.02214076e23","mol^-1"),createBoltzmann=unitFactory("boltzmann","1.380649e-23","J K^-1"),createFaraday=unitFactory("faraday","96485.33212331001","C mol^-1"),createFirstRadiation=unitFactory("firstRadiation","3.7417718521927573e-16","W m^2"),createLoschmidt=unitFactory("loschmidt","2.686780111798444e25","m^-3"),createGasConstant=unitFactory("gasConstant","8.31446261815324","J K^-1 mol^-1"),createMolarPlanckConstant=unitFactory("molarPlanckConstant","3.990312712893431e-10","J s mol^-1"),createMolarVolume=unitFactory("molarVolume","0.022413969545014137","m^3 mol^-1"),createSackurTetrode=numberFactory("sackurTetrode",-1.16487052358),createSecondRadiation=unitFactory("secondRadiation","0.014387768775039337","m K"),createStefanBoltzmann=unitFactory("stefanBoltzmann","5.67037441918443e-8","W m^-2 K^-4"),createWienDisplacement=unitFactory("wienDisplacement","2.897771955e-3","m K"),createMolarMass=unitFactory("molarMass","0.99999999965e-3","kg mol^-1"),createMolarMassC12=unitFactory("molarMassC12","11.9999999958e-3","kg mol^-1"),createGravity=unitFactory("gravity","9.80665","m s^-2"),createPlanckLength=unitFactory("planckLength","1.616255e-35","m"),createPlanckMass=unitFactory("planckMass","2.176435e-8","kg"),createPlanckTime=unitFactory("planckTime","5.391245e-44","s"),createPlanckCharge=unitFactory("planckCharge","1.87554603778e-18","C"),createPlanckTemperature=unitFactory("planckTemperature","1.416785e+32","K");function unitFactory(e,t,r){return factory(e,["config","Unit","BigNumber"],(e=>{var{config:n,Unit:i,BigNumber:a}=e,o=new i("BigNumber"===n.number?new a(t):parseFloat(t),r);return o.fixPrefix=!0,o}))}function numberFactory(e,t){return factory(e,["config","BigNumber"],(e=>{var{config:r,BigNumber:n}=e;return"BigNumber"===r.number?new n(t):t}))}var name$h="apply",dependencies$h=["typed","isInteger"],createApplyTransform=factory(name$h,dependencies$h,(e=>{var{typed:t,isInteger:r}=e,n=createApply({typed:t,isInteger:r});return t("apply",{"...any":function(e){var t=e[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1));try{return n.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$g="column",dependencies$g=["typed","Index","matrix","range"],createColumnTransform=factory(name$g,dependencies$g,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e,a=createColumn({typed:t,Index:r,matrix:n,range:i});return t("column",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)&&(e[t]=r-1);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0});function compileInlineExpression(e,t,r){var n=e.filter((function(e){return isSymbolNode(e)&&!(e.name in t)&&!r.has(e.name)}))[0];if(!n)throw new Error('No undefined variable found in inline expression "'+e+'"');var i=n.name,a=createSubScope(r),o=e.compile();return function(e){return a.set(i,e),o.evaluate(a)}}var name$f="filter",dependencies$f=["typed"],createFilterTransform=factory(name$f,dependencies$f,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("filter",{"Array, function":_filter,"Matrix, function":function(e,t){return e.create(_filter(e.toArray(),t))},"Array, RegExp":filterRegExp,"Matrix, RegExp":function(e,t){return e.create(filterRegExp(e.toArray(),t))}});return r}),{isTransformFunction:!0});function _filter(e,t){var r=maxArgumentCount(t);return filter$2(e,(function(e,n,i){return 1===r?t(e):2===r?t(e,[n+1]):t(e,[n+1],i)}))}var name$e="forEach",dependencies$e=["typed"],createForEachTransform=factory(name$e,dependencies$e,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("forEach",{"Array | Matrix, function":function(e,t){var r=maxArgumentCount(t);!function n(i,a){Array.isArray(i)?forEach$1(i,(function(e,t){n(e,a.concat(t+1))})):1===r?t(i):2===r?t(i,a):t(i,a,e)}(e.valueOf(),[])}});return r}),{isTransformFunction:!0}),name$d="index",dependencies$d=["Index"],createIndexTransform=factory(name$d,dependencies$d,(e=>{var{Index:t}=e;return function(){for(var e=[],r=0,n=arguments.length;r0?0:2;else if(i&&!0===i.isSet)i=i.map((function(e){return e-1}));else if(isArray$1(i)||isMatrix(i))i=i.map((function(e){return e-1}));else if(isNumber$1(i))i--;else if(isBigNumber(i))i=i.toNumber()-1;else if("string"!=typeof i)throw new TypeError("Dimension must be an Array, Matrix, number, string, or Range");e[r]=i}var a=new t;return t.apply(a,e),a}}),{isTransformFunction:!0}),name$c="map",dependencies$c=["typed"],createMapTransform=factory(name$c,dependencies$c,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("map",{"Array, function":function(e,t){return _map(e,t,e)},"Matrix, function":function(e,t){return e.create(_map(e.valueOf(),t,e))}});return r}),{isTransformFunction:!0});function _map(e,t,r){var n=maxArgumentCount(t);return function e(i,a){return Array.isArray(i)?map$2(i,(function(t,r){return e(t,a.concat(r+1))})):1===n?t(i):2===n?t(i,a):t(i,a,r)}(e,[])}function lastDimToZeroBase(e){if(2===e.length&&isCollection(e[0])){var t=(e=e.slice())[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1))}return e}var name$b="max",dependencies$b=["typed","config","numeric","larger"],createMaxTransform=factory(name$b,dependencies$b,(e=>{var{typed:t,config:r,numeric:n,larger:i}=e,a=createMax({typed:t,config:r,numeric:n,larger:i});return t("max",{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$a="mean",dependencies$a=["typed","add","divide"],createMeanTransform=factory(name$a,dependencies$a,(e=>{var{typed:t,add:r,divide:n}=e,i=createMean({typed:t,add:r,divide:n});return t("mean",{"...any":function(e){e=lastDimToZeroBase(e);try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$9="min",dependencies$9=["typed","config","numeric","smaller"],createMinTransform=factory(name$9,dependencies$9,(e=>{var{typed:t,config:r,numeric:n,smaller:i}=e,a=createMin({typed:t,config:r,numeric:n,smaller:i});return t("min",{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$8="range",dependencies$8=["typed","config","?matrix","?bignumber","smaller","smallerEq","larger","largerEq"],createRangeTransform=factory(name$8,dependencies$8,(e=>{var{typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u}=e,c=createRange({typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u});return t("range",{"...any":function(e){return"boolean"!=typeof e[e.length-1]&&e.push(!0),c.apply(null,e)}})}),{isTransformFunction:!0}),name$7="row",dependencies$7=["typed","Index","matrix","range"],createRowTransform=factory(name$7,dependencies$7,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e,a=createRow({typed:t,Index:r,matrix:n,range:i});return t("row",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)&&(e[t]=r-1);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$6="subset",dependencies$6=["typed","matrix"],createSubsetTransform=factory(name$6,dependencies$6,(e=>{var{typed:t,matrix:r}=e,n=createSubset({typed:t,matrix:r});return t("subset",{"...any":function(e){try{return n.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$5="concat",dependencies$5=["typed","matrix","isInteger"],createConcatTransform=factory(name$5,dependencies$5,(e=>{var{typed:t,matrix:r,isInteger:n}=e,i=createConcat({typed:t,matrix:r,isInteger:n});return t("concat",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)?e[t]=r-1:isBigNumber(r)&&(e[t]=r.minus(1));try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$4="diff",dependencies$4=["typed","matrix","subtract","number","bignumber"],createDiffTransform=factory(name$4,dependencies$4,(e=>{var{typed:t,matrix:r,subtract:n,number:i,bignumber:a}=e,o=createDiff({typed:t,matrix:r,subtract:n,number:i,bignumber:a});return t(name$4,{"...any":function(e){e=lastDimToZeroBase(e);try{return o.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$3="std",dependencies$3=["typed","sqrt","variance"],createStdTransform=factory(name$3,dependencies$3,(e=>{var{typed:t,sqrt:r,variance:n}=e,i=createStd({typed:t,sqrt:r,variance:n});return t("std",{"...any":function(e){e=lastDimToZeroBase(e);try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$2="sum",dependencies$2=["typed","config","add","numeric"],createSumTransform=factory(name$2,dependencies$2,(e=>{var{typed:t,config:r,add:n,numeric:i}=e,a=createSum({typed:t,config:r,add:n,numeric:i});return t(name$2,{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$1="cumsum",dependencies$1=["typed","add","unaryPlus"],createCumSumTransform=factory(name$1,dependencies$1,(e=>{var{typed:t,add:r,unaryPlus:n}=e,i=createCumSum({typed:t,add:r,unaryPlus:n});return t(name$1,{"...any":function(e){if(2===e.length&&isCollection(e[0])){var t=e[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1))}try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name="variance",dependencies=["typed","add","subtract","multiply","divide","apply","isNaN"],createVarianceTransform=factory(name,dependencies,(e=>{var{typed:t,add:r,subtract:n,multiply:i,divide:a,apply:o,isNaN:s}=e,u=createVariance({typed:t,add:r,subtract:n,multiply:i,divide:a,apply:o,isNaN:s});return t(name,{"...any":function(e){e=lastDimToZeroBase(e);try{return u.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),allFactories=Object.freeze({__proto__:null,createTyped:createTyped,createResultSet:createResultSet,createBigNumberClass:createBigNumberClass,createComplexClass:createComplexClass,createFractionClass:createFractionClass,createRangeClass:createRangeClass,createMatrixClass:createMatrixClass,createDenseMatrixClass:createDenseMatrixClass,createClone:createClone,createIsInteger:createIsInteger,createIsNegative:createIsNegative,createIsNumeric:createIsNumeric,createHasNumericValue:createHasNumericValue,createIsPositive:createIsPositive,createIsZero:createIsZero,createIsNaN:createIsNaN,createTypeOf:createTypeOf,createEqualScalar:createEqualScalar,createSparseMatrixClass:createSparseMatrixClass,createNumber:createNumber,createString:createString,createBoolean:createBoolean,createBignumber:createBignumber,createComplex:createComplex,createFraction:createFraction,createMatrix:createMatrix,createMatrixFromFunction:createMatrixFromFunction,createMatrixFromRows:createMatrixFromRows,createMatrixFromColumns:createMatrixFromColumns,createSplitUnit:createSplitUnit,createUnaryMinus:createUnaryMinus,createUnaryPlus:createUnaryPlus,createAbs:createAbs,createApply:createApply,createAddScalar:createAddScalar,createCbrt:createCbrt,createCeil:createCeil,createCube:createCube,createExp:createExp,createExpm1:createExpm1,createFix:createFix,createFloor:createFloor,createGcd:createGcd,createLcm:createLcm,createLog10:createLog10,createLog2:createLog2,createMod:createMod,createMultiplyScalar:createMultiplyScalar,createMultiply:createMultiply,createNthRoot:createNthRoot,createSign:createSign,createSqrt:createSqrt,createSquare:createSquare,createSubtract:createSubtract,createXgcd:createXgcd,createInvmod:createInvmod,createDotMultiply:createDotMultiply,createBitAnd:createBitAnd,createBitNot:createBitNot,createBitOr:createBitOr,createBitXor:createBitXor,createArg:createArg,createConj:createConj,createIm:createIm,createRe:createRe,createNot:createNot,createOr:createOr,createXor:createXor,createConcat:createConcat,createColumn:createColumn,createCount:createCount,createCross:createCross,createDiag:createDiag,createFilter:createFilter,createFlatten:createFlatten,createForEach:createForEach,createGetMatrixDataType:createGetMatrixDataType,createIdentity:createIdentity,createKron:createKron,createMap:createMap,createDiff:createDiff,createOnes:createOnes,createRange:createRange,createReshape:createReshape,createResize:createResize,createRotate:createRotate,createRotationMatrix:createRotationMatrix,createRow:createRow,createSize:createSize,createSqueeze:createSqueeze,createSubset:createSubset,createTranspose:createTranspose,createCtranspose:createCtranspose,createZeros:createZeros,createFft:createFft,createIfft:createIfft,createErf:createErf,createMode:createMode,createProd:createProd,createFormat:createFormat,createBin:createBin,createOct:createOct,createHex:createHex,createPrint:createPrint,createTo:createTo,createIsPrime:createIsPrime,createNumeric:createNumeric,createDivideScalar:createDivideScalar,createPow:createPow,createRound:createRound,createLog:createLog,createLog1p:createLog1p,createNthRoots:createNthRoots,createDotPow:createDotPow,createDotDivide:createDotDivide,createLsolve:createLsolve,createUsolve:createUsolve,createLsolveAll:createLsolveAll,createUsolveAll:createUsolveAll,createLeftShift:createLeftShift,createRightArithShift:createRightArithShift,createRightLogShift:createRightLogShift,createAnd:createAnd,createCompare:createCompare,createCompareNatural:createCompareNatural,createCompareText:createCompareText,createEqual:createEqual,createEqualText:createEqualText,createSmaller:createSmaller,createSmallerEq:createSmallerEq,createLarger:createLarger,createLargerEq:createLargerEq,createDeepEqual:createDeepEqual,createUnequal:createUnequal,createPartitionSelect:createPartitionSelect,createSort:createSort,createMax:createMax,createMin:createMin,createImmutableDenseMatrixClass:createImmutableDenseMatrixClass,createIndexClass:createIndexClass,createFibonacciHeapClass:createFibonacciHeapClass,createSpaClass:createSpaClass,createUnitClass:createUnitClass,createUnitFunction:createUnitFunction,createSparse:createSparse,createCreateUnit:createCreateUnit,createAcos:createAcos,createAcosh:createAcosh,createAcot:createAcot,createAcoth:createAcoth,createAcsc:createAcsc,createAcsch:createAcsch,createAsec:createAsec,createAsech:createAsech,createAsin:createAsin,createAsinh:createAsinh,createAtan:createAtan,createAtan2:createAtan2,createAtanh:createAtanh,createCos:createCos,createCosh:createCosh,createCot:createCot,createCoth:createCoth,createCsc:createCsc,createCsch:createCsch,createSec:createSec,createSech:createSech,createSin:createSin,createSinh:createSinh,createTan:createTan,createTanh:createTanh,createSetCartesian:createSetCartesian,createSetDifference:createSetDifference,createSetDistinct:createSetDistinct,createSetIntersect:createSetIntersect,createSetIsSubset:createSetIsSubset,createSetMultiplicity:createSetMultiplicity,createSetPowerset:createSetPowerset,createSetSize:createSetSize,createSetSymDifference:createSetSymDifference,createSetUnion:createSetUnion,createAdd:createAdd,createHypot:createHypot,createNorm:createNorm,createDot:createDot,createTrace:createTrace,createIndex:createIndex,createNode:createNode,createAccessorNode:createAccessorNode,createArrayNode:createArrayNode,createAssignmentNode:createAssignmentNode,createBlockNode:createBlockNode,createConditionalNode:createConditionalNode,createConstantNode:createConstantNode,createFunctionAssignmentNode:createFunctionAssignmentNode,createIndexNode:createIndexNode,createObjectNode:createObjectNode,createOperatorNode:createOperatorNode,createParenthesisNode:createParenthesisNode,createRangeNode:createRangeNode,createRelationalNode:createRelationalNode,createSymbolNode:createSymbolNode,createFunctionNode:createFunctionNode,createParse:createParse,createCompile:createCompile,createEvaluate:createEvaluate,createParserClass:createParserClass,createParser:createParser,createLup:createLup,createQr:createQr,createSlu:createSlu,createLusolve:createLusolve,createHelpClass:createHelpClass,createChainClass:createChainClass,createHelp:createHelp,createChain:createChain,createDet:createDet,createInv:createInv,createPinv:createPinv,createEigs:createEigs,createExpm:createExpm,createSqrtm:createSqrtm,createDivide:createDivide,createDistance:createDistance,createIntersect:createIntersect,createSum:createSum,createCumSum:createCumSum,createMean:createMean,createMedian:createMedian,createMad:createMad,createVariance:createVariance,createQuantileSeq:createQuantileSeq,createStd:createStd,createCombinations:createCombinations,createCombinationsWithRep:createCombinationsWithRep,createGamma:createGamma,createLgamma:createLgamma,createFactorial:createFactorial,createKldivergence:createKldivergence,createMultinomial:createMultinomial,createPermutations:createPermutations,createPickRandom:createPickRandom,createRandom:createRandom,createRandomInt:createRandomInt,createStirlingS2:createStirlingS2,createBellNumbers:createBellNumbers,createCatalan:createCatalan,createComposition:createComposition,createLeafCount:createLeafCount,createSimplify:createSimplify,createSimplifyCore:createSimplifyCore,createResolve:createResolve,createSymbolicEqual:createSymbolicEqual,createDerivative:createDerivative,createRationalize:createRationalize,createReviver:createReviver,createReplacer:createReplacer,createE:createE,createUppercaseE:createUppercaseE,createFalse:createFalse,createI:createI,createInfinity:createInfinity,createLN10:createLN10,createLN2:createLN2,createLOG10E:createLOG10E,createLOG2E:createLOG2E,createNaN:createNaN,createNull:createNull,createPhi:createPhi,createPi:createPi,createUppercasePi:createUppercasePi,createSQRT1_2:createSQRT1_2,createSQRT2:createSQRT2,createTau:createTau,createTrue:createTrue,createVersion:createVersion,createAtomicMass:createAtomicMass,createAvogadro:createAvogadro,createBohrMagneton:createBohrMagneton,createBohrRadius:createBohrRadius,createBoltzmann:createBoltzmann,createClassicalElectronRadius:createClassicalElectronRadius,createConductanceQuantum:createConductanceQuantum,createCoulomb:createCoulomb,createDeuteronMass:createDeuteronMass,createEfimovFactor:createEfimovFactor,createElectricConstant:createElectricConstant,createElectronMass:createElectronMass,createElementaryCharge:createElementaryCharge,createFaraday:createFaraday,createFermiCoupling:createFermiCoupling,createFineStructure:createFineStructure,createFirstRadiation:createFirstRadiation,createGasConstant:createGasConstant,createGravitationConstant:createGravitationConstant,createGravity:createGravity,createHartreeEnergy:createHartreeEnergy,createInverseConductanceQuantum:createInverseConductanceQuantum,createKlitzing:createKlitzing,createLoschmidt:createLoschmidt,createMagneticConstant:createMagneticConstant,createMagneticFluxQuantum:createMagneticFluxQuantum,createMolarMass:createMolarMass,createMolarMassC12:createMolarMassC12,createMolarPlanckConstant:createMolarPlanckConstant,createMolarVolume:createMolarVolume,createNeutronMass:createNeutronMass,createNuclearMagneton:createNuclearMagneton,createPlanckCharge:createPlanckCharge,createPlanckConstant:createPlanckConstant,createPlanckLength:createPlanckLength,createPlanckMass:createPlanckMass,createPlanckTemperature:createPlanckTemperature,createPlanckTime:createPlanckTime,createProtonMass:createProtonMass,createQuantumOfCirculation:createQuantumOfCirculation,createReducedPlanckConstant:createReducedPlanckConstant,createRydberg:createRydberg,createSackurTetrode:createSackurTetrode,createSecondRadiation:createSecondRadiation,createSpeedOfLight:createSpeedOfLight,createStefanBoltzmann:createStefanBoltzmann,createThomsonCrossSection:createThomsonCrossSection,createVacuumImpedance:createVacuumImpedance,createWeakMixingAngle:createWeakMixingAngle,createWienDisplacement:createWienDisplacement,createApplyTransform:createApplyTransform,createColumnTransform:createColumnTransform,createFilterTransform:createFilterTransform,createForEachTransform:createForEachTransform,createIndexTransform:createIndexTransform,createMapTransform:createMapTransform,createMaxTransform:createMaxTransform,createMeanTransform:createMeanTransform,createMinTransform:createMinTransform,createRangeTransform:createRangeTransform,createRowTransform:createRowTransform,createSubsetTransform:createSubsetTransform,createConcatTransform:createConcatTransform,createDiffTransform:createDiffTransform,createStdTransform:createStdTransform,createSumTransform:createSumTransform,createCumSumTransform:createCumSumTransform,createVarianceTransform:createVarianceTransform}),BigNumber=createBigNumberClass({config:config$2}),Complex=createComplexClass({}),e=createE({BigNumber:BigNumber,config:config$2}),_false=createFalse({}),fineStructure=createFineStructure({BigNumber:BigNumber,config:config$2}),Fraction=createFractionClass({}),i=createI({Complex:Complex}),_Infinity=createInfinity({BigNumber:BigNumber,config:config$2}),LN10=createLN10({BigNumber:BigNumber,config:config$2}),LOG10E=createLOG10E({BigNumber:BigNumber,config:config$2}),Matrix=createMatrixClass({}),_NaN=createNaN({BigNumber:BigNumber,config:config$2}),_null=createNull({}),phi=createPhi({BigNumber:BigNumber,config:config$2}),Range=createRangeClass({}),ResultSet=createResultSet({}),SQRT1_2=createSQRT1_2({BigNumber:BigNumber,config:config$2}),sackurTetrode=createSackurTetrode({BigNumber:BigNumber,config:config$2}),tau=createTau({BigNumber:BigNumber,config:config$2}),_true=createTrue({}),version$1=createVersion({}),DenseMatrix=createDenseMatrixClass({Matrix:Matrix}),efimovFactor=createEfimovFactor({BigNumber:BigNumber,config:config$2}),LN2=createLN2({BigNumber:BigNumber,config:config$2}),pi=createPi({BigNumber:BigNumber,config:config$2}),replacer=createReplacer({}),SQRT2=createSQRT2({BigNumber:BigNumber,config:config$2}),typed=createTyped({BigNumber:BigNumber,Complex:Complex,DenseMatrix:DenseMatrix,Fraction:Fraction}),unaryPlus=createUnaryPlus({BigNumber:BigNumber,config:config$2,typed:typed}),weakMixingAngle=createWeakMixingAngle({BigNumber:BigNumber,config:config$2}),abs$1=createAbs({typed:typed}),acos$1=createAcos({Complex:Complex,config:config$2,typed:typed}),acot$1=createAcot({BigNumber:BigNumber,typed:typed}),acsc$1=createAcsc({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),addScalar=createAddScalar({typed:typed}),arg=createArg({typed:typed}),asech$1=createAsech({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),asinh$1=createAsinh({typed:typed}),atan$1=createAtan({typed:typed}),atanh$1=createAtanh({Complex:Complex,config:config$2,typed:typed}),bignumber=createBignumber({BigNumber:BigNumber,typed:typed}),bitNot=createBitNot({typed:typed}),boolean=createBoolean({typed:typed}),clone$1=createClone({typed:typed}),combinations=createCombinations({typed:typed}),complex=createComplex({Complex:Complex,typed:typed}),conj$1=createConj({typed:typed}),cosh$1=createCosh({typed:typed}),coth$1=createCoth({BigNumber:BigNumber,typed:typed}),csc$1=createCsc({BigNumber:BigNumber,typed:typed}),cube=createCube({typed:typed}),equalScalar=createEqualScalar({config:config$2,typed:typed}),erf$1=createErf({typed:typed}),exp$1=createExp({typed:typed}),expm1=createExpm1({Complex:Complex,typed:typed}),filter$1=createFilter({typed:typed}),forEach=createForEach({typed:typed}),format=createFormat({typed:typed}),getMatrixDataType=createGetMatrixDataType({typed:typed}),hex=createHex({format:format,typed:typed}),im$1=createIm({typed:typed}),isInteger=createIsInteger({typed:typed}),isNegative=createIsNegative({typed:typed}),isPositive=createIsPositive({typed:typed}),isZero=createIsZero({typed:typed}),LOG2E=createLOG2E({BigNumber:BigNumber,config:config$2}),lgamma=createLgamma({Complex:Complex,typed:typed}),log10$1=createLog10({Complex:Complex,config:config$2,typed:typed}),log2=createLog2({Complex:Complex,config:config$2,typed:typed}),map$1=createMap({typed:typed}),multiplyScalar=createMultiplyScalar({typed:typed}),not=createNot({typed:typed}),number=createNumber({typed:typed}),oct=createOct({format:format,typed:typed}),pickRandom=createPickRandom({config:config$2,typed:typed}),print=createPrint({typed:typed}),random$1=createRandom({config:config$2,typed:typed}),re$1=createRe({typed:typed}),sec$1=createSec({BigNumber:BigNumber,typed:typed}),sign$1=createSign({BigNumber:BigNumber,Fraction:Fraction,complex:complex,typed:typed}),sin$1=createSin({typed:typed}),SparseMatrix=createSparseMatrixClass({Matrix:Matrix,equalScalar:equalScalar,typed:typed}),splitUnit=createSplitUnit({typed:typed}),square=createSquare({typed:typed}),string=createString({typed:typed}),tan$1=createTan({typed:typed}),typeOf=createTypeOf({typed:typed}),acosh$1=createAcosh({Complex:Complex,config:config$2,typed:typed}),acsch$1=createAcsch({BigNumber:BigNumber,typed:typed}),apply=createApply({isInteger:isInteger,typed:typed}),asec$1=createAsec({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),bin=createBin({format:format,typed:typed}),combinationsWithRep=createCombinationsWithRep({typed:typed}),cos$1=createCos({typed:typed}),csch$1=createCsch({BigNumber:BigNumber,typed:typed}),isNaN$2=createIsNaN({typed:typed}),isPrime=createIsPrime({typed:typed}),randomInt=createRandomInt({config:config$2,typed:typed}),sech$1=createSech({BigNumber:BigNumber,typed:typed}),sinh$1=createSinh({typed:typed}),sparse=createSparse({SparseMatrix:SparseMatrix,typed:typed}),sqrt$1=createSqrt({Complex:Complex,config:config$2,typed:typed}),tanh$1=createTanh({typed:typed}),unaryMinus=createUnaryMinus({typed:typed}),acoth$1=createAcoth({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),cot$1=createCot({BigNumber:BigNumber,typed:typed}),fraction=createFraction({Fraction:Fraction,typed:typed}),isNumeric=createIsNumeric({typed:typed}),matrix$2=createMatrix({DenseMatrix:DenseMatrix,Matrix:Matrix,SparseMatrix:SparseMatrix,typed:typed}),matrixFromFunction=createMatrixFromFunction({isZero:isZero,matrix:matrix$2,typed:typed}),mod$1=createMod({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),nthRoot=createNthRoot({BigNumber:BigNumber,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),numeric=createNumeric({bignumber:bignumber,fraction:fraction,number:number}),or=createOr({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),prod=createProd({config:config$2,multiplyScalar:multiplyScalar,numeric:numeric,typed:typed}),reshape=createReshape({isInteger:isInteger,matrix:matrix$2,typed:typed}),size$1=createSize({matrix:matrix$2,config:config$2,typed:typed}),smaller=createSmaller({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),squeeze=createSqueeze({matrix:matrix$2,typed:typed}),subset=createSubset({matrix:matrix$2,typed:typed}),subtract$1=createSubtract({DenseMatrix:DenseMatrix,addScalar:addScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed,unaryMinus:unaryMinus}),to=createTo({matrix:matrix$2,typed:typed}),transpose=createTranspose({matrix:matrix$2,typed:typed}),xgcd=createXgcd({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),zeros=createZeros({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),and=createAnd({equalScalar:equalScalar,matrix:matrix$2,not:not,typed:typed,zeros:zeros}),bitAnd=createBitAnd({equalScalar:equalScalar,matrix:matrix$2,typed:typed}),bitXor=createBitXor({DenseMatrix:DenseMatrix,matrix:matrix$2,typed:typed}),cbrt=createCbrt({BigNumber:BigNumber,Complex:Complex,Fraction:Fraction,config:config$2,isNegative:isNegative,matrix:matrix$2,typed:typed,unaryMinus:unaryMinus}),compare=createCompare({BigNumber:BigNumber,DenseMatrix:DenseMatrix,Fraction:Fraction,config:config$2,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),compareText=createCompareText({matrix:matrix$2,typed:typed}),concat=createConcat({isInteger:isInteger,matrix:matrix$2,typed:typed}),count=createCount({prod:prod,size:size$1,typed:typed}),ctranspose=createCtranspose({conj:conj$1,transpose:transpose,typed:typed}),diag=createDiag({DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,matrix:matrix$2,typed:typed}),divideScalar=createDivideScalar({numeric:numeric,typed:typed}),dotDivide=createDotDivide({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),equal$1=createEqual({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),fft=createFft({addScalar:addScalar,divideScalar:divideScalar,exp:exp$1,i:i,matrix:matrix$2,multiplyScalar:multiplyScalar,tau:tau,typed:typed}),flatten$3=createFlatten({matrix:matrix$2,typed:typed}),gcd=createGcd({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),hasNumericValue=createHasNumericValue({isNumeric:isNumeric,typed:typed}),hypot=createHypot({abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,isPositive:isPositive,multiplyScalar:multiplyScalar,smaller:smaller,sqrt:sqrt$1,typed:typed}),ifft=createIfft({conj:conj$1,dotDivide:dotDivide,fft:fft,typed:typed}),kron=createKron({matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),largerEq=createLargerEq({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),leftShift=createLeftShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),lsolve=createLsolve({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),matrixFromColumns=createMatrixFromColumns({flatten:flatten$3,matrix:matrix$2,size:size$1,typed:typed}),min$1=createMin({config:config$2,numeric:numeric,smaller:smaller,typed:typed}),mode=createMode({isNaN:isNaN$2,isNumeric:isNumeric,typed:typed}),nthRoots=createNthRoots({Complex:Complex,config:config$2,divideScalar:divideScalar,typed:typed}),ones=createOnes({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),partitionSelect=createPartitionSelect({compare:compare,isNaN:isNaN$2,isNumeric:isNumeric,typed:typed}),resize=createResize({config:config$2,matrix:matrix$2}),rightArithShift=createRightArithShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),round$1=createRound({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),smallerEq=createSmallerEq({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),unequal=createUnequal({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),usolve=createUsolve({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),xor=createXor({DenseMatrix:DenseMatrix,matrix:matrix$2,typed:typed}),add$1=createAdd({DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,addScalar:addScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),atan2$1=createAtan2({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),bitOr=createBitOr({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),catalan=createCatalan({addScalar:addScalar,combinations:combinations,divideScalar:divideScalar,isInteger:isInteger,isNegative:isNegative,multiplyScalar:multiplyScalar,typed:typed}),compareNatural=createCompareNatural({compare:compare,typed:typed}),cumsum=createCumSum({add:add$1,typed:typed,unaryPlus:unaryPlus}),deepEqual=createDeepEqual({equal:equal$1,typed:typed}),diff=createDiff({matrix:matrix$2,number:number,subtract:subtract$1,typed:typed}),dot=createDot({addScalar:addScalar,conj:conj$1,multiplyScalar:multiplyScalar,size:size$1,typed:typed}),equalText=createEqualText({compareText:compareText,isZero:isZero,typed:typed}),floor=createFloor({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,round:round$1,typed:typed,zeros:zeros}),identity$1=createIdentity({BigNumber:BigNumber,DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,config:config$2,matrix:matrix$2,typed:typed}),invmod=createInvmod({BigNumber:BigNumber,add:add$1,config:config$2,equal:equal$1,isInteger:isInteger,mod:mod$1,smaller:smaller,typed:typed,xgcd:xgcd}),larger=createLarger({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),log$1=createLog({Complex:Complex,config:config$2,divideScalar:divideScalar,typed:typed}),lsolveAll=createLsolveAll({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),matrixFromRows=createMatrixFromRows({flatten:flatten$3,matrix:matrix$2,size:size$1,typed:typed}),multiply$1=createMultiply({addScalar:addScalar,dot:dot,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),qr=createQr({addScalar:addScalar,complex:complex,conj:conj$1,divideScalar:divideScalar,equal:equal$1,identity:identity$1,isZero:isZero,matrix:matrix$2,multiplyScalar:multiplyScalar,sign:sign$1,sqrt:sqrt$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus,zeros:zeros}),range$1=createRange({bignumber:bignumber,matrix:matrix$2,config:config$2,larger:larger,largerEq:largerEq,smaller:smaller,smallerEq:smallerEq,typed:typed}),rightLogShift=createRightLogShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),setSize=createSetSize({compareNatural:compareNatural,typed:typed}),slu=createSlu({SparseMatrix:SparseMatrix,abs:abs$1,add:add$1,divideScalar:divideScalar,larger:larger,largerEq:largerEq,multiply:multiply$1,subtract:subtract$1,transpose:transpose,typed:typed}),sum=createSum({add:add$1,config:config$2,numeric:numeric,typed:typed}),trace=createTrace({add:add$1,matrix:matrix$2,typed:typed}),usolveAll=createUsolveAll({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),asin$1=createAsin({Complex:Complex,config:config$2,typed:typed}),ceil=createCeil({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,round:round$1,typed:typed,zeros:zeros}),composition=createComposition({addScalar:addScalar,combinations:combinations,isInteger:isInteger,isNegative:isNegative,isPositive:isPositive,larger:larger,typed:typed}),cross=createCross({matrix:matrix$2,multiply:multiply$1,subtract:subtract$1,typed:typed}),det=createDet({divideScalar:divideScalar,isZero:isZero,matrix:matrix$2,multiply:multiply$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),distance=createDistance({abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,multiplyScalar:multiplyScalar,sqrt:sqrt$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),dotMultiply=createDotMultiply({equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),FibonacciHeap=createFibonacciHeapClass({larger:larger,smaller:smaller}),fix=createFix({Complex:Complex,DenseMatrix:DenseMatrix,ceil:ceil,equalScalar:equalScalar,floor:floor,matrix:matrix$2,typed:typed,zeros:zeros}),ImmutableDenseMatrix=createImmutableDenseMatrixClass({DenseMatrix:DenseMatrix,smaller:smaller}),Index=createIndexClass({ImmutableDenseMatrix:ImmutableDenseMatrix}),intersect=createIntersect({abs:abs$1,add:add$1,addScalar:addScalar,config:config$2,divideScalar:divideScalar,equalScalar:equalScalar,flatten:flatten$3,isNumeric:isNumeric,isZero:isZero,matrix:matrix$2,multiply:multiply$1,multiplyScalar:multiplyScalar,smaller:smaller,subtract:subtract$1,typed:typed}),lcm=createLcm({equalScalar:equalScalar,matrix:matrix$2,typed:typed}),log1p=createLog1p({Complex:Complex,config:config$2,divideScalar:divideScalar,log:log$1,typed:typed}),max$1=createMax({config:config$2,larger:larger,numeric:numeric,typed:typed}),quantileSeq=createQuantileSeq({add:add$1,compare:compare,multiply:multiply$1,partitionSelect:partitionSelect,typed:typed}),row=createRow({Index:Index,matrix:matrix$2,range:range$1,typed:typed}),setCartesian=createSetCartesian({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setDistinct=createSetDistinct({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setIsSubset=createSetIsSubset({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setPowerset=createSetPowerset({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),sort=createSort({compare:compare,compareNatural:compareNatural,matrix:matrix$2,typed:typed}),column=createColumn({Index:Index,matrix:matrix$2,range:range$1,typed:typed}),index=createIndex({Index:Index,typed:typed}),inv=createInv({abs:abs$1,addScalar:addScalar,det:det,divideScalar:divideScalar,identity:identity$1,matrix:matrix$2,multiply:multiply$1,typed:typed,unaryMinus:unaryMinus}),pinv=createPinv({Complex:Complex,add:add$1,ctranspose:ctranspose,deepEqual:deepEqual,divideScalar:divideScalar,dot:dot,dotDivide:dotDivide,equal:equal$1,inv:inv,matrix:matrix$2,multiply:multiply$1,typed:typed}),pow$1=createPow({Complex:Complex,config:config$2,fraction:fraction,identity:identity$1,inv:inv,matrix:matrix$2,multiply:multiply$1,number:number,typed:typed}),setDifference=createSetDifference({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setMultiplicity=createSetMultiplicity({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),Spa=createSpaClass({FibonacciHeap:FibonacciHeap,addScalar:addScalar,equalScalar:equalScalar}),sqrtm=createSqrtm({abs:abs$1,add:add$1,identity:identity$1,inv:inv,max:max$1,multiply:multiply$1,size:size$1,sqrt:sqrt$1,subtract:subtract$1,typed:typed}),Unit=createUnitClass({BigNumber:BigNumber,Complex:Complex,Fraction:Fraction,abs:abs$1,addScalar:addScalar,config:config$2,divideScalar:divideScalar,equal:equal$1,fix:fix,format:format,isNumeric:isNumeric,multiplyScalar:multiplyScalar,number:number,pow:pow$1,round:round$1,subtract:subtract$1}),vacuumImpedance=createVacuumImpedance({BigNumber:BigNumber,Unit:Unit,config:config$2}),wienDisplacement=createWienDisplacement({BigNumber:BigNumber,Unit:Unit,config:config$2}),atomicMass=createAtomicMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),bohrMagneton=createBohrMagneton({BigNumber:BigNumber,Unit:Unit,config:config$2}),boltzmann=createBoltzmann({BigNumber:BigNumber,Unit:Unit,config:config$2}),conductanceQuantum=createConductanceQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),createUnit=createCreateUnit({Unit:Unit,typed:typed}),deuteronMass=createDeuteronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),dotPow=createDotPow({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,pow:pow$1,typed:typed}),electricConstant=createElectricConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),elementaryCharge=createElementaryCharge({BigNumber:BigNumber,Unit:Unit,config:config$2}),expm=createExpm({abs:abs$1,add:add$1,identity:identity$1,inv:inv,multiply:multiply$1,typed:typed}),faraday=createFaraday({BigNumber:BigNumber,Unit:Unit,config:config$2}),firstRadiation=createFirstRadiation({BigNumber:BigNumber,Unit:Unit,config:config$2}),gamma$1=createGamma({BigNumber:BigNumber,Complex:Complex,config:config$2,multiplyScalar:multiplyScalar,pow:pow$1,typed:typed}),gravitationConstant=createGravitationConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),hartreeEnergy=createHartreeEnergy({BigNumber:BigNumber,Unit:Unit,config:config$2}),klitzing=createKlitzing({BigNumber:BigNumber,Unit:Unit,config:config$2}),loschmidt=createLoschmidt({BigNumber:BigNumber,Unit:Unit,config:config$2}),magneticConstant=createMagneticConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarMass=createMolarMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarPlanckConstant=createMolarPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),neutronMass=createNeutronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),nuclearMagneton=createNuclearMagneton({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckCharge=createPlanckCharge({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckLength=createPlanckLength({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckTemperature=createPlanckTemperature({BigNumber:BigNumber,Unit:Unit,config:config$2}),protonMass=createProtonMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),reducedPlanckConstant=createReducedPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),rydberg=createRydberg({BigNumber:BigNumber,Unit:Unit,config:config$2}),setIntersect=createSetIntersect({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),speedOfLight=createSpeedOfLight({BigNumber:BigNumber,Unit:Unit,config:config$2}),stefanBoltzmann=createStefanBoltzmann({BigNumber:BigNumber,Unit:Unit,config:config$2}),thomsonCrossSection=createThomsonCrossSection({BigNumber:BigNumber,Unit:Unit,config:config$2}),avogadro=createAvogadro({BigNumber:BigNumber,Unit:Unit,config:config$2}),bohrRadius=createBohrRadius({BigNumber:BigNumber,Unit:Unit,config:config$2}),coulomb=createCoulomb({BigNumber:BigNumber,Unit:Unit,config:config$2}),divide$1=createDivide({divideScalar:divideScalar,equalScalar:equalScalar,inv:inv,matrix:matrix$2,multiply:multiply$1,typed:typed}),electronMass=createElectronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),factorial$1=createFactorial({gamma:gamma$1,typed:typed}),gravity=createGravity({BigNumber:BigNumber,Unit:Unit,config:config$2}),inverseConductanceQuantum=createInverseConductanceQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),lup=createLup({DenseMatrix:DenseMatrix,Spa:Spa,SparseMatrix:SparseMatrix,abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,equalScalar:equalScalar,larger:larger,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),magneticFluxQuantum=createMagneticFluxQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarMassC12=createMolarMassC12({BigNumber:BigNumber,Unit:Unit,config:config$2}),multinomial=createMultinomial({add:add$1,divide:divide$1,factorial:factorial$1,isInteger:isInteger,isPositive:isPositive,multiply:multiply$1,typed:typed}),permutations=createPermutations({factorial:factorial$1,typed:typed}),planckMass=createPlanckMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),quantumOfCirculation=createQuantumOfCirculation({BigNumber:BigNumber,Unit:Unit,config:config$2}),secondRadiation=createSecondRadiation({BigNumber:BigNumber,Unit:Unit,config:config$2}),stirlingS2=createStirlingS2({bignumber:bignumber,addScalar:addScalar,combinations:combinations,divideScalar:divideScalar,factorial:factorial$1,isInteger:isInteger,isNegative:isNegative,larger:larger,multiplyScalar:multiplyScalar,number:number,pow:pow$1,subtract:subtract$1,typed:typed}),unit=createUnitFunction({Unit:Unit,typed:typed}),bellNumbers=createBellNumbers({addScalar:addScalar,isInteger:isInteger,isNegative:isNegative,stirlingS2:stirlingS2,typed:typed}),eigs=createEigs({abs:abs$1,add:add$1,addScalar:addScalar,atan:atan$1,bignumber:bignumber,column:column,complex:complex,config:config$2,cos:cos$1,diag:diag,divideScalar:divideScalar,dot:dot,equal:equal$1,flatten:flatten$3,im:im$1,inv:inv,larger:larger,matrix:matrix$2,matrixFromColumns:matrixFromColumns,multiply:multiply$1,multiplyScalar:multiplyScalar,number:number,qr:qr,re:re$1,sin:sin$1,smaller:smaller,sqrt:sqrt$1,subtract:subtract$1,typed:typed,usolve:usolve,usolveAll:usolveAll}),fermiCoupling=createFermiCoupling({BigNumber:BigNumber,Unit:Unit,config:config$2}),mean=createMean({add:add$1,divide:divide$1,typed:typed}),molarVolume=createMolarVolume({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckConstant=createPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),setSymDifference=createSetSymDifference({Index:Index,concat:concat,setDifference:setDifference,size:size$1,subset:subset,typed:typed}),classicalElectronRadius=createClassicalElectronRadius({BigNumber:BigNumber,Unit:Unit,config:config$2}),lusolve=createLusolve({DenseMatrix:DenseMatrix,lsolve:lsolve,lup:lup,matrix:matrix$2,slu:slu,typed:typed,usolve:usolve}),median=createMedian({add:add$1,compare:compare,divide:divide$1,partitionSelect:partitionSelect,typed:typed}),setUnion=createSetUnion({Index:Index,concat:concat,setIntersect:setIntersect,setSymDifference:setSymDifference,size:size$1,subset:subset,typed:typed}),variance=createVariance({add:add$1,apply:apply,divide:divide$1,isNaN:isNaN$2,multiply:multiply$1,subtract:subtract$1,typed:typed}),kldivergence=createKldivergence({divide:divide$1,dotDivide:dotDivide,isNumeric:isNumeric,log:log$1,matrix:matrix$2,multiply:multiply$1,sum:sum,typed:typed}),norm=createNorm({abs:abs$1,add:add$1,conj:conj$1,ctranspose:ctranspose,eigs:eigs,equalScalar:equalScalar,larger:larger,matrix:matrix$2,multiply:multiply$1,pow:pow$1,smaller:smaller,sqrt:sqrt$1,typed:typed}),planckTime=createPlanckTime({BigNumber:BigNumber,Unit:Unit,config:config$2}),rotationMatrix=createRotationMatrix({BigNumber:BigNumber,DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,addScalar:addScalar,config:config$2,cos:cos$1,matrix:matrix$2,multiplyScalar:multiplyScalar,norm:norm,sin:sin$1,typed:typed,unaryMinus:unaryMinus}),gasConstant=createGasConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),std=createStd({sqrt:sqrt$1,typed:typed,variance:variance}),mad=createMad({abs:abs$1,map:map$1,median:median,subtract:subtract$1,typed:typed}),rotate=createRotate({multiply:multiply$1,rotationMatrix:rotationMatrix,typed:typed}),math$2={},mathWithTransform={},classes={},Chain=createChainClass({math:math$2}),Node=createNode({mathWithTransform:mathWithTransform}),ObjectNode=createObjectNode({Node:Node}),OperatorNode=createOperatorNode({Node:Node}),ParenthesisNode=createParenthesisNode({Node:Node}),RelationalNode=createRelationalNode({Node:Node}),ArrayNode=createArrayNode({Node:Node}),BlockNode=createBlockNode({Node:Node,ResultSet:ResultSet}),ConditionalNode=createConditionalNode({Node:Node}),ConstantNode=createConstantNode({Node:Node}),RangeNode=createRangeNode({Node:Node}),reviver=createReviver({classes:classes}),chain$1=createChain({Chain:Chain,typed:typed}),FunctionAssignmentNode=createFunctionAssignmentNode({Node:Node,typed:typed}),AccessorNode=createAccessorNode({Node:Node,subset:subset}),AssignmentNode=createAssignmentNode({matrix:matrix$2,Node:Node,subset:subset}),IndexNode=createIndexNode({Node:Node,size:size$1}),SymbolNode=createSymbolNode({Unit:Unit,Node:Node,math:math$2}),FunctionNode=createFunctionNode({Node:Node,SymbolNode:SymbolNode,math:math$2}),parse$2=createParse({AccessorNode:AccessorNode,ArrayNode:ArrayNode,AssignmentNode:AssignmentNode,BlockNode:BlockNode,ConditionalNode:ConditionalNode,ConstantNode:ConstantNode,FunctionAssignmentNode:FunctionAssignmentNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,RangeNode:RangeNode,RelationalNode:RelationalNode,SymbolNode:SymbolNode,config:config$2,numeric:numeric,typed:typed}),resolve=createResolve({ConstantNode:ConstantNode,FunctionNode:FunctionNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,parse:parse$2}),simplifyCore=createSimplifyCore({AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,divide:divide$1,equal:equal$1,isZero:isZero,multiply:multiply$1,pow:pow$1,subtract:subtract$1}),compile=createCompile({parse:parse$2,typed:typed}),Help=createHelpClass({parse:parse$2}),leafCount=createLeafCount({parse:parse$2,typed:typed}),simplify$2=createSimplify({bignumber:bignumber,fraction:fraction,AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,config:config$2,divide:divide$1,equal:equal$1,isZero:isZero,mathWithTransform:mathWithTransform,matrix:matrix$2,multiply:multiply$1,parse:parse$2,pow:pow$1,resolve:resolve,simplifyCore:simplifyCore,subtract:subtract$1,typed:typed}),symbolicEqual=createSymbolicEqual({OperatorNode:OperatorNode,parse:parse$2,simplify:simplify$2,typed:typed}),evaluate$1=createEvaluate({parse:parse$2,typed:typed}),help=createHelp({Help:Help,mathWithTransform:mathWithTransform,typed:typed}),Parser=createParserClass({evaluate:evaluate$1}),rationalize=createRationalize({bignumber:bignumber,fraction:fraction,AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,config:config$2,divide:divide$1,equal:equal$1,isZero:isZero,mathWithTransform:mathWithTransform,matrix:matrix$2,multiply:multiply$1,parse:parse$2,pow:pow$1,simplify:simplify$2,simplifyCore:simplifyCore,subtract:subtract$1,typed:typed}),derivative$1=createDerivative({ConstantNode:ConstantNode,FunctionNode:FunctionNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,config:config$2,equal:equal$1,isZero:isZero,numeric:numeric,parse:parse$2,simplify:simplify$2,typed:typed}),parser=createParser({Parser:Parser,typed:typed});_extends$1(math$2,{e:e,false:_false,fineStructure:fineStructure,i:i,Infinity:_Infinity,LN10:LN10,LOG10E:LOG10E,NaN:_NaN,null:_null,phi:phi,SQRT1_2:SQRT1_2,sackurTetrode:sackurTetrode,tau:tau,true:_true,E:e,version:version$1,efimovFactor:efimovFactor,LN2:LN2,pi:pi,replacer:replacer,reviver:reviver,SQRT2:SQRT2,typed:typed,unaryPlus:unaryPlus,PI:pi,weakMixingAngle:weakMixingAngle,abs:abs$1,acos:acos$1,acot:acot$1,acsc:acsc$1,addScalar:addScalar,arg:arg,asech:asech$1,asinh:asinh$1,atan: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o=a.length,s=Array(o+1);for(s[0]=0,r=0;r=u){if(i[l]=m[c],0===c)return;++l,s=f[--c],u=p[c]}else 0===n[o=a[r[s]]]?(n[o]=1,f[c]=s,m[++c]=o,s=t[o],p[c]=u=t[o+1]):++s},numeric.ccsLPSolve=function(e,t,r,n,i,a,o){var s=e[0],u=e[1],c=e[2];s.length;var l,f,p,m,d,h,y,g,v,x=t[0],b=t[1],_=t[2];for(f=x[i],p=x[i+1],n.length=0,l=f;la&&(o=i,a=s);for(_(v[r])=c){if(i[f]=a[d[l]],0===l)return;++f,u=p[--l],c=m[l]}else 0===n[s=r[u]]?(n[s]=1,p[l]=u,d[++l]=s,u=t[s=a[s]],m[l]=c=t[s+1]):++u}},numeric.ccsLPSolve0=function(e,t,r,n,i,a,o,s){var u=e[0],c=e[1],l=e[2];u.length;var f,p,m,d,h,y,g,v,x,b=t[0],_=t[1],w=t[2];for(p=b[i],m=b[i+1],n.length=0,f=p;fa&&(o=i,a=s);for(_(v[w[r]])r[n]&&(r[n]=t.length),t)t.hasOwnProperty(i)&&e(t[i],r,n+1);return r},numeric.sclone=function e(t,r,n){void 0===r&&(r=0),void 0===n&&(n=numeric.sdim(t).length);var i,a=Array(t.length);if(r===n-1){for(i in t)t.hasOwnProperty(i)&&(a[i]=t[i]);return a}for(i in t)t.hasOwnProperty(i)&&(a[i]=e(t[i],r+1,n));return a},numeric.sdiag=function(e){var t,r,n=e.length,i=Array(n);for(t=n-1;t>=1;t-=2)r=t-1,i[t]=[],i[t][t]=e[t],i[r]=[],i[r][r]=e[r];return 0===t&&(i[0]=[],i[0][0]=e[t]),i},numeric.sidentity=function(e){return numeric.sdiag(numeric.rep([e],1))},numeric.stranspose=function(e){var t,r,n,i=[];for(t in e.length,e)if(e.hasOwnProperty(t))for(r in n=e[t])n.hasOwnProperty(r)&&("object"!=typeof i[r]&&(i[r]=[]),i[r][t]=n[r]);return i},numeric.sLUP=function(e,t){throw new Error("The function numeric.sLUP had a bug in it and has been removed. 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numeric.sdotMM(e,t);default:throw new Error("numeric.sdot not implemented for tensors of order "+r+" and "+n)}},numeric.sscatter=function(e){var t,r,n,i,a=e[0].length,o=e.length,s=[];for(r=a-1;r>=0;--r)if(e[o-1][r]){for(i=s,n=0;n=0;--a)r[a]=[];for(a=i;a>=0;--a)r[a].push(n[a]);r[i+1].push(o)}}else e(o,r,n);return n.length>i&&n.pop(),r},numeric.cLU=function(e){var t,r,n,i,a,o,s=e[0],u=e[1],c=e[2],l=s.length,f=0;for(t=0;tf&&(f=s[t]);f++;var p,m=Array(f),d=Array(f),h=numeric.rep([f],1/0),y=numeric.rep([f],-1/0);for(n=0;ny[t]&&(y[t]=r);for(t=0;ty[t+1]&&(y[t+1]=y[t]);for(t=f-1;t>=1;t--)h[t]=0;p--){for(;c[m]>p;)i[p]-=l[m]*i[c[m]],m--;i[p]/=l[m],m--}return i},numeric.cgrid=function(e,t){"number"==typeof e&&(e=[e,e]);var r,n,i,a=numeric.rep(e,-1);if("function"!=typeof t)if("L"===t)t=function(t,r){return t>=e[0]/2||ri&&(i=a[n]);for(i++,r=numeric.rep([i],0),n=0;n1;)i[n=o((t+r)/2)]<=e?t=n:r=n;return this._at(e,t)}a=e.length;var s,u=Array(a);for(s=a-1;-1!==s;--s)u[s]=this.at(e[s]);return u},numeric.Spline.prototype.diff=function(){var e,t,r,n=this.x,i=this.yl,a=this.yr,o=this.kl,s=this.kr,u=i.length,c=o,l=s,f=Array(u),p=Array(u),m=numeric.add,d=numeric.mul,h=numeric.div,y=numeric.sub;for(e=u-1;-1!==e;--e)t=n[e+1]-n[e],r=y(a[e+1],i[e]),f[e]=h(m(d(r,6),d(o[e],-4*t),d(s[e+1],-2*t)),t*t),p[e+1]=h(m(d(r,-6),d(o[e],2*t),d(s[e+1],4*t)),t*t);return new numeric.Spline(n,c,l,f,p)},numeric.Spline.prototype.roots=function(){function e(e){return e*e}var t=[],r=this.x,n=this.yl,i=this.yr,a=this.kl,o=this.kr;"number"==typeof n[0]&&(n=[n],i=[i],a=[a],o=[o]);var s,u,c,l,f,p,m,d,h,y,g,v,x,b,_,w,N,$,A,M,S,E,T,O=n.length,C=r.length-1,k=(t=Array(O),Math.sqrt);for(s=0;s!==O;++s){for(l=n[s],f=i[s],p=a[s],m=o[s],d=[],u=0;u!==C;u++){for(u>0&&f[u]*l[u]<0&&d.push(r[u]),w=r[u+1]-r[u],r[u],g=l[u],v=f[u+1],h=p[u]/w,x=(y=m[u+1]/w)+3*g+2*h-3*v,b=3*(y+h+2*(g-v)),(_=e(h-y+3*(g-v))+12*y*g)<=0?N=($=x/b)>r[u]&&$r[u]&&$r[u]&&A0)S=E,$=A;else{for(var D=0;!((T=($*E-A*S)/($-A))<=S||T>=E);)if((M=this._at(T,u))*A>0)E=T,A=M,-1===D&&($*=.5),D=-1;else{if(!(M*$>0))break;S=T,$=M,1===D&&(A*=.5),D=1}d.push(T),S=N[c+1],$=this._at(S,u)}else d.push(S),S=E,$=A;0===A&&d.push(E)}t[s]=d}return"number"==typeof this.yl[0]?t[0]:t},numeric.spline=function(e,t,r,n){var i,a=e.length,o=[],s=[],u=[],c=numeric.sub,l=numeric.mul,f=numeric.add;for(i=a-2;i>=0;i--)s[i]=e[i+1]-e[i],u[i]=c(t[i+1],t[i]);"string"!=typeof r&&"string"!=typeof n||(r=n="periodic");var p=[[],[],[]];switch(typeof r){case"undefined":o[0]=l(3/(s[0]*s[0]),u[0]),p[0].push(0,0),p[1].push(0,1),p[2].push(2/s[0],1/s[0]);break;case"string":o[0]=f(l(3/(s[a-2]*s[a-2]),u[a-2]),l(3/(s[0]*s[0]),u[0])),p[0].push(0,0,0),p[1].push(a-2,0,1),p[2].push(1/s[a-2],2/s[a-2]+2/s[0],1/s[0]);break;default:o[0]=r,p[0].push(0),p[1].push(0),p[2].push(1)}for(i=1;i20)throw new Error("Numerical gradient 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s,u,c,l,f,p,m,d,h,y,g,v,x,b=[e],_=[r],w=[n(e,r)],N=[],$=[3/40,9/40],A=[44/45,-56/15,32/9],M=[19372/6561,-25360/2187,64448/6561,-212/729],S=[9017/3168,-355/33,46732/5247,49/176,-5103/18656],E=[35/384,0,500/1113,125/192,-2187/6784,11/84],T=[.10013431883002395,0,.3918321794184259,-.02982460176594817,.05893268337240795,-.04497888809104361,5618549.5/235043384],O=[.2,.3,.8,8/9,1,1],C=[-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,1/40],k=0,D=(t-e)/10,I=0,B=numeric.add,z=numeric.mul,R=Math.min,P=Math.abs,q=numeric.norminf,L=Math.pow,F=numeric.any,j=numeric.lt,U=numeric.and;numeric.sub;var G=new numeric.Dopri(b,_,w,N,-1,"");for("function"==typeof o&&(g=o(e,r));et&&(D=t-e),s=n(e+O[0]*D,B(r,z(.2*D,w[k]))),u=n(e+O[1]*D,B(B(r,z($[0]*D,w[k])),z($[1]*D,s))),c=n(e+O[2]*D,B(B(B(r,z(A[0]*D,w[k])),z(A[1]*D,s)),z(A[2]*D,u))),l=n(e+O[3]*D,B(B(B(B(r,z(M[0]*D,w[k])),z(M[1]*D,s)),z(M[2]*D,u)),z(M[3]*D,c))),f=n(e+O[4]*D,B(B(B(B(B(r,z(S[0]*D,w[k])),z(S[1]*D,s)),z(S[2]*D,u)),z(S[3]*D,c)),z(S[4]*D,l))),p=n(e+D,h=B(B(B(B(B(r,z(w[k],D*E[0])),z(u,D*E[2])),z(c,D*E[3])),z(l,D*E[4])),z(f,D*E[5]))),(y="number"==typeof(m=B(B(B(B(B(z(w[k],D*C[0]),z(u,D*C[2])),z(c,D*C[3])),z(l,D*C[4])),z(f,D*C[5])),z(p,D*C[6])))?P(m):q(m))>i){if(e+(D=.2*D*L(i/y,.25))===e){G.msg="Step size became too small";break}}else{if(N[k]=B(B(B(B(B(B(r,z(w[k],D*T[0])),z(u,D*T[2])),z(c,D*T[3])),z(l,D*T[4])),z(f,D*T[5])),z(p,D*T[6])),b[++k]=e+D,_[k]=h,w[k]=p,"function"==typeof o){var V,Z,H=e,X=e+.5*D;if(v=o(X,N[k-1]),F(x=U(j(g,0),j(0,v)))||(H=X,g=v,v=o(X=e+D,h),x=U(j(g,0),j(0,v))),F(x)){for(var W,Q,Y=0,J=1,K=1;;){if("number"==typeof g)Z=(K*v*H-J*g*X)/(K*v-J*g);else 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t=e[0],r=e.slice(1);if("apply"===t){if("string"!=typeof r[0])throw Error("Non string functions not implemented for conversion to mathjs");if("factorial"===r[0])return new math.OperatorNode("!","factorial",[this.convert(r[1])]);let e=functionConverstions[r[0]];e||(e=r[0]);const t=new math.SymbolNode(e),n=r[1];let i;return i="tuple"===n[0]?n.slice(1).map(function(e,t){return this.convert(e)}.bind(this)):[this.convert(n)],new math.FunctionNode(t,i)}if("lts"===t||"gts"===t){const e=r[0],n=r[1];if("tuple"!==e[0]||"tuple"!==n[0])throw new Error("Badly formed ast");const i=e.slice(1).map(function(e,t){return this.convert(e)}.bind(this));let a=[];for(let r=1;r","larger",i.slice(r-1,r+1))):"lts"===t?a.push(new math.OperatorNode("<=","smallerEq",i.slice(r-1,r+1))):a.push(new math.OperatorNode(">=","largerEq",i.slice(r-1,r+1)));let o=new math.OperatorNode("and","and",a.slice(0,2));for(let e=2;e=","largerEq",[e,o])):u.push(new math.OperatorNode(">","larger",[e,o])),a[2]?u.push(new 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math.OperatorNode("and","and",p);return"notsubset"!==t&&"notsuperset"!==t||(m=new math.OperatorNode("not","not",[m])),m}if("matrix"===t){let e=r[0],t=e[1],n=e[2],i=r[1];if(!Number.isInteger(t)||!Number.isInteger(n))throw Error("Matrix must have integer dimensions");let a=[];for(let e=1;e<=t;e++){let t=[];for(let r=1;r<=n;r++)t.push(this.convert(i[e][r]));a.push(new math.ArrayNode(t))}return new math.ArrayNode(a)}if(t in operators$2)return operators$2[t](r.map(function(e,t){return this.convert(e)}.bind(this)));throw Error("Operator "+t+" not implemented for conversion to mathjs")}}var function_normalizations={ln:"log",arccos:"acos",arccosh:"acosh",arcsin:"asin",arcsinh:"asinh",arctan:"atan",arctanh:"atanh",arcsec:"asec",arcsech:"asech",arccsc:"acsc",arccsch:"acsch",arccot:"acot",arccoth:"acoth",cosec:"csc"},create_trig_inverses_for=["cos","cosh","sin","sinh","tan","tanh","sec","sech","csc","csch","cot","coth"],move_exponents_outside_for=["cos","cosh","sin","sinh","tan","tanh","sec","sech","csc","csch","cot","coth"];function normalize_function_names(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("apply"===r){if("sqrt"===n[0])return["^",normalize_function_names(n[1]),.5];var i=normalize_function_names_sub(n[0]);i=["apply",i];var a=n.slice(1).map((function(e){return normalize_function_names(e)}));return a=a.length>1?["tuple"].concat(a):a[0],i.push(a),i}return"^"===r&&"e"===n[0]&&math$1.define_e?["apply","exp",normalize_function_names(n[1])]:"binom"===r?["apply","nCr",["tuple",normalize_function_names(n[0]),normalize_function_names(n[1])]]:[r].concat(n.map((function(e){return normalize_function_names(e)})))}function normalize_function_names_sub(e){if("string"==typeof e)return e in function_normalizations?function_normalizations[e]:e;if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if("^"===t&&2===r.length&&-1===r[1]){let e=normalize_function_names_sub(r[0]);if(create_trig_inverses_for.includes(e))return"a"+e}return[t].concat(r.map((function(e){return normalize_function_names_sub(e)})))}function normalize_applied_functions(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("apply"===r){let e=n[0];if("^"===e[0]){let t=e[1],r=e[2];return-1!==r&&move_exponents_outside_for.includes(t)?["^",["apply",t,normalize_applied_functions(n[1])],r]:["apply",e,normalize_applied_functions(n[1])]}let t=0;for(;"prime"===e[0];)t+=1,e=e[1];let r=["apply",e,normalize_applied_functions(n[1])];for(let e=0;e2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_integer_ast(e,o[0],r),is_integer_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_integer_ast(a[0],n,r);if("*"===i){return!!a.every((function(e){return is_integer_ast(e,n,r)}))||void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!is_positive_ast(a[1],n,!0,r))return;if(!1===e)return!0}let t=is_integer_ast(a[0],n,r),i=is_integer_ast(a[1],n,r);if(!t)return t;if(!i)return;return!!is_positive_ast(a[1],n,!1,r)||void 0}if("+"===i){let e=0;for(let t=0;t0)return;e+=1}if(void 0===i)return}return 0===e}if("apply"===i)return!!(functions.C.Z&&functions.C.Z.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.Z&&functions.R.Z.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.Z&&functions.nonzeroC.Z.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.Z&&functions.nonneg.Z.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.Z&&functions.pos.Z.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("/"===i||"prime"===i)return;return!1}return!1}function is_real_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e)return Number.isFinite(e);var n=evaluate_to_constant(e,!1);if(null!==n)return"number"==typeof n&&Number.isFinite(n);if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}if("in"===a&&o[0]===e&&"R"===o[1])return negate_adjust(!0,s);if("notin"===a&&o[0]===e&&"R"===o[1])return negate_adjust(!1,s);if(!1===s){if("in"===a&&o[0]===e&&"Z"===o[1])return!0}else if("notin"===a&&o[0]===e&&"Z"===o[1])return!0;if("<"===a||"le"===a){let t=variables(n),r=functions$2(n);if(-1!==t.indexOf(e)&&0===r.length)return!0}if("="===a&&!s||"ne"===a&&s){let t=narrow_assumptions(i,r);if(o[0]===e)return is_real_ast(o[1],t);if(o[1]===e)return is_real_ast(o[0],t)}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_real_ast(e,o[0],r),is_real_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_real_ast(a[0],n,r);if("*"===i||"+"===i){if(a.length>2&&(a=(e=unflattenRight(e)).slice(1)),"*"===i&&(!1===is_nonzero_ast(a[0],n,r)||!1===is_nonzero_ast(a[1],n,r)))return!0;let t=is_real_ast(a[0],n,r),o=is_real_ast(a[1],n,r);return!(!t||!o)||!(t&&!1===o||o&&!1===t)&&void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r),t=is_positive_ast(a[1],n,!0,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!t)return;if(!1===e)return!0}let i=is_real_ast(a[0],n,r),o=is_real_ast(a[1],n,r);if(!i||!o)return;if(!is_positive_ast(a[0],n,!1,r)){return!!is_integer_ast(a[1],n,r)||void 0}return!!is_positive_ast(a[0],n,!0,r)||(!!t||void 0)}if("/"===i){if(!is_nonzero_ast(a[1],n,r))return;if(!1===is_nonzero_ast(a[0],n,r))return!0;if(!is_real_ast(a[0],n,r)||!is_real_ast(a[1],n,r))return;return!0}if("apply"===i)return!!(functions.C.R&&functions.C.R.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.R&&functions.R.R.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.R&&functions.nonzeroC.R.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.R&&functions.nonneg.R.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.R&&functions.pos.R.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("prime"===i)return;return!1}return!1}function is_complex_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e)return Number.isFinite(e);var n=evaluate_to_constant(e,!1);if(null!==n)return"number"==typeof n?Number.isFinite(n):!(void 0===n.re||!Number.isFinite(n.re)||void 0===n.im||!Number.isFinite(n.im));if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}if("in"===a&&o[0]===e&&"C"===o[1])return negate_adjust(!0,s);if("notin"===a&&o[0]===e&&"C"===o[1])return negate_adjust(!1,s);if(!1===s){if("in"===a){if(o[0]===e&&"Z"===o[1])return!0;if(o[0]===e&&"R"===o[1])return!0}}else if("notin"===a){if(o[0]===e&&"Z"===o[1])return!0;if(o[0]===e&&"R"===o[1])return!0}if("<"===a||"le"===a){let t=variables(n),r=functions$2(n);if(-1!==t.indexOf(e)&&0===r.length)return!0}if("="===a&&!s||"ne"===a&&s){let t=narrow_assumptions(i,r);if(o[0]===e)return is_complex_ast(o[1],t);if(o[1]===e)return is_complex_ast(o[0],t)}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_complex_ast(e,o[0],r),is_complex_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_complex_ast(a[0],n,r);if("*"===i||"+"===i){if("*"===i&&!a.every((e=>!1!==is_nonzero_ast(e,n,r))))return!0;return!!a.every((e=>is_complex_ast(e,n,r)))||void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r),t=is_positive_ast(a[1],n,!0,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!t)return;if(!1===e)return!0}let i=is_complex_ast(a[0],n,r),o=is_complex_ast(a[1],n,r);return!(!i||!o)||void 0}if("/"===i){if(!is_nonzero_ast(a[1],n,r))return;if(!1===is_nonzero_ast(a[0],n,r))return!0;if(!is_complex_ast(a[0],n,r)||!is_complex_ast(a[1],n,r))return;return!0}if("apply"===i)return!!(functions.C.C&&functions.C.C.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.C&&functions.R.C.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.C&&functions.nonzeroC.C.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.C&&functions.nonneg.C.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.C&&functions.pos.C.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("prime"===i)return;return!1}return!1}function is_nonzero_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e){if(Number.isFinite(e))return 0!==e;if(Number.isNaN(e))return;return!0}var n=evaluate_to_constant(e,!1);if(null!==n){if("number"==typeof n){if(Number.isFinite(n))return 0!==n;if(Number.isNaN(n))return;return!0}return void 0!==n.re&&void 0!==n.im&&(0!==n.re||0!==n.im)||void 0}if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}let u=narrow_assumptions(i,r);if("="===a&&!s||"ne"===a&&s){if(o[0]===e)return is_nonzero_ast(o[1],u);if(o[1]===e)return is_nonzero_ast(o[0],u)}if("ne"===a&&!s||"="===a&&s){if(o[0]===e&&!1===is_nonzero_ast(o[1],u))return!0;if(o[1]===e&&!1===is_nonzero_ast(o[0],u))return!0}if("<"===a)if(s){if(o[0]===e&&is_positive_ast(o[1],u,!0))return!0;if(o[1]===e&&is_negative_ast(o[0],u,!0))return!0}else{if(o[0]===e&&is_negative_ast(o[1],u,!1))return!0;if(o[1]===e&&is_positive_ast(o[0],u,!1))return!0}if("le"===a)if(s){if(o[0]===e&&is_positive_ast(o[1],u,!1))return!0;if(o[1]===e&&is_negative_ast(o[0],u,!1))return!0}else{if(o[0]===e&&is_negative_ast(o[1],u,!0))return!0;if(o[1]===e&&is_positive_ast(o[0],u,!0))return!0}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_nonzero_ast(e,o[0],r),is_nonzero_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_nonzero_ast(a[0],n,r);if("+"===i){if(a.length>2&&(a=(e=unflattenRight(e)).slice(1)),equal(a[0],simplify(["-",a[1]],r)))return!1;let t=is_nonzero_ast(a[0],n,r),i=is_nonzero_ast(a[1],n,r);if(!1===t)return i;if(!1===i)return t;let o=is_real_ast(a[0],n,r),s=is_real_ast(a[1],n,r);if(!o||!s)return!0===o?!1===s||void 0:!0===s&&!1===o||void 0;let u=is_positive_ast(a[0],n,!1,r),c=is_positive_ast(a[1],n,!1,r),l=is_positive_ast(a[0],n,!0,r),f=is_positive_ast(a[1],n,!0,r);return!!(u&&f||l&&c)||(!1===u&&!1===f||!1===l&&!1===c||void 0)}if("*"===i){let e=!0;for(let t=0;t0:e>=0);var i=is_real_ast(e,t,n);if(!i)return i;var a=evaluate_to_constant(e,!1);if(null!==a)return"number"==typeof a&&(!!Number.isFinite(a)&&(r?a>0:a>=0));if("string"==typeof e){let i;if(i=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(i))return;let a=i,o=i[0],s=i.slice(1),u=!1;for(;"not"===o;){if(u=!u,i=s[0],!Array.isArray(i))return;o=i[0],s=i.slice(1)}let c=narrow_assumptions(a,n);if("="===o&&!u||"ne"===o&&u){if(s[0]===e)return is_positive_ast(s[1],c,r);if(s[1]===e)return is_positive_ast(s[0],c,r)}if("<"===o)if(u){if(s[0]===e&&is_positive_ast(s[1],c,r))return!0;if(s[1]===e&&is_negative_ast(s[0],c,!r))return!1}else{if(s[0]===e&&is_negative_ast(s[1],c,!1))return!1;if(s[1]===e&&is_positive_ast(s[0],c,!1))return!0}if("le"===o)if(u){if(s[0]===e&&is_positive_ast(s[1],c,!1))return!0;if(s[1]===e&&is_negative_ast(s[0],c,!1))return!1}else{if(s[0]===e&&is_negative_ast(s[1],c,!r))return!1;if(s[1]===e&&is_positive_ast(s[0],c,r))return!0}if("and"!==o&&"or"!==o)return;if(u)return;return s.length>2&&(i=unflattenRight(i),s=i.slice(1)),simple_assumption_combination(o,is_positive_ast(e,s[0],r,n),is_positive_ast(e,s[1],r,n))}if(Array.isArray(e)){let i;i=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let a=e[0],o=e.slice(1);if("-"===a)return is_negative_ast(o[0],i,r,n);if("+"===a){o.length>2&&(o=(e=unflattenRight(e)).slice(1));let t=is_positive_ast(o[0],i,!1,n),a=is_positive_ast(o[1],i,!1,n),s=is_positive_ast(o[0],i,!0,n),u=is_positive_ast(o[1],i,!0,n);if(r){if(t&&u||s&&a)return!0}else if(t&&a)return!0;if(r){if(!1===s&&!1===u)return!1}else if(!1===t&&!1===u||!1===s&&!1===a)return!1;return}if("*"===a){if(!o.every((e=>!1!==is_nonzero_ast(e,i,n))))return!r;o.length>2&&(o=(e=unflattenRight(e)).slice(1));let t=is_real_ast(o[0],i,n),a=is_real_ast(o[1],i,n);if(void 0===t||void 0===a)return;if(!1===t)return!1===a&&void 0;if(!1===a)return!1;let s=is_positive_ast(o[0],i,!1,n),u=is_positive_ast(o[1],i,!1,n),c=is_positive_ast(o[0],i,!0,n),l=is_positive_ast(o[1],i,!0,n);if(r){if(c&&l||!1===s&&!1===u)return!0;if(!1===c&&u||s&&!1===l)return!1}else{if(s&&u||!1===c&&!1===l)return!0;if(c&&!1===u||!1===s&&l)return!1}return}if("/"===a){if(!is_nonzero_ast(o[1],i,n))return;if(!1===is_nonzero_ast(o[0],i,n))return!r;let e=is_positive_ast(o[1],i,!0,n);if(void 0===e)return;let t=e?r:!r,a=is_positive_ast(o[0],i,t,n);if(void 0===a)return;return!0===a?!0===e:!0!==e}if("^"===a){let e=is_nonzero_ast(o[0],i,n);if(e){if(!1===is_nonzero_ast(o[1],i,n)){if(o[0]===1/0||o[0]===-1/0)return;return!0}}else{if(!is_positive_ast(o[1],i,!0,n))return;if(!1===e)return!r;if(r)return}if(!0!==is_real_ast(o[0],i,n))return;if(!is_positive_ast(o[0],i,r,n)){return!!is_integer_ast(simplify(["/",o[1],2],n),i,n)||void 0}return!!is_real_ast(o[1],i,n)||void 0}if("apply"===a&&!r)return!!(functions.C.nonneg&&functions.C.nonneg.includes(o[0])&&is_complex_ast(o[1],i,n))||(!!(functions.R.nonneg&&functions.R.nonneg.includes(o[0])&&is_real_ast(o[1],i,n))||(!!(functions.nonzeroC.nonneg&&functions.nonzeroC.nonneg.includes(o[0])&&is_nonzero_ast(o[1],i,n)&&is_complex_ast(o[1],i,n))||(!!(functions.nonneg.nonneg&&functions.nonneg.nonneg.includes(o[0])&&is_positive_ast(o[1],i,!1,n))||(!!(functions.pos.nonneg&&functions.pos.nonneg.includes(o[0])&&is_positive_ast(o[1],i,!0,n))||void 0))));if("apply"===a&&r)return!!(functions.C.pos&&functions.C.pos.includes(o[0])&&is_complex_ast(o[1],i,n))||(!!(functions.R.pos&&functions.R.pos.includes(o[0])&&is_real_ast(o[1],i,n))||(!!(functions.nonzeroC.pos&&functions.nonzeroC.pos.includes(o[0])&&is_nonzero_ast(o[1],i,n)&&is_complex_ast(o[1],i,n))||(!!(functions.nonneg.pos&&functions.nonneg.pos.includes(o[0])&&is_positive_ast(o[1],i,!1,n))||(!!(functions.pos.pos&&functions.pos.pos.includes(o[0])&&is_positive_ast(o[1],i,!0,n))||void 0))));if("prime"===a)return;return!1}return!1}function is_negative_ast(e,t,r,n){void 0===r&&(r=!0);var i=is_real_ast(e,t,n);if(!0===i){let i=is_positive_ast(e,t,!r,n);return!1===i||!0!==i&&void 0}return i}function tuples_to_vectors(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("tuple"===r){return["vector"].concat(n.map((function(e,t){return tuples_to_vectors(e)})))}if("apply"===r){if("tuple"===n[1][0]){let e=tuples_to_vectors(n[0]),t=n[1].slice(1);return["apply",e,["tuple"].concat(t.map((function(e,t){return tuples_to_vectors(e)})))]}}else if("gts"===r||"lts"===r||"interval"===r){let e=n[0],t=n[1];if("tuple"!==e[0]||"tuple"!==t[0])throw new Error("Badly formed ast");return[r,["tuple"].concat(e.slice(1).map((function(e,t){return tuples_to_vectors(e)}))),t]}return[r].concat(n.map((function(e,t){return tuples_to_vectors(e)})))}function to_intervals(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("tuple"===r&&2===n.length){let e=["tuple"].concat(n.map((function(e,t){return to_intervals(e)})));return e=["interval",e,["tuple",!1,!1]],e}if("array"===r&&2===n.length){let e=["tuple"].concat(n.map((function(e,t){return to_intervals(e)})));return e=["interval",e,["tuple",!0,!0]],e}if("apply"===r){if("tuple"===n[1][0]){let e=to_intervals(n[0]),t=n[1].slice(1);return["apply",e,["tuple"].concat(t.map((function(e,t){return to_intervals(e)})))]}}else if("gts"===r||"lts"===r||"interval"===r){let e=n[0],t=n[1];if("tuple"!==e[0]||"tuple"!==t[0])throw new Error("Badly formed ast");return[r,["tuple"].concat(e.slice(1).map((function(e,t){return to_intervals(e)}))),t]}return[r].concat(n.map((function(e,t){return to_intervals(e)})))}function altvectors_to_vectors(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("altvector"===r){return["vector"].concat(n.map((function(e,t){return altvectors_to_vectors(e)})))}return[r].concat(n.map((function(e,t){return altvectors_to_vectors(e)})))}function ParseError(e,t){this.name="ParseError",this.message=e||"Error parsing input",this.stack=(new Error).stack,this.location=t}functions.C.nonneg=["abs"],functions.C.nonzero=["exp"],functions.C.R=["abs","arg"],functions.C.C=["abs","arg","exp","sign","cos","cosh","sin","sinh","erf","sqrt","log","ln","log10"],functions.R.pos=["exp"],functions.R.nonneg=["abs","exp","arg"],functions.R.R=["abs","arg","exp","sign","cos","cosh","sin","sinh","erf"],functions.R.Z=["sign"],functions.nonzeroC.pos=["abs"],functions.nonneg.nonneg=["abs","exp","arg","sqrt","erf"],functions.nonzeroC.nonzero=["abs"],functions.nonneg.R=[...new Set(functions.R.R.concat(functions.nonneg.nonneg))],functions.pos.pos=["abs","exp","sqrt","erf"],functions.pos.nonneg=functions.pos.pos,functions.pos.nonzero=["abs","exp","sqrt","erf"],functions.pos.R=functions.nonneg.R.concat(["log","ln","log10"]),ParseError.prototype=Object.create(Error.prototype),ParseError.prototype.constructor=ParseError;class lexer{constructor(e,t="\\s"){this.input="",this.location=0,this.token_rules=[],this.initial_whitespace=new RegExp("^("+t+")+");for(let t of e)this.token_rules.push([new RegExp("^"+t[0])].concat(t.slice(1)))}set_input(e){if("string"!=typeof e)throw new Error("Input must be a string");this.input=e,this.location=0}return_state(){return{input:this.input,location:this.location}}set_state({input:e=null,location:t=0}={}){null!==e&&(this.input=e,this.location=t)}advance({remove_initial_space:e=!0}={}){let t=this.initial_whitespace.exec(this.input);if(t){let r=t[0].length;if(this.input=this.input.slice(r),this.location+=r,!e)return{token_type:"SPACE",token_text:t[0],original_text:t[0]}}if(0===this.input.length)return{token_type:"EOF",token_text:"",original_text:""};for(var r of(t=null,this.token_rules))if(t=r[0].exec(this.input),t){let e=t[0].length;this.input=this.input.slice(e),this.location+=e;break}return null===t?{token_type:"INVALID",token_text:this.input[0],original_text:this.input[0]}:r.length>2?{token_type:r[1],token_text:r[2],original_text:t[0]}:{token_type:r[1],token_text:t[0],original_text:t[0]}}unput(e){if("string"!=typeof e)throw new Error("Input must be a string");this.location-=e.length,this.input=e+this.input}}var is_associative={"+":!0,"*":!0,and:!0,or:!0,union:!0,intersect:!0};function flatten(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if(r=r.map((function(e,t){return flatten(e)})),is_associative[t]){for(var n=[],i=0;i2?n=n.concat(r[i].slice(1)):n.push(r[i]);r=n}return[t].concat(r)}const sci_notat_exp_regex$1="(E[+\\-]?[0-9]+\\s*($|(?=\\,|\\||\\)|\\}|\\])))?",number_rules_sci$1=[["[0-9]+(\\.[0-9]*)?"+sci_notat_exp_regex$1,"NUMBER"],["\\.[0-9]+"+sci_notat_exp_regex$1,"NUMBER"]],number_rules_non_sci$1=[["[0-9]+(\\.[0-9]*)?","NUMBER"],["\\.[0-9]+","NUMBER"]],base_text_rules=[["\\*\\*","^"],["\\*","*"],["\\xB7","*"],["·","*"],["•","*"],["⋅","*"],["×","*"],["/","/"],["-","-"],["֊","-"],["־","-"],["᠆","-"],["‐","-"],["‑","-"],["‒","-"],["–","-"],["—","-"],["―","-"],["⁻","-"],["₋","-"],["−","-"],["⸺","-"],["⸻","-"],["﹘","-"],["﹣","-"],["－","-"],["\\+","+"],["\\^","^"],["‸","^"],["ʌ","^"],["\\|","|"],["\\(","("],["\\)",")"],["\\[","["],["\\]","]"],["\\{","{"],["\\}","}"],["⟨","LANGLE"],["⟩","RANGLE"],["〈","LANGLE"],["〉","RANGLE"],[",",","],[":",":"],["α","VARMULTICHAR","alpha"],["β","VARMULTICHAR","beta"],["ϐ","VARMULTICHAR","beta"],["Γ","VARMULTICHAR","Gamma"],["γ","VARMULTICHAR","gamma"],["Δ","VARMULTICHAR","Delta"],["δ","VARMULTICHAR","delta"],["ε","VARMULTICHAR","epsilon"],["ϵ","VARMULTICHAR","epsilon"],["ζ","VARMULTICHAR","zeta"],["η","VARMULTICHAR","eta"],["Θ","VARMULTICHAR","Theta"],["ϴ","VARMULTICHAR","Theta"],["θ","VARMULTICHAR","theta"],["ᶿ","VARMULTICHAR","theta"],["ϑ","VARMULTICHAR","theta"],["ι","VARMULTICHAR","iota"],["κ","VARMULTICHAR","kappa"],["Λ","VARMULTICHAR","Lambda"],["λ","VARMULTICHAR","lambda"],["μ","VARMULTICHAR","mu"],["µ","VARMULTICHAR","mu"],["ν","VARMULTICHAR","nu"],["Ξ","VARMULTICHAR","Xi"],["ξ","VARMULTICHAR","xi"],["Π","VARMULTICHAR","Pi"],["π","VARMULTICHAR","pi"],["ϖ","VARMULTICHAR","pi"],["ρ","VARMULTICHAR","rho"],["ϱ","VARMULTICHAR","rho"],["Σ","VARMULTICHAR","Sigma"],["σ","VARMULTICHAR","sigma"],["ς","VARMULTICHAR","sigma"],["τ","VARMULTICHAR","tau"],["Υ","VARMULTICHAR","Upsilon"],["υ","VARMULTICHAR","upsilon"],["Φ","VARMULTICHAR","Phi"],["φ","VARMULTICHAR","phi"],["ϕ","VARMULTICHAR","phi"],["Ψ","VARMULTICHAR","Psi"],["ψ","VARMULTICHAR","psi"],["Ω","VARMULTICHAR","Omega"],["ω","VARMULTICHAR","omega"],["oo(?![a-zA-Z0-9])","INFINITY"],["OO(?![a-zA-Z0-9])","INFINITY"],["infty(?![a-zA-Z0-9])","INFINITY"],["infinity(?![a-zA-Z0-9])","INFINITY"],["Infinity(?![a-zA-Z0-9])","INFINITY"],["∞","INFINITY"],["ℯ","VAR","e"],["♠","VARMULTICHAR","spade"],["♡","VARMULTICHAR","heart"],["♢","VARMULTICHAR","diamond"],["♣","VARMULTICHAR","club"],["★","VARMULTICHAR","bigstar"],["◯","VARMULTICHAR","bigcirc"],["◊","VARMULTICHAR","lozenge"],["△","VARMULTICHAR","bigtriangleup"],["▽","VARMULTICHAR","bigtriangledown"],["⧫","VARMULTICHAR","blacklozenge"],["■","VARMULTICHAR","blacksquare"],["▲","VARMULTICHAR","blacktriangle"],["▼","VARMULTICHAR","blacktriangledown"],["◀","VARMULTICHAR","blacktriangleleft"],["▶","VARMULTICHAR","blacktriangleright"],["□","VARMULTICHAR","Box"],["∘","VARMULTICHAR","circ"],["⋆","VARMULTICHAR","star"],["and(?![a-zA-Z0-9])","AND"],["\\&\\&?","AND"],["∧","AND"],["or(?![a-zA-Z0-9])","OR"],["∨","OR"],["not(?![a-zA-Z0-9])","NOT"],["¬","NOT"],["=","="],["᐀","="],["゠","="],["!=","NE"],["≠","NE"],["<=","LE"],["≤","LE"],[">=","GE"],["≥","GE"],["<","<"],[">",">"],["forall(?![a-zA-Z0-9])","FORALL"],["∀","FORALL"],["exists(?![a-zA-Z0-9])","EXISTS"],["∃","EXISTS"],["elementof(?![a-zA-Z0-9])","IN"],["∈","IN"],["notelementof(?![a-zA-Z0-9])","NOTIN"],["∉","NOTIN"],["containselement(?![a-zA-Z0-9])","NI"],["∋","NI"],["notcontainselement(?![a-zA-Z0-9])","NOTNI"],["∌","NOTNI"],["subset(?![a-zA-Z0-9])","SUBSET"],["⊂","SUBSET"],["subseteq(?![a-zA-Z0-9])","SUBSETEQ"],["⊆","SUBSETEQ"],["notsubset(?![a-zA-Z0-9])","NOTSUBSET"],["⊄","NOTSUBSET"],["notsubseteq(?![a-zA-Z0-9])","NOTSUBSETEQ"],["⊈","NOTSUBSETEQ"],["superset(?![a-zA-Z0-9])","SUPERSET"],["⊃","SUPERSET"],["superseteq(?![a-zA-Z0-9])","SUPERSETEQ"],["⊇","SUPERSETEQ"],["notsuperset(?![a-zA-Z0-9])","NOTSUPERSET"],["⊅","NOTSUPERSET"],["notsuperseteq(?![a-zA-Z0-9])","NOTSUPERSETEQ"],["⊉","NOTSUPERSETEQ"],["union(?![a-zA-Z0-9])","UNION"],["∪","UNION"],["intersect(?![a-zA-Z0-9])","INTERSECT"],["∩","INTERSECT"],["perp(?![a-zA-Z0-9])","PERP"],["⟂","PERP"],["parallel(?![a-zA-Z0-9])","PARALLEL"],["∥","PARALLEL"],["angle(?![a-zA-Z0-9])","ANGLE"],["∠","ANGLE"],["int(?![a-zA-Z0-9])","INT"],["∫","INT"],["!","!"],["'","'"],["_","_"],["\\.\\.\\.","LDOTS"],["[a-zA-Z∂][a-zA-Z∂0-9]*","VAR"],["[＿$%]","VAR"]],allowSimplifiedFunctionApplicationDefault$1=!0,splitSymbolsDefault=!0,unsplitSymbolsDefault=["alpha","beta","gamma","Gamma","delta","Delta","epsilon","zeta","eta","theta","Theta","iota","kappa","lambda","Lambda","mu","nu","xi","Xi","pi","Pi","rho","sigma","Sigma","tau","Tau","upsilon","Upsilon","phi","Phi","chi","psi","Psi","omega","Omega","angle","deg"],appliedFunctionSymbolsDefault$1=["abs","exp","log","ln","log10","sign","sqrt","erf","cos","cosh","acos","acosh","arccos","arccosh","cot","coth","acot","acoth","arccot","arccoth","csc","csch","acsc","acsch","arccsc","arccsch","sec","sech","asec","asech","arcsec","arcsech","sin","sinh","asin","asinh","arcsin","arcsinh","tan","tanh","atan","atan2","atanh","arctan","arctanh","arg","conj","re","im","det"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textToAst$4{constructor({allowSimplifiedFunctionApplication:e=allowSimplifiedFunctionApplicationDefault$1,splitSymbols:t=splitSymbolsDefault,unsplitSymbols:r=unsplitSymbolsDefault,appliedFunctionSymbols:n=appliedFunctionSymbolsDefault$1,functionSymbols:i=functionSymbolsDefault$1,operatorSymbols:a=operatorSymbolsDefault$1,units:o=unitsDefault$1,parseLeibnizNotation:s=parseLeibnizNotationDefault$1,parseScientificNotation:u=!0}={}){this.allowSimplifiedFunctionApplication=e,this.splitSymbols=t,this.unsplitSymbols=r,this.appliedFunctionSymbols=n,this.functionSymbols=i,this.operatorSymbols=a,this.units=o,this.parseLeibnizNotation=s;let c=base_text_rules;c=u?[...number_rules_sci$1,...c]:[...number_rules_non_sci$1,...c],this.lexer=new lexer(c)}advance(e){if(this.token=this.lexer.advance(e),"INVALID"===this.token.token_type)throw new ParseError("Invalid symbol '"+this.token.original_text+"'",this.lexer.location)}return_state(){return{lexer_state:this.lexer.return_state(),token:Object.assign({},this.token)}}set_state(e){this.lexer.set_state(e.lexer_state),this.token=Object.assign({},e.token)}convert(e){this.lexer.set_input(e),this.advance();var t=this.statement_list();if("EOF"!==this.token.token_type)throw new ParseError("Invalid location of '"+this.token.original_text+"'",this.lexer.location);return flatten(t)}statement_list(){for(var e=[this.statement()];","===this.token.token_type;)this.advance(),e.push(this.statement());return e=e.length>1?["list"].concat(e):e[0]}statement({inside_absolute_value:e=0}={}){if("LDOTS"===this.token.token_type)return this.advance(),["ldots"];var t;try{t=this.return_state();let r=this.statement_a({inside_absolute_value:e});return":"!==this.token.token_type?r:(this.advance(),[":",r,this.statement_a()])}catch(e){try{this.set_state(t);let r=this.statement_a({parse_absolute_value:!1});if("|"!==this.token.token_type)throw e;return this.advance(),["|",r,this.statement_a({parse_absolute_value:!1})]}catch(t){throw e}}}statement_a({inside_absolute_value:e=0,parse_absolute_value:t=!0}={}){for(var r=this.statement_b({inside_absolute_value:e,parse_absolute_value:t});"OR"===this.token.token_type;){let n=this.token.token_type.toLowerCase();this.advance(),r=[n,r,this.statement_b({inside_absolute_value:e,parse_absolute_value:t})]}return r}statement_b(e){for(var t=this.relation(e);"AND"===this.token.token_type;){let r=this.token.token_type.toLowerCase();this.advance(),t=[r,t,this.relation(e)]}return t}relation(e){if("NOT"===this.token.token_type||"!"===this.token.token_type)return this.advance(),["not",this.relation(e)];if("FORALL"===this.token.token_type||"EXISTS"===this.token.token_type){let t=this.token.token_type.toLowerCase();return this.advance(),[t,this.relation(e)]}for(var t=this.expression(e);"="===this.token.token_type||"NE"===this.token.token_type||"<"===this.token.token_type||">"===this.token.token_type||"LE"===this.token.token_type||"GE"===this.token.token_type||"IN"===this.token.token_type||"NOTIN"===this.token.token_type||"NI"===this.token.token_type||"NOTNI"===this.token.token_type||"SUBSET"===this.token.token_type||"NOTSUBSET"===this.token.token_type||"SUBSETEQ"===this.token.token_type||"NOTSUBSETEQ"===this.token.token_type||"SUPERSET"===this.token.token_type||"NOTSUPERSET"===this.token.token_type||"SUPERSETEQ"===this.token.token_type||"NOTSUPERSETEQ"===this.token.token_type;){let r=this.token.token_type.toLowerCase(),n=0;"<"===this.token.token_type||"LE"===this.token.token_type?n=-1:">"!==this.token.token_type&&"GE"!==this.token.token_type||(n=1),this.advance();let i=this.expression(e);if(-1===n)if("<"===this.token.token_type||"LE"===this.token.token_type){let n=["tuple"];"<"===r?n.push(!0):n.push(!1);let a=["tuple",t,i];for(;"<"===this.token.token_type||"LE"===this.token.token_type;)"<"===this.token.token_type?n.push(!0):n.push(!1),this.advance(),a.push(this.expression(e));t=["lts",a,n]}else t=[r,t,i];else if(1===n)if(">"===this.token.token_type||"GE"===this.token.token_type){let n=["tuple"];">"===r?n.push(!0):n.push(!1);let a=["tuple",t,i];for(;">"===this.token.token_type||"GE"===this.token.token_type;)">"===this.token.token_type?n.push(!0):n.push(!1),this.advance(),a.push(this.expression(e));t=["gts",a,n]}else t=[r,t,i];else if("="===r)for(t=["=",t,i];"="===this.token.token_type;)this.advance(),t.push(this.expression(e));else t=[r,t,i]}return t}expression(e){let t=!1;"+"===this.token.token_type&&(t=!0,this.advance());let r=!1;"-"===this.token.token_type&&(r=!0,this.advance());var n=this.term(e);if(r||t){if(!1===n)return(t?"+":"")+(r?"-":"");if("string"==typeof n&&[...n].every((e=>["+","-"].includes(e))))return(t?"+":"")+(r?"-":"")+n}for(!1===n&&(n="＿"),r&&(n=n>0?-n:["-",n]),t&&(n=["+",n]);["+","-","UNION","INTERSECT","PERP","PARALLEL"].includes(this.token.token_type);){let t=this.token.token_type.toLowerCase(),r=!1,i=!1;"-"===this.token.token_type?(t="+",r=!0,this.advance()):(this.advance(),"+"===t&&"-"===this.token.token_type&&(r=!0,i=!0,this.advance()));let a=this.term(e);if("+"===t){if(!1===a&&("number"==typeof n||"string"==typeof n))return i?n+"+-":r?n+"-":n+"+";if("string"==typeof a&&[...a].every((e=>["+","-"].includes(e)))&&("number"==typeof n||"string"==typeof n))return i?n+"+-"+a:r?n+"-"+a:n+"+"+a}!1===a&&(a="＿"),r&&(a=a>0?-a:["-",a]),n=[t,n,a]}return n}term(e){var t=this.factor(e),r=!1;do{if(r=!1,"*"===this.token.token_type){this.advance(),!1===t&&(t="＿");let n=this.factor(e);!1===n&&(n="＿"),t=["*",t,n],r=!0}else if("/"===this.token.token_type){this.advance(),!1===t&&(t="＿");let n=this.factor(e);!1===n&&(n="＿"),t=["/",t,n],r=!0}else{let n=Object.assign({},e);n.allow_absolute_value_closing=!0;let i=this.nonMinusFactor(n);!1!==i&&(!1===t&&(t="＿"),t=["*",t,i],r=!0)}}while(r);return this.convert_units_in_term(flatten(t))}convert_units_in_term(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("*"===t){let t=r.length;for(let[e,n]of r.entries()){let i=this.units[n];if(i){if(i.prefix&&e0){let a,o=n;return i.substitute&&(o=i.substitute),a=1===e?["unit",r[0],o]:["unit",["*",...r.slice(0,e)],o],e===t-1?a:this.convert_units_in_term(["*",a,...r.slice(e+1)])}}}return e}return"/"===t?["/",this.convert_units_in_term(r[0]),this.convert_units_in_term(r[1])]:e}factor(e){if("+"===this.token.token_text){this.advance();let t=this.factor(e);return!1===t?"+":"string"==typeof t&&[...t].every((e=>["+","-"].includes(e)))?"+"+t:["+",t]}if("-"===this.token.token_type){this.advance();let t=this.factor(e);return t>0?-t:!1===t?"-":"string"==typeof t&&[...t].every((e=>["+","-"].includes(e)))?"-"+t:["-",t]}let t=this.nonMinusFactor(e);return!1===t&&"PERP"===this.token.token_type&&(t="perp",this.advance()),t}nonMinusFactor(e){for(var t=this.baseFactor(e);"^"===this.token.token_type||"!"===this.token.token_type||"'"===this.token.token_type;)if(!1===t&&(t="＿"),"^"===this.token.token_type){this.advance(),t=["^",t,this.get_subsuperscript(e)]}else"!"===this.token.token_type?(t=["apply","factorial",t],this.advance()):(t=["prime",t],this.advance());return t}get_subsuperscript({parse_absolute_value:e}){if(["+","-","PERP"].includes(this.token.token_type)){let e=this.token.token_type.toLowerCase();return this.advance(),e}{let t=this.baseFactor({parse_absolute_value:e,in_subsuperscript_with_no_delimiters:!0});return!1===t&&(t="＿"),t}}baseFactor({inside_absolute_value:e=0,parse_absolute_value:t=!0,allow_absolute_value_closing:r=!1,in_subsuperscript_with_no_delimiters:n=!1}={}){var i=!1;if("NUMBER"===this.token.token_type)i=parseFloat(this.token.token_text),this.advance();else if("INFINITY"===this.token.token_type)i=1/0,this.advance();else if("VAR"===this.token.token_type||"VARMULTICHAR"===this.token.token_type){if(i=this.token.token_text,this.appliedFunctionSymbols.includes(i)||this.functionSymbols.includes(i)){let e=!1;if(this.appliedFunctionSymbols.includes(i)&&(e=!0),this.advance(),"_"===this.token.token_type){this.advance();let e=this.get_subsuperscript({parse_absolute_value:t});i="log"===i&&10===e?"log10":["_",i,e]}if(n)e&&(i=["apply",i,"＿"]);else{for(;"'"===this.token.token_type;)i=["prime",i],this.advance();for(;"^"===this.token.token_type;){this.advance(),i=["^",i,this.get_subsuperscript({parse_absolute_value:t})]}if("("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),"list"===e[0]&&(e[0]="tuple"),i=["apply",i,e]}else if(e){if(!this.allowSimplifiedFunctionApplication)throw new ParseError("Expecting ( after function",this.lexer.location);let e=this.factor({parse_absolute_value:t});!1===e&&(e="＿"),i=["apply",i,e]}}return i}if(this.operatorSymbols.includes(i))if(this.advance(),"("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),i="list"===e[0]?[i,...e.slice(1)]:[i,e]}else{let e=this.factor({parse_absolute_value:t});!1===e&&(e="＿"),i=[i,e]}else{if(this.parseLeibnizNotation){let e=this.return_state(),t=this.leibniz_notation();if(t)return t;this.set_state(e)}let n=this.splitSymbols;if(n&&("VARMULTICHAR"===this.token.token_type||this.unsplitSymbols.includes(i)||1===i.length||i.match(/[\d]/g))&&(n=!1),n){for(let e=i.length-1;e>=0;e--)this.lexer.unput(" "),this.lexer.unput(i[e]);return this.advance(),this.baseFactor({inside_absolute_value:e,parse_absolute_value:t,allow_absolute_value_closing:r})}this.advance()}}else if("("===this.token.token_type||"["===this.token.token_type||"{"===this.token.token_type||"LANGLE"===this.token.token_type){let e,t,r=this.token.token_type;"("===this.token.token_type?(e=")",t="]"):"["===this.token.token_type?(e="]",t=")"):"{"===this.token.token_type?(e="}",t=null):(e="RANGLE",t=null),this.advance();let n=1;if("list"===(i=this.statement_list())[0]&&(n=i.length-1),this.token.token_type!==e){if(2!==n||null===t)throw new ParseError("Expecting "+e,this.lexer.location);if(this.token.token_type!==t)throw new ParseError("Expecting ) or ]",this.lexer.location);let a;i[0]="tuple",a="("===r?["tuple",!1,!0]:["tuple",!0,!1],(i=["interval",i]).push(a)}else n>=2?i[0]="("===r?"tuple":"["===r?"array":"{"===r?"set":"altvector":"{"===r&&(i=("|"===i[0]||i[0],["set",i]));this.advance()}else if("|"!==this.token.token_type||!t||0!==e&&r){if("ANGLE"===this.token.token_type)if(this.advance(),"("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),"list"===e[0]?i=["angle",...e.slice(1)]:"*"===e[0]&&(i=["angle",e])}else{let e=[],r=this.nonMinusFactor({parse_absolute_value:t});for(;!1!==r;)e.push(r),r=this.nonMinusFactor({parse_absolute_value:t});i=0===e.length?"angle":["angle",...e]}else if("INT"===this.token.token_type){this.advance();let e="int";if("_"===this.token.token_type){this.advance(),e=["_",e,this.get_subsuperscript({parse_absolute_value:t})]}if("^"===this.token.token_type){this.advance(),e=["^",e,this.get_subsuperscript({parse_absolute_value:t})]}let r=flatten(this.term({parse_absolute_value:t}));if(Array.isArray(r)&&"*"===r[0]){let e=[];for(let t=0;t2&&(this.lexer.unput(this.token.token_text.slice(2)),this.token.token_text=this.token.token_text.slice(0,2));let s=this.token.token_text;if(2===s.length){if(!/[a-zA-Z]/.exec(s[1]))return!1;i.push(s[1])}else{if(this.advance(),("VAR"!==this.token.token_type||this.token.token_text.includes("∂"))&&"VARMULTICHAR"!==this.token.token_type)return!1;i.push(this.token.token_text)}let u=1,c=!1;if(this.advance({remove_initial_space:!1}),"SPACE"===this.token.token_type&&(c=!0,this.advance()),"^"===this.token.token_type){if(this.advance(),"NUMBER"!==this.token.token_type)return!1;if(u=parseFloat(this.token.token_text),!Number.isInteger(u))return!1;c=!1,this.advance({remove_initial_space:!1}),"SPACE"===this.token.token_type&&(c=!0,this.advance())}if(a.push(u),o+=u,o>r)return!1;if(o===r){if(!c&&("VAR"===this.token.token_type||"VARMULTICHAR"===this.token.token_type))return!1;"SPACE"===this.token.token_type&&this.advance();let o="derivative_leibniz";"∂"===t&&(o="partial_"+o),e=[o],1===r?e.push(n):e.push(["tuple",n,r]);let s=[];for(let e=0;et[e+1]));if(t.length!==n||i.length!==n)return subtree;let a=["+",...t.map(((e,t)=>["*",e,i[t]]))];r.push(a)}s.push(r)}return{success:!0,newMatrix:["matrix",["tuple",r,i],s]}}function a(e,t){let r=e[1][1],n=e[1][2],i=e[2],a=["tuple"];for(let e=0;e=0;t--){let n=r[t][0];if("matrix"===n){let n=i(r[t],e);if(!n.success)break;e=n.newMatrix,r.pop()}else{if(["tuple","list","vector","altvector","interval","set","array"].includes(n))break;1!==r[t]&&(e=a(e,r[t])),r.pop()}}for(;n.length>0;){let t=n[0][0];if("matrix"===t){let t=i(e,n[0]);if(!t.success)break;e=t.newMatrix,n.splice(0,1)}else{if(["tuple","list","vector","altvector","interval","set","array"].includes(t))break;1!==n[0]&&(e=a(e,n[0])),n.splice(0,1)}}return r.length>0||n.length>0?["*",...r,e,...n]:e}return e})),(t||r)&&(o=["*",["matrix",["tuple","m","n"],"matrixData"],"b"],s={variables:{n:Number.isInteger,m:Number.isInteger,matrixData:!0,b:!0}},n=transform(n,(function(e){let n=match$2(e,o,s);if(n){let i,a=n.m,o=n.n,s=n.b,u=n.matrixData,c=[];t&&(c.push("vector"),c.push("altvector")),r&&c.push("tuple");let l=[];if(c.includes(s[0]))i=s;else{if(!Array.isArray(s)||"*"!==s[0]||!c.includes(s[1][0]))return e;i=s[1],l=s.slice(2)}let f=i.slice(1);if(f.length!==o)return e;let p=[i[0]];for(let e=0;e["*",e,f[t]]))];p.push(t)}return l.length>0?["*",p,...l]:p}return e}))),n}function perform_vector_scalar_multiplications(e,t=!0){var r=get_tree(e);let n=function(e,t){let r=["*","a",[t,"vectorData"],"b"],n={allow_implicit_identities:["a","b"]};return e=transform(e,(function(e){let i=match$2(e,r,n);if(i){if(1===i.a&&1===i.b)return e;let r=i.vectorData;r=Array.isArray(r)&&r[0]===t?r.slice(1):[r];let n=[],a=[];Array.isArray(i.a)&&"*"===i.a[0]?n.push(...i.a.slice(1)):n.push(i.a),Array.isArray(i.b)&&"*"===i.b[0]?a.push(...i.b.slice(1)):a.push(i.b);for(let e=n.length-1;e>=0;e--){let t=n[e][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t))break;1!==n[e]&&(r=r.map((t=>["*",t,n[e]]))),n.pop()}for(;a.length>0;){let e=a[0][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(e))break;1!==a[0]&&(r=r.map((e=>["*",e,a[0]]))),a.splice(0,1)}let o=[t,...r];return n.length>0||a.length>0?["*",...n,o,...a]:o}return e})),e};return r=n(r,"vector"),r=n(r,"altvector"),t&&(r=n(r,"tuple")),r}function perform_matrix_scalar_multiplications(e){var t=get_tree(e);let r=["*","a",["matrix","size","matrixData"],"b"],n={allow_implicit_identities:["a","b"]};return t=transform(t,(function(e){let t=match$2(e,r,n);if(t){if(1===t.a&&1===t.b)return e;let r=t.matrixData,n=[],i=[];Array.isArray(t.a)&&"*"===t.a[0]?n.push(...t.a.slice(1)):n.push(t.a),Array.isArray(t.b)&&"*"===t.b[0]?i.push(...t.b.slice(1)):i.push(t.b);for(let e=n.length-1;e>=0;e--){let t=n[e][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t))break;1!==n[e]&&(r=r.map((t=>"tuple"===t?t:t.map((t=>"tuple"===t?t:["*",t,n[e]]))))),n.pop()}for(;i.length>0;){let e=i[0][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(e))break;1!==i[0]&&(r=r.map((e=>"tuple"===e?e:e.map((e=>"tuple"===e?e:["*",e,i[0]]))))),i.splice(0,1)}let a=["matrix",t.size,r];return n.length>0||i.length>0?["*",...n,a,...i]:a}return e})),t}function expand_relations(e){var t=get_tree(e);return transform(t,expand_relations_transform)}function expand_relations_transform(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if("="===t){if(r.length<=2)return e;let t=["and"];for(let e=0;e":"lts"===t?"le":"ge",i.push([a,e[r],e[r+1]])}let a=["and",i[0],i[1]];for(let e=2;e",n,c]),s[2]?a?f.push([">",n,l]):f.push(["le",n,l]):a?f.push(["ge",n,l]):f.push(["<",n,l]),u=a?["or"].concat(f):["and"].concat(f),u}if("subset"===t||"notsubset"===t||"superset"===t||"notsuperset"===t){let n,i,a=!1;if("notsubset"!==t&&"notsuperset"!==t||(a=!0),"subset"===t||"notsubset"===t?(n=r[0],i=r[1]):(n=r[1],i=r[0]),n=to_intervals(n),i=to_intervals(i),"interval"!==n[0]||"interval"!==i[0])return e;let o=n[1],s=n[2],u=i[1],c=i[2];if("tuple"!==o[0]||"tuple"!==s[0]||"tuple"!==u[0]||"tuple"!==c[0])throw new Error("Badly formed ast");let l,f=o[1],p=o[2],m=u[1],d=u[2],h=[];return s[1]&&!c[1]?a?h.push(["le",f,m]):h.push([">",f,m]):a?h.push(["<",f,m]):h.push(["ge",f,m]),s[2]&&!c[2]?a?h.push(["ge",p,d]):h.push(["<",p,d]):a?h.push([">",p,d]):h.push(["le",p,d]),l=a?["or"].concat(h):["and"].concat(h),l}return e}function substitute(e,t){var r=get_tree(e),n={};for(let e in t)n[e]=get_tree(t[e]);return substitute$1(r,n)}function substitute_component(e,t,r){let n=get_tree(e);if(get_tree(r),"number"==typeof t)t=[t];else if(!Array.isArray(t))throw Error("Invalid substitute_component: "+t);let i=["list","tuple","vector","altvector","array"];return function e(t,n,a){if(0===n.length)return r;if(!Array.isArray(t))throw Error("Invalid substitute_component: expected list, tuple, vector, or array");let o=t[0],s=t.slice(1);if(!i.includes(o))throw Error("Invalid substitute_component: expected list, tuple, vector, or array");let u=n[0];if(u<0||u>s.length-1)throw Error("Invalid substitute_component: component out of range");let c=n.slice(1),l=e(s[u],c);return[o,...s.slice(0,u),l,...s.slice(u+1)]}(n,t)}function get_component(e,t){let r=get_tree(e);if("number"==typeof t)t=[t];else if(!Array.isArray(t))throw Error("Invalid get_component: "+t);let n=["list","tuple","vector","altvector","array"];return function e(t,r){if(0===r.length)return t;if(!Array.isArray(t))throw Error("Invalid get_component: expected list, tuple, vector, or array");let i=t[0],a=t.slice(1);if(!n.includes(i))throw Error("Invalid get_component: expected list, tuple, vector, or array");let o=r[0];if(o<0||o>a.length-1)throw Error("Invalid get_component: component out of range");let s=r.slice(1);return e(a[o],s)}(r,t)}var transformation=Object.freeze({__proto__:null,expand:expand,expand_relations:expand_relations,substitute:substitute,substitute_component:substitute_component,get_component:get_component,perform_vector_scalar_multiplications:perform_vector_scalar_multiplications,perform_matrix_scalar_multiplications:perform_matrix_scalar_multiplications,perform_matrix_multiplications:perform_matrix_multiplications});function clean(e){return flatten$5(get_tree(e))}function evalf(e,t){return parseFloat(math$1.format(e,{notation:"exponential",precision:t}))}function collapse_unary_minus(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if(n=n.map((e=>collapse_unary_minus(e))),"-"===r){if("number"==typeof n[0])return-n[0];if(Array.isArray(n[0])&&"*"===n[0][0]&&"number"==typeof n[0][1])return["*",-n[0][1]].concat(n[0].slice(2));if(Array.isArray(n[0])&&"/"===n[0][0]){if("number"==typeof n[0][1])return["/",-n[0][1],n[0][2]];if(Array.isArray(n[0][1])&&"*"===n[0][1][0]&&"number"==typeof n[0][1][1])return["/",["*",-n[0][1][1]].concat(n[0][1].slice(2)),n[0][2]]}}return[r].concat(n)}function simplify(e,t,r){var n=get_tree(e);return contains_blank(n)?n:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),n=evaluate_numbers(n,{assumptions:t,max_digits:r,evaluate_functions:!0}),Array.isArray(n)?n=collect_like_terms_factors(n=perform_vector_matrix_additions_scalar_multiplications(n=simplify_logical(n,t)),t,r):n)}function simplify_logical(e,t){var r=get_tree(e);if(contains_blank(r))return r;void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),r=evaluate_numbers(r,{assumptions:t}),r=unflattenRight(r);var n=[];return n.push([["not",["not","a"]],"a"]),n.push([["not",["and","a","b"]],["or",["not","a"],["not","b"]]]),n.push([["not",["or","a","b"]],["and",["not","a"],["not","b"]]]),n.push([["not",["=","a","b"]],["ne","a","b"]]),n.push([["not",["ne","a","b"]],["=","a","b"]]),n.push([["not",["<","a","b"]],["le","b","a"]]),n.push([["not",["le","a","b"]],["not",["le","a","b"]]]),n.push([["not",["in","a","b"]],["notin","a","b"]]),n.push([["not",["subset","a","b"]],["notsubset","a","b"]]),r=flatten$5(r=applyAllTransformations(r,n,20))}function perform_vector_matrix_additions_scalar_multiplications(e,t=!0){var r=get_tree(e);r=perform_vector_scalar_multiplications(r=perform_matrix_scalar_multiplications(r),t);let n=["+","a","b"];return r=transform(r,(function(e){let r=match$2(e,n,{allow_permutations:!0});if(r){let n=["vector","altvector"];t&&n.push("tuple");let i={},a={},o=[];if(n.includes(r.a[0])){let e=r.a.length-1;i[e]||(i[e]=[]),i[e].push(r.a)}else if("matrix"===r.a[0]){let e=r.a[1].slice(1).toString();a[e]||(a[e]=[]),a[e].push(r.a)}else o.push(r.a);if(n.includes(r.b[0])){let e=r.b.length-1;i[e]||(i[e]=[]),i[e].push(r.b)}else if("matrix"===r.b[0]){let e=r.b[1].slice(1).toString();a[e]||(a[e]=[]),a[e].push(r.b)}else if("+"===r.b[0])for(let e of r.b.slice(1))if(n.includes(e[0])){let t=e.length-1;i[t]||(i[t]=[]),i[t].push(e)}else if("matrix"===e[0]){let t=e[1].slice(1).toString();a[t]||(a[t]=[]),a[t].push(e)}else o.push(e);else o.push(r.b);if(Object.values(i).every((e=>e.length<2))&&Object.values(a).every((e=>e.length<2)))return e;let s=o;for(let e in i)if(i[e].length<2)s.push(...i[e]);else{let t,r=i[e].some((e=>"vector"===e[0])),n=i[e].some((e=>"tuple"===e[0])),a=i[e].some((e=>"altvector"===e[0]));t=r||n&&a?["vector"]:a?["altvector"]:["tuple"];for(let r=0;re[r+1]))]);s.push(t)}for(let e in a)if(a[e].length<2)s.push(...a[e]);else{let[t,r]=e.split(",").map(Number),n=["tuple"];for(let i=0;ie[2][i+1][n+1]))]);n.push(t)}let i=["matrix",["tuple",t,r],n];s.push(i)}return 1===s.length?s[0]:["+",...s]}return e})),r}function contains_decimal_number(e){return"string"!=typeof e&&("number"==typeof e?!(!Number.isFinite(e)||Number.isInteger(e)):!!Array.isArray(e)&&e.slice(1).some((e=>contains_decimal_number(e))))}function contains_only_numbers(e,{include_number_symbols:t=!1,evaluate_functions:r=!1}={}){if("string"==typeof e){if(t){if("e"===e&&math$1.define_e)return!0;if("pi"===e&&math$1.define_pi)return!0}return!("i"!==e||!math$1.define_i)}return"number"==typeof e||!!Array.isArray(e)&&(r&&"apply"===e[0]?e.slice(2).every((e=>contains_only_numbers(e,{include_number_symbols:t}))):e.slice(1).every((e=>contains_only_numbers(e,{include_number_symbols:t}))))}function try_evaluate_sum_of_numbers(e,t,r){if("number"==typeof e){if(0===e)return t;if("number"==typeof t)return e+t;if(Array.isArray(t)&&"+"===t[0]&&"number"==typeof t[1])return["+",e+t[1],t[2]];if(!r&&Array.isArray(t)&&"+"===t[0]&&"number"==typeof t[2])return["+",e+t[2],t[1]]}return"number"==typeof t&&0===t?e:null}function try_evaluate_negate_number(e){if("number"==typeof e)return-e;if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1])return["*",-e[1]].concat(e.slice(2));if(Array.isArray(e)&&"/"===e[0]){if("number"==typeof e[1])return["/",-e[1],e[2]];if(Array.isArray(e[1])&&"*"===e[1][0]&&"number"==typeof e[1][1])return["/",["*",-e[1][1]].concat(e[1].slice(2)),e[2]]}return null}function try_evaluate_product_of_numbers(e,t){if("number"==typeof e){if(isNaN(e))return NaN;if("number"==typeof t)return e*t;if(!isFinite(e))return e===1/0&&is_negative_ast(t)||e===-1/0&&is_positive_ast(t)?-1/0:!1===is_nonzero_ast(t)?NaN:1/0;if(0===e)return 0;if(1===e)return t;if(-1===e)return["-",t];if(Array.isArray(t)&&"*"===t[0]&&"number"==typeof t[1])return e*=t[1],t=t[2],1===e?t:-1===e?["-",t]:["*",e,t]}if("number"==typeof t){if(isNaN(t))return NaN;if(!isFinite(t))return t===1/0&&is_negative_ast(e)||t===-1/0&&is_positive_ast(e)?-1/0:!1===is_nonzero_ast(e)?NaN:1/0;if(0===t)return 0;if(1===t)return e;if(-1===t)return["-",e];if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1])return t*=e[1],e=e[2],1===t?e:-1===t?["-",e]:["*",e,t]}if(math$1.define_i&&"i"===e){if("i"===t)return-1;if(Array.isArray(t)&&"*"===t[0]&&"i"===t[1])return["-",t[2]]}else if(math$1.define_i&&"i"===t&&Array.isArray(e)&&"*"===e[0]&&"i"===e[1])return["-",e[2]];return null}function try_evaluate_quotient_of_numbers(e,t,r,n){if("number"==typeof e){if(0===e){let e=is_nonzero_ast(t,r);if(e)return 0;if(!1===e)return NaN}if("number"==typeof t){let r=e/t;if(n===1/0||math$1.round(r,n)===r)return r;if(t<0)return["/",-e,-t]}if(Array.isArray(t)&&"*"===t[0]&&"number"==typeof t[1]){let r=e/t[1];if(n===1/0||math$1.round(r,n)===r)return["/",r,t[2]]}}else if("number"==typeof t){if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1]){let r=e[1]/t;if(n===1/0||math$1.round(r,n)===r)return 1===r?e[2]:["*",r,e[2]];if(t<0)return["/",["*",-e[1],e[2]],-t]}let r=1/t;if(n===1/0||math$1.round(r,n)===r)return["*",r,e];if(t<0)return Array.isArray(e)&&"-"===e[0]?["/",e[1],-t]:["-",["/",e,-t]]}return null}function evaluate_numbers_sub(e,t,r,n,i,a){if(void 0===e)return e;if("number"==typeof e)return a>0&&math$1.abs(e)0&&math$1.abs(t)evaluate_numbers_sub(e,t,r,n,i,a)));if("+"===s){let e=u[0],t=u[1];if(void 0===t)return e;let r=try_evaluate_sum_of_numbers(e,t,n);if(null!==r)return r;if("unit"===e[0]&&"unit"===t[0]){let r=get_unit_of_tree(e),i=get_unit_of_tree(t);if(r&&r===i){let i=try_evaluate_sum_of_numbers(remove_units(e,!1),remove_units(t,!1),n);if(null!==i)return add_unit(i,r)}}return[s].concat(u)}if("-"===s){let e=try_evaluate_negate_number(u[0]);if(null!==e)return e;if("unit"===u[0][0]){let e=get_unit_of_tree(u[0]);if(e){let t=try_evaluate_negate_number(remove_units(u[0],!1));if(null!==t)return add_unit(t,e)}}return[s].concat(u)}if("*"===s){let e=u[0],t=u[1];if(void 0===t)return e;let r=try_evaluate_product_of_numbers(e,t);if(null!==r)return r;if("unit"===e[0]&&"unit"!==t[0]){let r=get_unit_of_tree(e);if(r){let n=try_evaluate_product_of_numbers(remove_units(e,!1),t);if(null!==n)return add_unit(n,r)}}if("unit"!==e[0]&&"unit"===t[0]){let r=get_unit_of_tree(t);if(r){let n=try_evaluate_product_of_numbers(e,remove_units(t,!1));if(null!==n)return add_unit(n,r)}}return[s].concat(u)}if("/"===s){let e=u[0],n=u[1],i=try_evaluate_quotient_of_numbers(e,n,t,r);if(null!==i)return i;if("unit"===e[0]&&"unit"!==n[0]){let i=get_unit_of_tree(e);if(i){let a=try_evaluate_quotient_of_numbers(remove_units(e,!1),n,t,r);if(null!==a)return add_unit(a,i)}}return[s].concat(u)}if("^"===s){let e=u[0],n=u[1];if("number"==typeof n)if(0===n){if(!math$1.pow_strict)return 1;let r=is_nonzero_ast(e,t);if(r&&e!==1/0&&e!==-1/0)return 1;if(!1===r)return NaN}else{if(1===n)return e;if("number"==typeof e){let t=math$1.pow(e,n);if(r===1/0||math$1.round(t,r)===t)return t}}else if(1===e)return 1;return[s].concat(u)}return[s].concat(u)}function evaluate_numbers(e,{assumptions:t,max_digits:r,skip_ordering:n=!1,evaluate_functions:i=!1,set_small_zero:a=0}={}){(void 0===r||!Number.isInteger(r)&&r!==1/0)&&(r=0),!0===a&&(a=1e-14);var o,s=get_tree(e);return contains_blank(s)?s:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),n?o=evaluate_numbers_sub(s=unflattenRight(flatten$5(s)),t,r,n,i,a):(s=move_units_outside_products(s),s=unflattenRight(default_order(flatten$5(s))),o=default_order(evaluate_numbers_sub(s,t,r,n,i,a)),o=default_order(evaluate_numbers_sub(unflattenRight(o),t,r,n,i,a))),flatten$5(o=set_negative_zeros_to_zero(o)))}function set_negative_zeros_to_zero(e){return 0===e?0:Array.isArray(e)?[e[0],...e.slice(1).map(set_negative_zeros_to_zero)]:e}function collect_like_terms_factors(e,t,r){function n(e){return"number"==typeof e||!(!Array.isArray(e)||"-"!==e[0]||"number"!=typeof e[1])}function i(e){return"number"==typeof e&&e<0||!(!Array.isArray(e)||"-"!==e[0]||"number"!=typeof e[1])}function a(e){if("number"==typeof e)return!0;if(Array.isArray(e)&&"-"===e[0]&&"number"==typeof e[1])return!0;let t=evaluate_to_constant(e,!1);return!("number"!=typeof t||!Number.isFinite(t))}var o=get_tree(e);if(contains_blank(o))return o;void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),o=evaluate_numbers(o,{assumptions:t,max_digits:r,evaluate_functions:!0});var s=[];s.push([["/","x",["^","y","a"]],["*","x",["^","y",["-","a"]]],{evaluate_numbers:!0,max_digits:r}]),s.push([["/","x",["apply","exp","a"]],["*","x",["apply","exp",["-","a"]]],{evaluate_numbers:!0,max_digits:r,variables:{x:!0,a:!0}}]),s.push([["/","x","y"],["*","x",["^","y",["-",1]]],{evaluate_numbers:!0,max_digits:r}]),o=applyAllTransformations(o,s,40),s=[];for(let e in all_units){all_units[e].prefix?(s.push([["+",["unit",e,"x"],["unit",e,"y"]],["unit",e,["+","x","y"]],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["unit",e,"x"],["-",["unit",e,"y"]]],["unit",e,["+","x",["-","y"]]],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}])):(s.push([["+",["unit","x",e],["unit","y",e]],["unit",["+","x","y"],e],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["unit","x",e],["-",["unit","y",e]]],["unit",["+","x",["-","y"]],e],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]))}return s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:e=>is_nonzero_ast(e,t),n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:!0,n:e=>n(e)&&is_positive_ast(e,t),m:e=>n(e)&&is_positive_ast(e,t)},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:!0,n:e=>n(e)&&is_negative_ast(e,t),m:e=>n(e)&&is_negative_ast(e,t)},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["apply","exp","n"],["apply","exp","m"]],["apply","exp",["+","n","m"]],{variables:{n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n","x"],["*","m","x"]],["*",["+","n","m"],"x"],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n1","x"],["*",["/","n2","m2"],"x"]],["*",["+","n1",["/","n2","m2"]],"x"],{variables:{x:!0,n1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n1","x"],["*",["-",["/","n2","m2"]],"x"]],["*",["+","n1",["-",["/","n2","m2"]]],"x"],{variables:{x:!0,n1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*",["/","n1","m1"],"x"],["*",["/","n2","m2"],"x"]],["*",["+",["/","n1","m1"],["/","n2","m2"]],"x"],{variables:{x:!0,n1:n,m1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m1","m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*",["/","n1","m1"],"x"],["*",["-",["/","n2","m2"]],"x"]],["*",["+",["/","n1","m1"],["-",["/","n2","m2"]]],"x"],{variables:{x:!0,n1:n,m1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m1","m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n","x"],["-",["*","m","x"]]],["*",["+","n",["-","m"]],"x"],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["^",["*","x","y"],"a"],["*",["^","x","a"],["^","y","a"]],{allow_permutations:!0}]),s.push([["^",["^","x","n"],"m"],["^","x",["*","n","m"]],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_permutations:!0}]),s.push([["-",["+","a","b"]],["+",["-","a"],["-","b"]]]),s.push([["*","x","y"],["*","x","y"],{variables:{x:a,y:a},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),o=applyAllTransformations(o,s,40),(s=[]).push([["*","x",["^","y",["-","a"]]],["/","x",["^","y","a"]],{allow_extended_match:!0,allow_permutations:!0,evaluate_numbers:!0,max_digits:r,max_group:1}]),s.push([["*","x",["apply","exp",["-","a"]]],["/","x",["apply","exp","a"]],{allow_extended_match:!0,allow_permutations:!0,evaluate_numbers:!0,max_digits:r,max_group:1,variables:{x:!0,a:!0}}]),s.push([["*","x",["^","y","n"]],["/","x",["^","y",["-","n"]]],{variables:{x:!0,y:!0,n:i},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*","x",["apply","exp","n"]],["/","x",["apply","exp",["-","n"]]],{variables:{x:!0,n:i},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),o=applyAllTransformations(o,s,40),(s=[]).push([["^","y","n"],["/",1,["^","y",["-","n"]]],{variables:{y:!0,n:i},evaluate_numbers:!0,max_digits:r}]),s.push([["apply","exp","n"],["/",1,["apply","exp",["-","n"]]],{variables:{n:i},evaluate_numbers:!0,max_digits:r}]),o=applyAllTransformations(o,s,40),(s=[]).push([["*","x",["/","y","z"]],["/",["*","x","y"],"z"],{allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["/",["/","x","y"],"z"],["/","x",["*","y","z"]],{allow_extended_match:!0,allow_permutations:!0}]),s.push([["/","x",["/","y","z"]],["/",["*","x","z"],"y"],{allow_extended_match:!0,allow_permutations:!0}]),o=evaluate_numbers(o=applyAllTransformations(o,s,40),{assumptions:t,max_digits:r})}function simplify_ratios(e,t){function r(e){var t=1;return e=e.map((function(e){if("number"==typeof e)return e<0?(t*=-1,-e):e;if(!Array.isArray(e))return e;if("-"===e[0])return t*=-1,e[1];if("+"!==e[0])return e;var r=!1;if(("number"==typeof e[1]&&e[1]<0||Array.isArray(e[1])&&"-"===e[1][0]||Array.isArray(e[1])&&"*"===e[1][0]&&Number(e[1][1])<0)&&(r=!0),r){t*=-1;var n=e.slice(1).map((e=>["-",e]));return evaluate_numbers(["+"].concat(n))}return e})),{factors:e,sign_change:t}}var n=get_tree(e);return contains_blank(n)?n:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),function e(t,n){if(!Array.isArray(t))return n?["-",t]:t;var i=t[0];if("-"===i)return e(t[1],n=!0);var a=t.slice(1).map((t=>e(t)));if("/"!==i)return n?["-",[i,...a]]:[i,...a];var o,s=a[0],u=a[1];s=default_order(s,{ignore_negatives:!0});var c,l=r(o=Array.isArray(s)&&"*"===s[0]?s.slice(1):[s]);o=l.factors,n&&(l.sign_change*=-1),u=default_order(u,{ignore_negatives:!0});var f=r(c=Array.isArray(u)&&"*"===u[0]?u.slice(1):[u]);return c=f.factors,l.sign_change*f.sign_change<0&&(o[0]=["-",o[0]]),["/",s=1===o.length?o[0]:["*"].concat(o),u=1===c.length?c[0]:["*"].concat(c)]}(n))}function contains_blank(e){return"＿"===e||!!Array.isArray(e)&&e.some(contains_blank)}let all_units=get_all_units();function remove_units(e,t=!0){var r=get_tree(e);if(!Array.isArray(r))return r;let n=r[0],i=r.slice(1);if("unit"===n){let e=all_units[get_unit_of_tree(r)];if(!e)return r;let n=remove_units(e.prefix?i[1]:i[0],t);return t?e.scale(n):n}return[n,...i.map((e=>remove_units(e,t)))]}function remove_scaling_units(e){var t=get_tree(e);if(!Array.isArray(t))return t;let r=t[0],n=t.slice(1);if("unit"===r){let e=all_units[get_unit_of_tree(t)];if(!e||!e.only_scales)return t;let r=remove_scaling_units(e.prefix?n[1]:n[0]);return e.scale(r)}return[r,...n.map((e=>remove_scaling_units(e)))]}function add_unit(e,t){var r=get_tree(e);let n=all_units[t];return n?n.prefix?["unit",t,r]:["unit",r,t]:r}function move_units_outside_products(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("*"===t){let e=[],t=[];for(let n of r){let r=get_unit_value_of_tree(n);r?(e.push(r[0]),t.push(r[1])):t.push(n)}let n=["*",...t];for(let t of e)n=add_unit(n,t);return n}return[t,...r.map(move_units_outside_products)]}var simplify$1=Object.freeze({__proto__:null,clean:clean,simplify:simplify,simplify_logical:simplify_logical,evaluate_numbers:evaluate_numbers,collect_like_terms_factors:collect_like_terms_factors,collapse_unary_minus:collapse_unary_minus,simplify_ratios:simplify_ratios,default_order:default_order,perform_vector_matrix_additions_scalar_multiplications:perform_vector_matrix_additions_scalar_multiplications,remove_units:remove_units,add_unit:add_unit,remove_scaling_units:remove_scaling_units});function solve_linear(e,t,r){if("string"==typeof t){void 0===r&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(r=e.context.get_assumptions([e.variables()]));var n=simplify(get_tree(e),r);if(Array.isArray(n)){var i=n[0],a=n.slice(1);if("="===i||"ne"===i||"<"===i||"le"===i||">"===i||"ge"===i){var o=simplify(["+",a[0],["-",a[1]]],r),s=e=>!variables(e).includes(t);if(variables(o=simplify(applyAllTransformations(o,[[["+",["*","_a",t],["*","_b",t]],["*",["+","_a","_b"],t],{variables:{_a:s,_b:s},allow_permutations:!0,allow_extended_match:!0,allow_implicit_identities:["_a","_b"],evaluate_numbers:!0}]],20))).includes(t)){var u=match$2(o,["+",["*","_a",t],"_b"],{variables:{_a:s,_b:s},allow_permutations:!0,allow_implicit_identities:["_a","_b"]});if(u){var c=simplify(u._a),l=simplify(u._b);if(is_nonzero_ast(c,r)){if("="===i||"ne"===i||is_positive_ast(c,r)){let e=simplify(["/",["-",l],c]);return[i,t,e]}if(is_negative_ast(c,r)){var f=simplify(["/",["-",l],c]);return[i="<"===i?">":"le"===i?"ge":">"===i?"<":"le",t,f]}}}}}}}}var 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n=this.factor(e);this.simple_factor_or_function_or_parens(e)||"_"===e[0]&&"string"==typeof e[1]||(n="\\left("+n+"\\right)");for(let e=0;e1?s=s.trimRight()+"^{"+a+"}"+this.stringConvert(o):s+=this.stringConvert(o),s="\\frac{ "+s+" }{ ";let u=1;Array.isArray(i)&&(u=i.length-1);for(let t=1;t<=u;t++){let r=i[t],n=1,a="";Array.isArray(r)?(a=r[1],n=r[2]):a=r,s=s+e+this.stringConvert(a),n>1&&(s=s+"^{"+n+"}"),s+=" "}return s+="}",s}if("apply"===t){if("abs"===r[0])return"\\left|"+this.statement(r[1])+"\\right|";if("floor"===r[0])return"\\left\\lfloor "+this.statement(r[1])+" \\right\\rfloor";if("ceil"===r[0])return"\\left\\lceil "+this.statement(r[1])+" \\right\\rceil";if("factorial"===r[0]){let e=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||"_"===r[1][0]&&"string"==typeof r[1][1]?e+"!":"\\left("+e+"\\right)!"}if("sqrt"===r[0])return"\\sqrt{"+this.statement(r[1])+"}";let e,t=r[0];if("^"===t[0]&&(t=t[1]),"_"===t[0]&&(t=t[1]),"int"===t){let e,t=this.factor(r[0]),n=r[1];if(Array.isArray(n)&&"*"===n[0]){let t=[],r=["*"];for(let e=1;e0&&(e[e.length-1].match(/[a-zA-Z]/)&&(e+="\\,"),e+=t.map((e=>"d"+this.factor(e[1]))).join("\\,"))}return e||(e=this.term(r[1])),t+" "+e}e="log10"===r[0]?"\\log_{10}":"re"===r[0]?"\\Re":"im"===r[0]?"\\Im":this.factor(r[0]);let n=this.statement(r[1]);return"tuple"!==r[1][0]&&(n="\\left("+n+"\\right)"),e+n}if("angle"===t){let e=r.every((e=>{if("string"==typeof e&&1===e.length)return!0;if(!Array.isArray(e))return!1;let t=e[0];return"_"===t||"^"===t||"prime"===t}));return operators$1[t](r.map(function(e,t){return this.statement(e)}.bind(this)),e)}return"+"===t&&2===e.length?"+ "+this.factor(e[1]):"\\left("+this.statement(e)+"\\right)"}factorWithParenthesesIfNegatedOrExplicitPlus(e){var t=this.factor(e);return t.match(/^-/)||t.match(/^\+/)?"\\left("+t+"\\right)":t}termWithPlusIfNotNegated(e){var t=this.term(e);return t.match(/^-/)?t.match(/^-[^ ]/)?"- "+t.slice(1):t:"+ "+t}}const textToAst$2=new textToAst$4,astToLatex=new astToLatex$1;var derivatives={sin:textToAst$2.convert("cos x"),cos:textToAst$2.convert("-(sin x)"),tan:textToAst$2.convert("(sec x)^2"),cot:textToAst$2.convert("-((csc x)^2)"),sec:textToAst$2.convert("(sec x)*(tan x)"),csc:textToAst$2.convert("-(csc x)*(cot x)"),sqrt:textToAst$2.convert("1/(2*sqrt(x))"),log:textToAst$2.convert("1/x"),ln:textToAst$2.convert("1/x"),exp:textToAst$2.convert("exp(x)"),arcsin:textToAst$2.convert("1/sqrt(1 - x^2)"),arccos:textToAst$2.convert("-1/sqrt(1 - x^2)"),arctan:textToAst$2.convert("1/(1 + x^2)"),arccsc:textToAst$2.convert("-1/(sqrt(-1/x^2 + 1)*x^2)"),arcsec:textToAst$2.convert("1/(sqrt(-1/x^2 + 1)*x^2)"),arccot:textToAst$2.convert("-1/(1 + x^2)"),abs:textToAst$2.convert("abs(x)/x")};function derivative(e,t,r=[]){var n=get_tree(e),i="\\frac{d}{d"+t+"} ";if("number"==typeof n)return r.push("The derivative of a constant is zero, that is, \\("+i+astToLatex.convert(n)+" = 0\\)."),0;if(variables(n).indexOf(t)<0)return r.push("The derivative of a constant is zero, that is, \\("+i+astToLatex.convert(n)+" = 0\\)."),0;if("string"==typeof n)return t===n?(r.push("We know the derivative of the identity function is one, that is, \\("+i+astToLatex.convert(n)+" = 1\\)."),1):(r.push("As far as \\("+astToLatex.convert(t)+"\\) is concerned, \\("+astToLatex.convert(n)+"\\) is constant, so "+i+astToLatex.convert(n)+" = 0\\)."),0);if(!Array.isArray(n))return null;var a=n[0],o=n.slice(1);if("+"===a||"-"===a||"~"===a){r.push("Using the sum rule, \\("+i+astToLatex.convert(n)+" = "+o.map((function(e,t){return i+astToLatex.convert(e)})).join(" + ")+"\\).");let e=[a].concat(o.map((function(e,n){return derivative(e,t,r)})));return e=simplify(e),r.push("So using the sum rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("*"===a){let e=[],a=[];for(let r=0;r0){if(0===e.length){return r.push("Since the derivative of a constant is zero, \\("+i+astToLatex.convert(n)+" = 0.\\)"),0}let o=["*"].concat(e);if(1===e.length&&(o=e[0]),o===t){r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+a.map((function(e,t){return astToLatex.convert(e)})).join(" \\cdot ")+"\\).");let e=["*"].concat(a);return e=simplify(e),e}r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+a.map((function(e,t){return astToLatex.convert(e)})).join(" \\cdot ")+" \\cdot "+i+"\\left("+astToLatex.convert(o)+"\\right)\\).");let s=derivative(o,t,r),u=["*"].concat(a.concat([s]));return u=simplify(u),r.push("And so \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}r.push("Using the product rule, \\("+i+astToLatex.convert(n)+" = "+o.map((function(e,t){return o.map((function(r,n){return t===n?i+"\\left("+astToLatex.convert(e)+"\\right)":astToLatex.convert(r)})).join(" \\cdot ")})).join(" + ")+"\\).");let s=o.slice(),u=["+"].concat(o.map((function(e,n){return["*"].concat(s.map((function(e,i){if(n===i){let n=derivative(e,t,r);return 1===n?null:n}return e})).filter((function(e){return null!=e})))})));return u=simplify(u),r.push("So using the product rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if("/"===a){let e=o[0],a=o[1];if(variables(a).indexOf(t)<0){r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(["/",1,a])+" \\cdot "+i+"\\left("+astToLatex.convert(e)+"\\right)\\).");let o=derivative(e,t,r),s=textToAst$2.convert("(1/g)*d"),u=substitute$1(s,{d:o,g:a});return u=simplify(u),r.push("So \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if(variables(e).indexOf(t)<0){1!==e&&r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+" \\cdot "+i+"\\left("+astToLatex.convert(["/",1,a])+"\\right)\\)."),r.push("Since \\(\\frac{d}{du} \\frac{1}{u}\\) is \\(\\frac{-1}{u^2}\\), the chain rule gives \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\cdot \\frac{-1}{ "+astToLatex.convert(a)+"^2} \\cdot "+i+astToLatex.convert(a)+"\\).");let o=derivative(a,t,r),s=textToAst$2.convert("f * (-a/(g^2))"),u=substitute$1(s,{f:e,a:o,g:a});return u=simplify(u),r.push("So since \\(\\frac{d}{du} \\frac{1}{u}\\) is \\(\\frac{-1}{u^2}\\), the chain rule gives \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}r.push("Using the quotient rule, \\("+i+astToLatex.convert(n)+" = \\frac{"+i+"\\left("+astToLatex.convert(e)+"\\right) \\cdot "+astToLatex.convert(a)+" - "+astToLatex.convert(e)+"\\cdot "+i+"\\left("+astToLatex.convert(a)+"\\right)}{ \\left( "+astToLatex.convert(a)+" \\right)^2} \\).");let s=derivative(e,t,r),u=derivative(a,t,r),c=textToAst$2.convert("(a * g - f * b)/(g^2)"),l=substitute$1(c,{a:s,b:u,f:e,g:a});return l=simplify(l),r.push("So using the quotient rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(l)+"\\)."),l}if("^"===a){let e=o[0],a=o[1];if(variables(a).indexOf(t)<0){if("string"==typeof e&&"x"===e){if("number"==typeof a){let t=textToAst$2.convert("n * (f^m)"),o=substitute$1(t,{n:a,m:a-1,f:e});return o=simplify(o),r.push("By the power rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"}\\)."),o}let t=textToAst$2.convert("n * (f^(n-1))"),o=substitute$1(t,{n:a,f:e});return o=simplify(o),r.push("By the power rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"}\\)."),o}1!==a&&r.push("By the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"} \\cdot "+i+astToLatex.convert(e)+"\\).");let o=derivative(e,t,r);if(1===a)return o;if("number"==typeof a){let t=textToAst$2.convert("n * (f^m) * a"),s=substitute$1(t,{n:a,m:a-1,f:e,a:o});return s=simplify(s),r.push("So by the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}let s=textToAst$2.convert("n * (f^(n-1)) * a"),u=substitute$1(s,{n:a,f:e,a:o});return u=simplify(u),r.push("So by the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if("e"===e&&math$1.define_e){if("string"==typeof a&&a===t){let e=textToAst$2.convert("e^(f)"),o=substitute$1(e,{f:a});return o=simplify(o),r.push("The derivative of \\(e^"+astToLatex.convert(t)+"\\) is itself, that is, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(n)+"\\)."),o}r.push("Using the rule for \\(e^x\\) and the chain rule, we know \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(n)+" \\cdot "+i+astToLatex.convert(a)+"\\).");let e=textToAst$2.convert("e^(f)*d"),o=derivative(a,t,r),s=substitute$1(e,{f:a,d:o});return s=simplify(s),r.push("So using the rule for \\(e^x\\) and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}if("number"==typeof e){if("string"==typeof a&&a===t){let o=textToAst$2.convert("a^(f) * log(a)"),s=substitute$1(o,{a:e,f:a});return s=simplify(s),r.push("The derivative of \\(a^"+astToLatex.convert(t)+"\\) is \\(a^{"+astToLatex.convert(t)+"} \\, \\log a\\), that is, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}let o=textToAst$2.convert("a^(f) * log(a)"),s=substitute$1(o,{a:e,f:a});r.push("Using the rule for \\(a^x\\) and the chain rule, we know \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+" \\cdot "+i+astToLatex.convert(a)+"\\).");let u=textToAst$2.convert("a^(b)*log(a)*d"),c=derivative(a,t,r),l=substitute$1(u,{a:e,b:a,d:c});return l=simplify(l),r.push("So using the rule for \\(a^x\\) and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(l)+"\\)."),l}let s=e,u=a;r.push("Recall the general rule for exponents, namely that \\(\\frac{d}{dx} u(x)^{v(x)} = u(x)^{v(x)} \\cdot \\left( v'(x) \\cdot \\log u(x) + \\frac{v(x) \\cdot u'(x)}{u(x)} \\right)\\). In this case, \\(u(x) = "+astToLatex.convert(s)+"\\) and \\(v(x) = "+astToLatex.convert(u)+"\\).");let c=derivative(s,t,r),l=derivative(u,t,r),f=textToAst$2.convert("(f^g)*(b * log(f) + (g * a)/f)"),p=substitute$1(f,{a:c,b:l,f:s,g:u});return p=simplify(p),r.push("So by the general rule for exponents, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(p)+"\\)."),p}if("apply"===a&&!(o[0]in derivatives)){let e=o[1];r.push("By the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(substitute$1(["apply",o[0]+"'","x"],{x:e}))+" \\cdot "+i+astToLatex.convert(e)+"\\).");let a=["*",substitute$1(["apply",o[0]+"'","x"],{x:e}),derivative(e,t,r)];return a=simplify(a),r.push("So by the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+"\\)."),a}if("apply"===a&&o[0]in derivatives||a in derivatives){let e=!1;"apply"===a&&(a=o[0],o=o.slice(1),e=!0);let s=o[0];if("number"==typeof s){let e=0;return r.push("The derivative of a constant is zero so \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("string"==typeof s&&s===t){let e=["*",substitute$1(derivatives[a],{x:s})];return e=simplify(e),r.push("It is the case that \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("string"==typeof s&&s!==t){let e=0;return r.push("Since the derivative of a constant is zero, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}{let o=[a,"u"];e&&(o=["apply"].concat(o)),r.push("Recall \\(\\frac{d}{du}"+astToLatex.convert(o)+" = "+astToLatex.convert(derivative(o,"u",[]))+"\\)."),r.push("By the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(substitute$1(derivatives[a],{x:s}))+" \\cdot "+i+astToLatex.convert(s)+"\\).");let u=["*",substitute$1(derivatives[a],{x:s}),derivative(s,t,r)];return u=simplify(u),r.push("So by the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}}return 0}function lowercaseFirstLetter(e){return e.charAt(0).toLowerCase()+e.slice(1)}function simplify_story(e){for(let t=e.length-1;t>=1;t--)e[t]===e[t-1]&&e.splice(t,1);for(let t=0;t":function(e){return e.join(" > ")},lts:function(e){return e.join(" < ")},gts:function(e){return e.join(" > ")},le:function(e){return e.join(" ≤ ")},ge:function(e){return e.join(" ≥ ")},ne:function(e){return e.join(" ≠ ")},forall:function(e){return"∀ "+e[0]},exists:function(e){return"∃ "+e[0]},in:function(e){return e[0]+" ∈ "+e[1]},notin:function(e){return e[0]+" ∉ "+e[1]},ni:function(e){return e[0]+" ∋ "+e[1]},notni:function(e){return e[0]+" ∌ "+e[1]},subset:function(e){return e[0]+" ⊂ "+e[1]},subseteq:function(e){return e[0]+" ⊆ "+e[1]},notsubset:function(e){return e[0]+" ⊄ "+e[1]},notsubseteq:function(e){return e[0]+" ⊈ "+e[1]},superset:function(e){return e[0]+" ⊃ "+e[1]},superseteq:function(e){return e[0]+" ⊇ "+e[1]},notsuperset:function(e){return e[0]+" ⊅ "+e[1]},notsuperseteq:function(e){return e[0]+" ⊉ "+e[1]},union:function(e){return e.join(" ∪ ")},intersect:function(e){return e.join(" ∩ ")},perp:function(e){return e.join(" ⟂ ")},parallel:function(e){return e.join(" ∥ ")},derivative_leibniz:function(e){return"d"+e[0]+"/d"+e[1]},partial_derivative_leibniz:function(e){return"∂"+e[0]+"/∂"+e[1]},"|":function(e){return e[0]+" | "+e[1]},":":function(e){return e[0]+" : "+e[1]},binom:function(e){return"binom( "+e[0]+", "+e[1]+" )"},vec:function(e){return"vec("+e[0]+")"},linesegment:function(e){return"linesegment( "+e.join(", ")+" )"},angle:function(e,t){return t?"∠"+e.join(""):"∠( "+e.join(", ")+" )"},unit:function(e){return e[0]+" "+e[1]}},nonunicode_operators={"+":function(e){return e.join(" ")},"-":function(e){return"-"+e[0]},"*":function(e){return e.join(" ")},"/":function(e){return e[0]+"/"+e[1]},_:function(e){return e[0]+"_"+e[1]},"^":function(e){return e[0]+"^"+e[1]},prime:function(e){return e[0]+"'"},tuple:function(e){return"( "+e.join(", ")+" )"},array:function(e){return"[ "+e.join(", ")+" ]"},list:function(e){return e.join(", ")},set:function(e){return"{ "+e.join(", ")+" }"},vector:function(e){return"( "+e.join(", ")+" )"},altvector:function(e){return"( "+e.join(", ")+" )"},interval:function(e){return"( "+e.join(", ")+" )"},matrix:function(e){return"( "+e.join(", ")+" )"},and:function(e){return e.join(" and ")},or:function(e){return e.join(" or ")},not:function(e){return"not "+e[0]},"=":function(e){return e.join(" = ")},"<":function(e){return e.join(" < ")},">":function(e){return e.join(" > ")},lts:function(e){return e.join(" < ")},gts:function(e){return e.join(" > ")},le:function(e){return e.join(" <= ")},ge:function(e){return e.join(" >= ")},ne:function(e){return e.join(" ne ")},forall:function(e){return"forall "+e[0]},exists:function(e){return"exists "+e[0]},in:function(e){return e[0]+" elementof "+e[1]},notin:function(e){return e[0]+" notelementof "+e[1]},ni:function(e){return e[0]+" containselement "+e[1]},notni:function(e){return e[0]+" notcontainselement "+e[1]},subset:function(e){return e[0]+" subset "+e[1]},subseteq:function(e){return e[0]+" subseteq "+e[1]},notsubset:function(e){return e[0]+" notsubset "+e[1]},notsubseteq:function(e){return e[0]+" notsubseteq "+e[1]},superset:function(e){return e[0]+" superset "+e[1]},superseteq:function(e){return e[0]+" superseteq "+e[1]},notsuperset:function(e){return e[0]+" notsuperset "+e[1]},notsuperseteq:function(e){return e[0]+" notsuperseteq "+e[1]},union:function(e){return e.join(" union ")},intersect:function(e){return e.join(" intersect ")},perp:function(e){return e.join(" perp ")},parallel:function(e){return e.join(" parallel ")},derivative_leibniz:function(e){return"d"+e[0]+"/d"+e[1]},partial_derivative_leibniz:function(e){return"∂"+e[0]+"/∂"+e[1]},"|":function(e){return e[0]+" | "+e[1]},":":function(e){return e[0]+" : "+e[1]},binom:function(e){return"binom( "+e[0]+", "+e[1]+" )"},vec:function(e){return"vec("+e[0]+")"},linesegment:function(e){return"linesegment( "+e.join(", ")+" )"},angle:function(e,t){return t?"angle "+e.join(""):"angle( "+e.join(", ")+" )"},unit:function(e){return e[0]+" "+e[1]}},output_unicodeDefault=!0;class astToText$2{constructor({output_unicode:e=output_unicodeDefault,padToDigits:t=null,padToDecimals:r=null,showBlanks:n=!0}={}){this.output_unicode=e,this.operators=unicode_operators,e||(this.operators=nonunicode_operators),this.padToDigits=t,this.padToDecimals=r,this.showBlanks=n}convert(e){return this.statement(e)}statement(e){if(!Array.isArray(e))return this.single_statement(e);let t=e[0],r=e.slice(1);if("ldots"===t)return"...";if(!(t in this.operators)&&"apply"!==t)throw new Error("Badly formed ast: operator "+t+" not recognized.");return"and"===t||"or"===t?this.operators[t](r.map(function(e,t){let r=this.single_statement(e);return r.match(/ /)&&!r.match(/^\(.*\)$/)?"("+r+")":r}.bind(this))):this.single_statement(e)}single_statement(e){if(!Array.isArray(e))return this.expression(e);let t=e[0],r=e.slice(1);if("not"===t)return this.operators[t](r.map(function(e,t){let r=this.single_statement(e);return r.match(/ /)&&!r.match(/^\(.*\)$/)?"("+r+")":r}.bind(this)));if("exists"===t||"forall"===t)return this.operators[t]([this.single_statement(r[0])]);if("="===t||"ne"===t||"<"===t||">"===t||"le"===t||"ge"===t||"in"===t||"notin"===t||"ni"===t||"notni"===t||"subset"===t||"notsubset"===t||"subseteq"===t||"notsubseteq"===t||"superset"===t||"notsuperset"===t||"superseteq"===t||"notsuperseteq"===t)return this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this)));if("lts"===t||"gts"===t){let e=r[0],n=r[1];if("tuple"!==e[0]||"tuple"!==n[0])throw new Error("Badly formed ast");let i=this.expression(e[1]);for(let r=1;r ":"lts"===t?this.output_unicode?i+=" ≤ ":i+=" <= ":this.output_unicode?i+=" ≥ ":i+=" >= ",i+=this.expression(e[r+1]);return i}return this.expression(e)}expression(e){if(!Array.isArray(e))return this.term(e);let t=e[0],r=e.slice(1);return"+"===t?1===r.length?"+"+this.term(r[0]):this.operators[t](r.map(function(e,t){return t>0?this.termWithPlusIfNotNegated(e):this.term(e)}.bind(this))):["union","intersect","perp","parallel"].includes(t)?this.operators[t](r.map(function(e,t){return this.term(e)}.bind(this))):this.term(e)}term(e){if(!Array.isArray(e))return this.factor(e);let t=e[0],r=e.slice(1);if("-"===t)return this.operators[t](r.map(function(e,t){return this.term(e)}.bind(this)));if("*"===t)return this.operators[t](r.map(function(e,t){let n;return t>0?(n=this.factorWithParenthesesIfNegatedOrExplicitPlus(e),n.match(/^[0-9]/)?"* "+n:"angle"===e[0]&&r.length>1?"( "+n+" )":n):(n=this.factor(e),"angle"===e[0]&&r.length>1?"( "+n+" )":n)}.bind(this)));if("/"===t){let e=this.factor(r[0]),n=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[0])||(e="("+e+")"),this.simple_factor_or_function_or_parens(r[1])||(n="("+n+")"),this.operators[t]([e,n])}return"unit"===t?this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this))):this.factor(e)}symbolConvert(e){let t={alpha:"α",beta:"β",Gamma:"Γ",gamma:"γ",Delta:"Δ",delta:"δ",epsilon:"ε",zeta:"ζ",eta:"η",Theta:"ϴ",theta:"θ",iota:"ι",kappa:"κ",Lambda:"Λ",lambda:"λ",mu:"μ",nu:"ν",Xi:"Ξ",xi:"ξ",Pi:"Π",pi:"π",rho:"ρ",Sigma:"Σ",sigma:"σ",tau:"τ",Upsilon:"Υ",upsilon:"υ",Phi:"Φ",phi:"ϕ",Psi:"Ψ",psi:"ψ",Omega:"Ω",omega:"ω",perp:"⟂",int:"∫"};return this.output_unicode&&e in t?t[e]:this.showBlanks||"＿"!==e?e:""}simple_factor_or_function_or_parens(e){let t=this.factor(e);return!!(t.length<=1||"string"==typeof e&&e.match(/^\w+$/)||Array.isArray(e)&&"apply"===e[0]||t.match(/^\(.*\)$/)||t.match(/^⟨.*⟩$/))||"number"==typeof e&&(e>=0&&!e.toString().includes("e"))}factor(e){if("string"==typeof e)return this.symbolConvert(e);if("number"==typeof e){if(e===1/0)return this.output_unicode?"∞":"infinity";if(e===-1/0)return this.output_unicode?"-∞":"-infinity";if(Number.isNaN(e))return"NaN";{let t=e.toString(),r=t.indexOf("e");if(-1===r)return null!==this.padToDigits?t=padNumberStringToDigits(t,this.padToDigits):null!==this.padToDecimals&&(t=padNumberStringToDecimals(t,this.padToDecimals)),t;let n=t.substring(0,r),i=t.substring(r+1);if(null!==this.padToDigits)n=padNumberStringToDigits(n,this.padToDigits);else if(null!==this.padToDecimals){let r=Number(i);if(r>0)return t=e.toLocaleString("fullwide",{useGrouping:!1}),padNumberStringToDecimals(t,this.padToDecimals);n=padNumberStringToDecimals(n,this.padToDecimals+r)}return"+"===i[0]?n+" * 10^"+i.substring(1):n+" * 10^("+i+")"}}if(!Array.isArray(e))return"";let t=e[0],r=e.slice(1);if("^"===t){if(Number.isInteger(r[0])&&Number.isInteger(r[1])){let e;return e=r[0]<0?"("+r[0].toString()+")":r[0].toString(),r[1]<0?e+"^("+r[1].toString()+")":e+"^"+r[1].toString()}let e=this.factor(r[0]),t=r[0];for(;"prime"===t[0];)t=t[1];this.simple_factor_or_function_or_parens(t)||"_"===t[0]&&"string"==typeof t[1]||(e="("+e.toString()+")");let n=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||(n="("+n.toString()+")"),e+"^"+n}if("_"===t)return this.operators[t](r.map(function(e,t){let r=this.factor(e);return this.simple_factor_or_function_or_parens(e)?r:"("+r+")"}.bind(this)));if("prime"===t){let e=r[0],t=1;for(;"prime"===e[0];)t+=1,e=e[1];let n=this.factor(e);this.simple_factor_or_function_or_parens(e)||"_"===e[0]&&"string"==typeof e[1]||(n="("+n+")");for(let e=0;e1&&(s=s+"^"+a),s=s+this.symbolConvert(o)+"/";let u=1;Array.isArray(i)&&(u=i.length-1);for(let t=1;t<=u;t++){let r=i[t],n=1,a="";Array.isArray(r)?(a=r[1],n=r[2]):a=r,s=s+e+this.symbolConvert(a),n>1&&(s=s+"^"+n)}return s}if("apply"===t){if("abs"===r[0])return"|"+this.statement(r[1])+"|";if("factorial"===r[0]){let e=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||"_"===r[1][0]&&"string"==typeof r[1][1]?e+"!":"("+e+")!"}let e=r[0];if("^"===e[0]&&(e=e[1]),"_"===e[0]&&(e=e[1]),"int"===e){let e,t=this.factor(r[0]),n=r[1];if(Array.isArray(n)&&"*"===n[0]){let t=[],r=["*"];for(let e=1;e0&&(e+=" "+t.map((e=>"d"+this.factor(e[1]))).join(" "))}return e||(e=this.term(r[1])),t+" "+e}let t=this.factor(r[0]),n=this.statement(r[1]);return"tuple"!==r[1][0]&&(n="("+n+")"),t+n}if("angle"===t){let e=r.every((e=>{if("string"==typeof e&&1===e.length)return!0;if(!Array.isArray(e))return!1;let t=e[0];return"_"===t||"^"===t||"prime"===t}));return this.operators[t](r.map(function(e,t){return this.statement(e)}.bind(this)),e)}return"+"===t&&2===e.length?"+ "+this.factor(e[1]):"("+this.statement(e)+")"}factorWithParenthesesIfNegatedOrExplicitPlus(e){var t=this.factor(e);return t.match(/^-/)||t.match(/^\+/)?"("+t+")":t}termWithPlusIfNotNegated(e){let t=this.term(e);return t.match(/^-/)?t.match(/^-[^ ]/)?"- "+t.slice(1):t:"+ "+t}}var astToText$1=new astToText$2;function subscripts_to_strings(e,t=!1){var r=get_tree(e);if(!Array.isArray(r))return r;let n=r[0],i=r.slice(1);return"_"===n&&(t||i.every((e=>["number","string"].includes(typeof e))))?astToText$1.convert(r):[n].concat(i.map((e=>subscripts_to_strings(e,t))))}function strings_to_subscripts(e){var t=get_tree(e);if("string"==typeof t){let e=t.match(/^([0-9a-zA-Z]+)_([a-zA-Z]+|[0-9]+)$/);if(e){let t=Number(e[1]);isNaN(t)&&(t=e[1]);let r=Number(e[2]);return isNaN(r)&&(r=e[2]),["_",t,r]}return t}if(!Array.isArray(t))return t;let r=t[0],n=t.slice(1);return[r].concat(n.map(strings_to_subscripts))}var normalization=Object.freeze({__proto__:null,normalize_function_names:normalize_function_names,normalize_applied_functions:normalize_applied_functions,log_subscript_to_two_arg_log:log_subscript_to_two_arg_log,substitute_abs:substitute_abs,default_order:default_order,constants_to_floats:constants_to_floats,normalize_angle_linesegment_arg_order:normalize_angle_linesegment_arg_order,tuples_to_vectors:tuples_to_vectors,to_intervals:to_intervals,altvectors_to_vectors:altvectors_to_vectors,subscripts_to_strings:subscripts_to_strings,strings_to_subscripts:strings_to_subscripts}),astToText=new astToText$2;function generate_random_integer(e,t,r){return e=math$1.ceil(e),t=math$1.floor(t),math$1.floor(r()*(t-e+1))+e}const equals$5=function({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,relative_tolerance:a=1e-12,absolute_tolerance:o=0,tolerance_for_zero:s=1e-15,allowed_error_in_numbers:u=0,include_error_in_number_exponents:c=!1,allowed_error_is_absolute:l=!1,rng:f}){if(Array.isArray(e.tree)&&Array.isArray(t.tree)){let p=e.tree[0],m=e.tree.slice(1),d=t.tree[0],h=t.tree.slice(1);if("tuple"===p||"vector"===p||"altvector"===p||"list"===p||"array"===p||"matrix"===p||"interval"===p){if(d!==p)return!1;if(h.length!==m.length)return!1;for(let e=0;e","<","ge","le"].includes(p)){if(2!==h.length)return!1;if(">"===p?(p="<",m=[m[1],m[0]]):"ge"===p&&(p="le",m=[m[1],m[0]]),">"===d?(d="<",h=[h[1],h[0]]):"ge"===d&&(d="le",h=[h[1],h[0]]),p!==d)return!1;let e=["+",m[0],["-",m[1]]],t=["+",h[0],["-",h[1]]],y="="!==p;return component_equals({expr:n.fromAst(e),other:i.fromAst(t),randomBindings:r,expr_context:n,other_context:i,allow_proportional:!0,require_positive_proportion:y,relative_tolerance:a,absolute_tolerance:o,tolerance_for_zero:s,allowed_error_in_numbers:u,include_error_in_number_exponents:c,allowed_error_is_absolute:l,rng:f})}}return component_equals({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,relative_tolerance:a,absolute_tolerance:o,tolerance_for_zero:s,allowed_error_in_numbers:u,include_error_in_number_exponents:c,allowed_error_is_absolute:l,rng:f})},component_equals=function({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,allow_proportional:a=!1,require_positive_proportion:o=!1,relative_tolerance:s,absolute_tolerance:u,tolerance_for_zero:c,allowed_error_in_numbers:l,include_error_in_number_exponents:f,allowed_error_is_absolute:p,rng:m}){var d=1e-20*Number.MAX_VALUE,h=0,y=10;e=e.normalize_function_names(),t=t.normalize_function_names(),e=e.log_subscript_to_two_arg_log(),t=t.log_subscript_to_two_arg_log(),e=e.subscripts_to_strings(),t=t.subscripts_to_strings(),e=e.normalize_applied_functions(),t=t.normalize_applied_functions();let g=rename_functions_with_exponents(e.tree),v=rename_functions_with_exponents(t.tree);e=n.fromAst(rename_vecs(g)),t=i.fromAst(rename_vecs(v));var x=[...new Set([...e.variables(),...t.variables()])];math$1.define_pi&&(x=x.filter((function(e){return"pi"!==e}))),math$1.define_i&&(x=x.filter((function(e){return"i"!==e}))),math$1.define_e&&(x=x.filter((function(e){return"e"!==e})));var b=[];for(let e=0;e1===e.length||e.includes("_")||e.includes("^"))),w=_.filter((e=>x.includes(e)));if(_=_.filter((e=>!x.includes(e))),w.length>0){let r=e.tree,a=t.tree,o="x1";for(;[..._,...x].includes(o);)o+="x1";let s="x2";for(;[..._,...x].includes(s);)s+="x2";for(let e of w){let t=e+e;for(;[..._,...x].includes(t);)t+=e;let n=[[["apply",e,o],["apply",t,o],{variables:{[o]:!0}}]];r=applyAllTransformations(r,n),a=applyAllTransformations(a,n),_.push(t)}e=n.fromAst(r),t=i.fromAst(a)}try{var N=e.f(),$=t.f()}catch(r){return e.equalsViaSyntax(t,{allow_blanks:!0})}let A,M,S;if(l>0){let t=replace_numbers_with_parameters({expr:e,variables:x,include_exponents:f});A=n.fromAst(t.expr_with_params),M=t.parameters;let r=Object.keys(M);if(r.length>0){let e=A.derivative(r[0]);if(p||(e=e.multiply(M[r[0]])),r.length>1)for(let t of r.slice(1)){let r=A.derivative(t);p||(r=r.multiply(M[t])),e=e.add(r)}let t=e.multiply(l);try{S=t.f()}catch(e){}}}var E=1,T=[10,1,100,.1,1e3,.01],O=0;let C=0,k=!0,D=0;for(let e=0;e<1e3;e++){try{var I=B(T[O],m)}catch(e){continue}if(!1===I.always_zero&&(k=!1),!I.equal&&!I.out_of_bounds&&!I.always_zero&&!1!==I.sufficient_finite_values&&(D++,D>100))return!1;if(I.equal){if(I.always_zero){if(!k)continue;if(C+=1,C>5&&(O+=1,C=0),O>=T.length)return!0;continue}return!0}}return!1;function B(e,t){var n,i=r(t,x,e);for(let e=0;eh)||!(0===m||m>h))return{out_of_bounds:!0,always_zero:!1};var g=Math.min(p,m),v=Math.max(p,m),w=1;let A=0;if(S){try{A=math$1.abs(S(n))}catch(e){return{equal_at_start:!1,always_zero:!1}}if(!Number.isFinite(A))return{equal_at_start:!1,always_zero:!1}}if(A+=g*s,A=Math.min(A,.1*g),A+=0!==A||0!==l&&0!==f?u:c,!(0===v||math$1.abs(math$1.subtract(l,f))0))return{equal_at_start:!1,always_zero:!1}}var T=0===v,O=0;for(let e=0;e<100;e++){var C,k=r(t,x,E/100,i);for(let e=0;e=y)return{equal:!0,always_zero:T}}}return{sufficient_finite_values:!1,always_zero:T}}};function replace_numbers_with_parameters({expr:e,variables:t,include_exponents:r=!1}){let n={},i=0;function a(){i++;let e="par"+i;for(;t.includes(e);)i++,e="par"+i;return e}return{expr_with_params:function e(t){if("number"==typeof t){if(0===t)return t;{let e=a();return n[e]=t,e}}if("string"==typeof t){if("pi"===t){if(math$1.define_pi){let e=a();return n[e]=math$1.PI,e}}else if("e"===t&&math$1.define_e){let e=a();return n[e]=math$1.e,e}return t}if(!Array.isArray(t))return t;let i=t[0],o=t.slice(1);return"^"!==i||r?[i,...o.map(e)]:[i,e(o[0]),o[1]]}((e=e.evaluate_numbers({max_digits:1/0})).tree),parameters:n}}function rename_functions_with_exponents(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("apply"===t){let e=r[0];return Array.isArray(e)&&"^"===e[0]&&e.slice(1).every((e=>["number","string"].includes(typeof e)))&&(e=astToText.convert(e)),["apply",e,r[1]]}return[t,...r.map(rename_functions_with_exponents)]}function rename_vecs(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);return"vec"===t&&1===r.length?"__vec_"+astToText.convert(r[0]):[t,...r.map(rename_vecs)]}function randomComplexBindings(e,t,r,n){var i={};return void 0===n?t.forEach((function(t){i[t]=math$1.complex(2*e()*r-r,2*e()*r-r)})):t.forEach((function(t){i[t]=math$1.complex(n[t].re+2*e()*r-r,n[t].im+2*e()*r-r)})),i}const equals$4=function(e,t,{relative_tolerance:r=1e-12,absolute_tolerance:n=0,tolerance_for_zero:i=1e-15,allowed_error_in_numbers:a=0,include_error_in_number_exponents:o=!1,allowed_error_is_absolute:s=!1,allow_blanks:u=!1}={}){if(!u&&(e.variables().includes("＿")||t.variables().includes("＿")))return!1;let c=seedrandom$1("complex_seed");return e=e.remove_scaling_units(),t=t.remove_scaling_units(),!(!e.isAnalytic({allow_abs:!0,allow_arg:!0,allow_relation:!0})||!t.isAnalytic({allow_abs:!0,allow_arg:!0,allow_relation:!0}))&&equals$5({expr:e,other:t,randomBindings:randomComplexBindings,expr_context:e.context,other_context:t.context,relative_tolerance:r,absolute_tolerance:n,tolerance_for_zero:i,allowed_error_in_numbers:a,include_error_in_number_exponents:o,allowed_error_is_absolute:s,rng:c})};function randomRealBindings(e,t,r,n){var i={};return void 0===n?t.forEach((function(t){i[t]=2*e()*r-r})):t.forEach((function(t){i[t]=n[t]+2*e()*r-r})),i}const equals$3=function(e,t,{relative_tolerance:r=1e-12,absolute_tolerance:n=0,tolerance_for_zero:i=1e-15,allowed_error_in_numbers:a=0,include_error_in_number_exponents:o=!1,allowed_error_is_absolute:s=!1}={}){if(!e.isAnalytic()||!t.isAnalytic())return!1;let u=seedrandom("real_seed");return equals$5({expr:e,other:t,randomBindings:randomRealBindings,expr_context:e.context,other_content:t.context,relative_tolerance:r,absolute_tolerance:n,tolerance_for_zero:i,allowed_error_in_numbers:a,include_error_in_number_exponents:o,allowed_error_is_absolute:s,rng:u})},equals$2=function(e,t,{allowed_error_in_numbers:r=0,include_error_in_number_exponents:n=!1,allowed_error_is_absolute:i=!1,allow_blanks:a=!1}={}){if(!a&&(e.variables().includes("＿")||t.variables().includes("＿")))return!1;let o=e.normalize_function_names().normalize_applied_functions().normalize_angle_linesegment_arg_order(),s=t.normalize_function_names().normalize_applied_functions().normalize_angle_linesegment_arg_order();return equal(o.tree,s.tree,{allowed_error_in_numbers:r,include_error_in_number_exponents:n,allowed_error_is_absolute:i})},equals$1=function(e,t,{min_elements_match:r=3,match_partial:n=!1}={}){if(!is_discrete_infinite_set(e))return!1;if(is_discrete_infinite_set(t)){var i=[];let r=e.context.get_assumptions(e);if(void 0!==r&&i.push(r),r=t.context.get_assumptions(t),void 0!==r&&i.push(r),i=0===i.length?void 0:1===i.length?i[0]:clean_assumptions(["and"].concat(i)),n){let r=contained_in(e.tree,t.tree,i,n);if(!1===r)return 0;let a=contained_in(t.tree,e.tree,i,n);return!1===a?0:!0===r?!0===a?1:a:!0===a?r:Math.min(r,a)}return contained_in(e.tree,t.tree,i,n)&&contained_in(t.tree,e.tree,i,n)}{let n=t.tree;if("list"!==n[0])return!1;let i=n.length-2;if("ldots"!==n[i+1][0])return!1;if(icontained_in(e,t,r)))}var i=e[1],a=e[2],o=e[3],s=e[4];if(!Array.isArray(o)||"-"!==o[0]||o[1]!==1/0||s!==1/0)return!1;i=simplify(["/",i,a],r,1/0);var u=t.slice(1),c=[];for(let e=0;ee[0])))];let f=0;for(let e of l){let t=c.map((function(t,r){let n=e/t[0];return Number.isInteger(n)?[t[0],n,r]:void 0})).filter((e=>e)),a=[];for(let n of t){let t=n[0],o=n[1],s=n[2],u=c[s][2],l=c[s][3];for(let n=0;nf&&(f=t)}}return!!(n&&f>0)&&f}function sequence_from_discrete_infinite(e,t){var r=e.tree.slice(1);if(r.length>1)return;let n=r[0][1],i=r[0][2],a=evaluate_numbers(r[0][3]),o=r[0][4];if(!Number.isInteger(a)||o!==1/0)return;let s=[];for(let e=0;e0))throw Error(`Have not implemented equality check with ${n} sign errors.`);if(n>1){let e=r;r=function(t,r){return equalSpecifiedSignErrors(t,r,{equalityFunction:e,n_sign_errors:n-1})}}var i,a,o=e.tree,s=[[o]],u=0;e.tree=["-",o];var c=r(e,t);if(e.tree=o,c)return!0;for(;i=s[u++];)if(i=i[0],Array.isArray(i))for(a=1;a"];function isAnalytic(e,{allow_abs:t=!1,allow_arg:r=!1,allow_relation:n=!1}={}){var i=normalize_applied_functions(normalize_function_names(e)),a=operators$3(i=subscripts_to_strings(i));for(let e=0;e+")},"-":function(e){return"-"+e.join("-")+""},"*":function(e){return e.join('\\cdot*')},"/":function(e){return astToGuppy$1.dfrac(e[0],e[1])},"^":function(e){return astToGuppy$1.power(e[0],e[1])},sin:function(e){return astToGuppy$1.trig("sin",e[0])},cos:function(e){return astToGuppy$1.trig("cos",e[0])},tan:function(e){return astToGuppy$1.trig("tan",e[0])},arcsin:function(e){return astToGuppy$1.trig("arcsin",e[0])},arccos:function(e){return astToGuppy$1.trig("arccos",e[0])},arctan:function(e){return astToGuppy$1.trig("arctan",e[0])},arccsc:function(e){return astToGuppy$1.trig("arccsc",e[0])},arcsec:function(e){return astToGuppy$1.trig("arcsec",e[0])},arccot:function(e){return astToGuppy$1.trig("arccot",e[0])},csc:function(e){return astToGuppy$1.trig("csc",e[0])},sec:function(e){return astToGuppy$1.trig("sec",e[0])},cot:function(e){return astToGuppy$1.trig("cot",e[0])},log:function(e){return astToGuppy$1.trig("log",e[0])},exp:function(e){return astToGuppy$1.trig("exp",e[0])},ln:function(e){return astToGuppy$1.trig("ln",e[0])},sqrt:function(e){return astToGuppy$1.sqrt(e[0])},abs:function(e){return astToGuppy$1.abs(e[0])}}}static dfrac(e,t){return'\\dfrac{}{}\\frac{}{}()/()'+e+''+t+""}static trig(e,t){return'\\'+e+'\\left(\\right) '+e+'()'+t+""}static sqrt(e){return'\\sqrt{}sqrt()'+e+""}static power(e,t){return'{}^{}()^()'+e+''+t+""}static abs(e){return'\\left|\\right|abs()'+e+""}static paren(e){return'\\left(\\right)()'+e+""}static isFunctionSymbol(e){return-1!==["sin","cos","tan","csc","sec","cot","arcsin","arccos","arctan","arccsc","arcsec","arccot","log","ln","exp","sqrt","abs","this.factorial"].indexOf(e)}static isGreekLetterSymbol(e){return-1!==["pi","theta","theta","Theta","alpha","nu","beta","xi","Xi","gamma","Gamma","delta","Delta","pi","Pi","epsilon","epsilon","rho","rho","zeta","sigma","Sigma","eta","tau","upsilon","Upsilon","iota","phi","phi","Phi","kappa","chi","lambda","Lambda","psi","Psi","omega","Omega"].indexOf(e)}factorWithParenthesesIfNegated(e){var t=this.factor(e);return t.toString().match(/^-/)?astToGuppy$1.paren(t.toString()):t}factor(e){if("string"==typeof e)return astToGuppy$1.isGreekLetterSymbol(e)?'\\'+e+' $'+e+"":""+e+"";if("number"==typeof e)return""+e+"";if(!Array.isArray(e))return"";var t=e[0],r=e.slice(1);return"apply"===t&&(t=e[1],r=e.slice(2)),"abs"===t?this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this))):astToGuppy$1.isFunctionSymbol(t)?"this.factorial"!==t||1!==r[0].toString().length&&!r[0].toString().match(/^[0-9]*$/)?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):this.operators[t](r):"^"===t||"~"===t?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):astToGuppy$1.paren(this.expression(e))}term(e){if(!Array.isArray(e))return this.factor(e);var t=e[0],r=e.slice(1);return"*"===t?this.operators[t](r.map(function(e,t){var r=this.factorWithParenthesesIfNegated(e);return r.toString().match(/^[0-9]/)&&t>0?" * "+r:r}.bind(this))):"/"===t?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):this.factor(e)}expression(e){if(!Array.isArray(e))return this.term(e);var t=e[0],r=e.slice(1);return"+"===t||"-"===t?this.operators[t](r.map(function(e,t){return this.factorWithParenthesesIfNegated(e)}.bind(this))):this.term(e)}convert(e){return(""+this.expression(e)+"").replace(/<\/e>/g,"")}}const glslOperators={"+":function(e){var t=e[0];return e.slice(1).forEach((function(e){t=t+"+"+e})),t},"-":function(e){var t="-"+e[0];return e.slice(1).forEach((function(e){t=t+"-"+e})),t},"~":function(e){var t="vec2(0.0,0.0)";return e.forEach((function(e){t=t+"-"+e})),t},"*":function(e){var t=e[0];return e.slice(1).forEach((function(e){t="cmul("+t+","+e+")"})),t},"/":function(e){var t=e[0];return e.slice(1).forEach((function(e){t="cdiv("+t+","+e+")"})),t},sin:function(e){return"csin("+e[0]+")"},cos:function(e){return"ccos("+e[0]+")"},tan:function(e){return"ctan("+e[0]+")"},sinh:function(e){return"csinh("+e[0]+")"},cosh:function(e){return"ccosh("+e[0]+")"},arcsin:function(e){return"carcsin("+e[0]+")"},arccos:function(e){return"carccos("+e[0]+")"},arctan:function(e){return"carctan("+e[0]+")"},arccsc:function(e){return"carcsin(cdiv(vec2(1.0,0),"+e[0]+"))"},arcsec:function(e){return"carccos(cdiv(vec2(1.0,0),"+e[0]+"))"},arccot:function(e){return"carctan(cdiv(vec2(1.0,0),"+e[0]+"))"},csc:function(e){return"ccsc("+e[0]+")"},sec:function(e){return"csec("+e[0]+")"},cot:function(e){return"ccot("+e[0]+")"},exp:function(e){return"cexp("+e[0]+")"},conj:function(e){return"conjugate("+e[0]+")"},sqrt:function(e){return"cpower("+e[0]+",vec2(0.5,0.0))"},log:function(e){return"clog("+e[0]+")"},ln:function(e){return"clog("+e[0]+")"},"^":function(e){return"cpower("+e[0]+","+e[1]+")"},abs:function(e){return"cabs("+e[0]+")"},apply:function(e){return"vec2(NaN,NaN)"}};class astToGLSL$1{constructor(){}convert(e){if("boolean"==typeof e)throw Error("no support for boolean");if("string"==typeof e)return"e"===e?"vec2(2.71828182845905,0.0)":"pi"===e?"vec2(3.14159265358979,0.0)":"i"===e?"vec2(0.0,1.0)":String(e);if("number"==typeof e)return"vec2("+String(e)+",0.0)";if("real"in e&&"imaginary"in e)return e;if(!Array.isArray(e))throw Error("Invalid ast");var t=e[0],r=e.slice(1);if("apply"===t){if("string"!=typeof r[0])throw Error("Non string functions not implemented for conversion to GLSL");t=r[0],r=r.slice(1);return glslOperators[t](r.map(function(e,t){return this.convert(e)}.bind(this)))}if(t in glslOperators)return glslOperators[t](r.map(function(e,t){return this.convert(e)}.bind(this)));throw Error("Operator "+t+" not implemented for conversion to mathjs")}}var astToGuppy=new astToGuppy$1,astToGLSL=new astToGLSL$1;const tex=function(e,t){return new astToLatex$1(t).convert(e.tree)},toLatex=tex,toString=function(e,t){return new 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e(t.start,t.end,t.step)},e}),{isClass:!0}),name$4x="Matrix",dependencies$4x=[],createMatrixClass=factory(name$4x,dependencies$4x,(()=>{function e(){if(!(this instanceof e))throw new SyntaxError("Constructor must be called with the new operator")}return e.prototype.type="Matrix",e.prototype.isMatrix=!0,e.prototype.storage=function(){throw new Error("Cannot invoke storage on a Matrix interface")},e.prototype.datatype=function(){throw new Error("Cannot invoke datatype on a Matrix interface")},e.prototype.create=function(e,t){throw new Error("Cannot invoke create on a Matrix interface")},e.prototype.subset=function(e,t,r){throw new Error("Cannot invoke subset on a Matrix interface")},e.prototype.get=function(e){throw new Error("Cannot invoke get on a Matrix interface")},e.prototype.set=function(e,t,r){throw new Error("Cannot invoke set on a Matrix interface")},e.prototype.resize=function(e,t){throw new Error("Cannot invoke resize on a Matrix interface")},e.prototype.reshape=function(e,t){throw new Error("Cannot invoke reshape on a Matrix interface")},e.prototype.clone=function(){throw new Error("Cannot invoke clone on a Matrix interface")},e.prototype.size=function(){throw new Error("Cannot invoke size on a Matrix interface")},e.prototype.map=function(e,t){throw new Error("Cannot invoke map on a Matrix interface")},e.prototype.forEach=function(e){throw new Error("Cannot invoke forEach on a Matrix interface")},e.prototype[Symbol.iterator]=function(){throw new Error("Cannot iterate a Matrix interface")},e.prototype.toArray=function(){throw new Error("Cannot invoke toArray on a Matrix interface")},e.prototype.valueOf=function(){throw new Error("Cannot invoke valueOf on a Matrix interface")},e.prototype.format=function(e){throw new Error("Cannot invoke format on a Matrix interface")},e.prototype.toString=function(){throw new Error("Cannot invoke toString on a Matrix 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a,o,s=n[0],u=n[1],c=[];for(a=0;a");if(1===a.length){t.dimension(0).forEach((function(t,i){validateIndex(t),e.set([t,0],r[i[0]],n)}))}else{var c=t.dimension(0),l=t.dimension(1);c.forEach((function(t,i){validateIndex(t),l.forEach((function(a,o){validateIndex(a),e.set([t,a],r[i[0]][o[0]],n)}))}))}}return e}(this,e,t,r);default:throw new SyntaxError("Wrong number of arguments")}},i.prototype.get=function(e){if(!isArray$1(e))throw new TypeError("Array expected");if(e.length!==this._size.length)throw new DimensionError(e.length,this._size.length);if(!this._values)throw new Error("Cannot invoke get on a Pattern only matrix");var t=e[0],r=e[1];validateIndex(t,this._size[0]),validateIndex(r,this._size[1]);var n=o(t,this._ptr[r],this._ptr[r+1],this._index);return nl-1||c>f-1)&&(u(this,Math.max(a+1,l),Math.max(c+1,f),i),l=this._size[0],f=this._size[1]),validateIndex(a,l),validateIndex(c,f);var d=o(a,this._ptr[c],this._ptr[c+1],this._index);return dArray.isArray(e)&&1===e.length?e[0]:e));if(2!==n.length)throw new Error("Only two dimensions matrix are supported");return n.forEach((function(e){if(!isNumber$1(e)||!isInteger$1(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(n)+")")})),u(r?this.clone():this,n[0],n[1],t)},i.prototype.reshape=function(e,t){if(!isArray$1(e))throw new TypeError("Array expected");if(2!==e.length)throw new Error("Sparse matrices can only be reshaped in two dimensions");e.forEach((function(t){if(!isNumber$1(t)||!isInteger$1(t)||t<=-2||0===t)throw new TypeError("Invalid size, must contain positive integers or -1 (size: "+format$1(e)+")")}));var r=this._size[0]*this._size[1];if(r!==(e=processSizesWildcard(e,r))[0]*e[1])throw new Error("Reshaping sparse matrix will result in the wrong number of elements");var n=t?this.clone():this;if(this._size[0]===e[0]&&this._size[1]===e[1])return n;for(var i=[],a=0;a=n&&b<=a&&h(e._values[x],b-n,y-o)}else{for(var _={},w=g;w 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0;i.splice(f,0,t),n&&n.splice(f,0,m),i.splice(f<=l?l+1:l,1),n&&n.splice(f<=l?l+1:l,1)}else if(f=c||i[l]!==e)){var d=n?n[f]:void 0;i.splice(l,0,e),n&&n.splice(l,0,d),i.splice(l<=f?f+1:f,1),n&&n.splice(l<=f?f+1:f,1)}}},i}),{isClass:!0}),name$4k="number",dependencies$4k=["typed"];function getNonDecimalNumberParts(e){var t=e.match(/(0[box])([0-9a-fA-F]*)\.([0-9a-fA-F]*)/);return t?{input:e,radix:{"0b":2,"0o":8,"0x":16}[t[1]],integerPart:t[2],fractionalPart:t[3]}:null}function makeNumberFromNonDecimalParts(e){for(var t=parseInt(e.integerPart,e.radix),r=0,n=0;n{var{typed:t}=e,r=t("number",{"":function(){return 0},number:function(e){return e},string:function(e){if("NaN"===e)return NaN;var t=getNonDecimalNumberParts(e);if(t)return makeNumberFromNonDecimalParts(t);var r=0,n=e.match(/(0[box][0-9a-fA-F]*)i([0-9]*)/);n&&(r=Number(n[2]),e=n[1]);var i=Number(e);if(isNaN(i))throw new SyntaxError('String "'+e+'" is no valid number');if(n){if(i>2**r-1)throw new SyntaxError('String "'.concat(e,'" is out 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e},number:function(e){return!!e},null:function(e){return!1},BigNumber:function(e){return!e.isZero()},string:function(e){var t=e.toLowerCase();if("true"===t)return!0;if("false"===t)return!1;var r=Number(e);if(""!==e&&!isNaN(r))return!!r;throw new Error('Cannot convert "'+e+'" to a boolean')},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$4h="bignumber",dependencies$4h=["typed","BigNumber"],createBignumber=factory(name$4h,dependencies$4h,(e=>{var{typed:t,BigNumber:r}=e;return t("bignumber",{"":function(){return new r(0)},number:function(e){return new r(e+"")},string:function(e){var t=e.match(/(0[box][0-9a-fA-F]*)i([0-9]*)/);if(t){var n=t[2],i=r(t[1]),a=new r(2).pow(Number(n));if(i.gt(a.sub(1)))throw new SyntaxError('String "'.concat(e,'" is out of range'));var o=new r(2).pow(Number(n)-1);return i.gte(o)?i.sub(a):i}return new r(e)},BigNumber:function(e){return e},Fraction:function(e){return new r(e.n).div(e.d).times(e.s)},null:function(e){return new r(0)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$4g="complex",dependencies$4g=["typed","Complex"],createComplex=factory(name$4g,dependencies$4g,(e=>{var{typed:t,Complex:r}=e;return t("complex",{"":function(){return r.ZERO},number:function(e){return new r(e,0)},"number, number":function(e,t){return new r(e,t)},"BigNumber, BigNumber":function(e,t){return new r(e.toNumber(),t.toNumber())},Fraction:function(e){return new r(e.valueOf(),0)},Complex:function(e){return e.clone()},string:function(e){return r(e)},null:function(e){return r(0)},Object:function(e){if("re"in e&&"im"in e)return new r(e.re,e.im);if("r"in e&&"phi"in e||"abs"in e&&"arg"in e)return new r(e);throw new Error("Expected object with properties (re and im) or (r and phi) or (abs and arg)")},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$4f="fraction",dependencies$4f=["typed","Fraction"],createFraction=factory(name$4f,dependencies$4f,(e=>{var{typed:t,Fraction:r}=e;return t("fraction",{number:function(e){if(!isFinite(e)||isNaN(e))throw new Error(e+" cannot be represented as a fraction");return new r(e)},string:function(e){return new r(e)},"number, number":function(e,t){return new r(e,t)},null:function(e){return new r(0)},BigNumber:function(e){return new r(e.toString())},Fraction:function(e){return e},Object:function(e){return new r(e)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$4e="matrix",dependencies$4e=["typed","Matrix","DenseMatrix","SparseMatrix"],createMatrix=factory(name$4e,dependencies$4e,(e=>{var{typed:t,Matrix:r,DenseMatrix:n,SparseMatrix:i}=e;return t(name$4e,{"":function(){return a([])},string:function(e){return a([],e)},"string, string":function(e,t){return a([],e,t)},Array:function(e){return a(e)},Matrix:function(e){return a(e,e.storage())},"Array | Matrix, string":a,"Array | Matrix, string, string":a});function a(e,t,r){if("dense"===t||"default"===t||void 0===t)return new n(e,r);if("sparse"===t)return new i(e,r);throw new TypeError("Unknown matrix type "+JSON.stringify(t)+".")}})),name$4d="matrixFromFunction",dependencies$4d=["typed","matrix","isZero"],createMatrixFromFunction=factory(name$4d,dependencies$4d,(e=>{var{typed:t,matrix:r,isZero:n}=e;return t(name$4d,{"Array | Matrix, function, string, string":function(e,t,r,n){return i(e,t,r,n)},"Array | Matrix, function, string":function(e,t,r){return i(e,t,r)},"Matrix, function":function(e,t){return i(e,t,"dense")},"Array, function":function(e,t){return i(e,t,"dense").toArray()},"Array | Matrix, string, function":function(e,t,r){return i(e,r,t)},"Array | Matrix, string, string, function":function(e,t,r,n){return i(e,n,t,r)}});function i(e,t,i,a){var o;return(o=void 0!==a?r(i,a):r(i)).resize(e),o.forEach((function(e,r){var i=t(r);n(i)||o.set(r,i)})),o}})),name$4c="matrixFromRows",dependencies$4c=["typed","matrix","flatten","size"],createMatrixFromRows=factory(name$4c,dependencies$4c,(e=>{var{typed:t,matrix:r,flatten:n,size:i}=e;return t(name$4c,{"...Array":function(e){return a(e)},"...Matrix":function(e){return r(a(e.map((e=>e.toArray()))))}});function a(e){if(0===e.length)throw new TypeError("At least one row is needed to construct a matrix.");var t=o(e[0]),r=[];for(var i of e){var a=o(i);if(a!==t)throw new TypeError("The vectors had different length: "+(0|t)+" ≠ "+(0|a));r.push(n(i))}return r}function o(e){var t=i(e);if(1===t.length)return t[0];if(2===t.length){if(1===t[0])return t[1];if(1===t[1])return t[0];throw new TypeError("At least one of the arguments is not a vector.")}throw new TypeError("Only one- or two-dimensional vectors are supported.")}})),name$4b="matrixFromColumns",dependencies$4b=["typed","matrix","flatten","size"],createMatrixFromColumns=factory(name$4b,dependencies$4b,(e=>{var{typed:t,matrix:r,flatten:n,size:i}=e;return t(name$4b,{"...Array":function(e){return a(e)},"...Matrix":function(e){return r(a(e.map((e=>e.toArray()))))}});function a(e){if(0===e.length)throw new TypeError("At least one column is needed to construct a matrix.");for(var t=o(e[0]),r=[],i=0;i{var{typed:t}=e;return t(name$4a,{"Unit, Array":function(e,t){return e.splitUnit(t)}})})),name$49="unaryMinus",dependencies$49=["typed"],createUnaryMinus=factory(name$49,dependencies$49,(e=>{var{typed:t}=e;return t(name$49,{number:unaryMinusNumber,Complex:function(e){return e.neg()},BigNumber:function(e){return e.neg()},Fraction:function(e){return e.neg()},Unit:function(e){var t=e.clone();return t.value=this(e.value),t},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$48="unaryPlus",dependencies$48=["typed","config","BigNumber"],createUnaryPlus=factory(name$48,dependencies$48,(e=>{var{typed:t,config:r,BigNumber:n}=e;return t(name$48,{number:unaryPlusNumber,Complex:function(e){return e},BigNumber:function(e){return e},Fraction:function(e){return e},Unit:function(e){return e.clone()},"Array | Matrix":function(e){return deepMap(e,this)},"boolean | string":function(e){return"BigNumber"===r.number?new n(+e):+e}})})),name$47="abs",dependencies$47=["typed"],createAbs=factory(name$47,dependencies$47,(e=>{var{typed:t}=e;return t(name$47,{number:absNumber,Complex:function(e){return e.abs()},BigNumber:function(e){return e.abs()},Fraction:function(e){return e.abs()},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.abs()}})})),name$46="apply",dependencies$46=["typed","isInteger"],createApply=factory(name$46,dependencies$46,(e=>{var{typed:t,isInteger:r}=e;return t(name$46,{"Array | Matrix, number | BigNumber, function":function(e,t,n){if(!r(t))throw new TypeError("Integer number expected for dimension");var i=Array.isArray(e)?arraySize(e):e.size();if(t<0||t>=i.length)throw new IndexError(t,i.length);return isMatrix(e)?e.create(_apply(e.valueOf(),t,n)):_apply(e,t,n)}})}));function _apply(e,t,r){var n,i,a;if(t<=0){if(Array.isArray(e[0])){for(a=_switch(e),i=[],n=0;n{var{typed:t}=e;return t(name$45,{"number, number":addNumber,"Complex, Complex":function(e,t){return e.add(t)},"BigNumber, BigNumber":function(e,t){return e.plus(t)},"Fraction, Fraction":function(e,t){return e.add(t)},"Unit, Unit":function(e,t){if(null===e.value||void 0===e.value)throw new Error("Parameter x contains a unit with undefined value");if(null===t.value||void 0===t.value)throw new Error("Parameter y contains a unit with undefined value");if(!e.equalBase(t))throw new Error("Units do not match");var r=e.clone();return r.value=this(r.value,t.value),r.fixPrefix=!1,r}})})),name$44="cbrt",dependencies$44=["config","typed","isNegative","unaryMinus","matrix","Complex","BigNumber","Fraction"],createCbrt=factory(name$44,dependencies$44,(e=>{var{config:t,typed:r,isNegative:n,unaryMinus:i,matrix:a,Complex:o,BigNumber:s,Fraction:u}=e;return r(name$44,{number:cbrtNumber,Complex:c,"Complex, boolean":c,BigNumber:function(e){return e.cbrt()},Unit:function(e){if(e.value&&isComplex(e.value)){var t=e.clone();return t.value=1,(t=t.pow(1/3)).value=c(e.value),t}var r,a=n(e.value);a&&(e.value=i(e.value)),r=isBigNumber(e.value)?new s(1).div(3):isFraction(e.value)?new u(1,3):1/3;var o=e.pow(r);return a&&(o.value=i(o.value)),o},"Array | Matrix":function(e){return deepMap(e,this)}});function c(e,r){var n=e.arg()/3,i=e.abs(),s=new o(cbrtNumber(i),0).mul(new o(0,n).exp());if(r){var u=[s,new o(cbrtNumber(i),0).mul(new o(0,n+2*Math.PI/3).exp()),new o(cbrtNumber(i),0).mul(new o(0,n-2*Math.PI/3).exp())];return"Array"===t.matrix?u:a(u)}return s}})),name$43="algorithm11",dependencies$43=["typed","equalScalar"],createAlgorithm11=factory(name$43,dependencies$43,(e=>{var{typed:t,equalScalar:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=r,h=0,y=i;"string"==typeof l&&(f=l,d=t.find(r,[f,f]),h=t.convert(0,f),n=t.convert(n,f),y=t.find(i,[f,f]));for(var g=[],v=[],x=[],b=0;b{var{typed:t,DenseMatrix:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=i;"string"==typeof l&&(f=l,n=t.convert(n,f),d=t.find(i,[f,f]));for(var h=[],y=[],g=[],v=0;v{var{typed:t}=e;return function(e,n,i,a){var o,s=e._data,u=e._size,c=e._datatype,l=i;"string"==typeof c&&(o=c,n=t.convert(n,o),l=t.find(i,[o,o]));var f=u.length>0?r(l,0,u,u[0],s,n,a):[];return e.createDenseMatrix({data:f,size:clone$3(u),datatype:o})};function r(e,t,n,i,a,o,s){var u=[];if(t===n.length-1)for(var c=0;c{var{typed:t,config:r,round:n}=e;return t(name$40,{number:function(e){return nearlyEqual$1(e,n(e),r.epsilon)?n(e):Math.ceil(e)},"number, number":function(e,t){if(nearlyEqual$1(e,n(e,t),r.epsilon))return n(e,t);var[i,a]="".concat(e,"e").split("e"),o=Math.ceil(Number("".concat(i,"e").concat(Number(a)+t)));return[i,a]="".concat(o,"e").split("e"),Number("".concat(i,"e").concat(Number(a)-t))}})})),createCeil=factory(name$40,dependencies$40,(e=>{var{typed:t,config:r,round:n,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}=e,u=createAlgorithm11({typed:t,equalScalar:a}),c=createAlgorithm12({typed:t,DenseMatrix:s}),l=createAlgorithm14({typed:t}),f=createCeilNumber({typed:t,config:r,round:n});return t("ceil",{number:f.signatures.number,"number,number":f.signatures["number,number"],Complex:function(e){return e.ceil()},"Complex, number":function(e,t){return e.ceil(t)},"Complex, BigNumber":function(e,t){return e.ceil(t.toNumber())},BigNumber:function(e){return nearlyEqual(e,n(e),r.epsilon)?n(e):e.ceil()},"BigNumber, BigNumber":function(e,t){return nearlyEqual(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),Decimal.ROUND_CEIL)},Fraction:function(e){return e.ceil()},"Fraction, number":function(e,t){return e.ceil(t)},"Fraction, BigNumber":function(e,t){return e.ceil(t.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},"Array, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(i(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return a(e,0)?o(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3$="cube",dependencies$3$=["typed"],createCube=factory(name$3$,dependencies$3$,(e=>{var{typed:t}=e;return t(name$3$,{number:cubeNumber,Complex:function(e){return e.mul(e).mul(e)},BigNumber:function(e){return e.times(e).times(e)},Fraction:function(e){return e.pow(3)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(3)}})})),name$3_="exp",dependencies$3_=["typed"],createExp=factory(name$3_,dependencies$3_,(e=>{var{typed:t}=e;return t(name$3_,{number:expNumber,Complex:function(e){return e.exp()},BigNumber:function(e){return e.exp()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3Z="expm1",dependencies$3Z=["typed","Complex"],createExpm1=factory(name$3Z,dependencies$3Z,(e=>{var{typed:t,Complex:r}=e;return t(name$3Z,{number:expm1Number,Complex:function(e){var t=Math.exp(e.re);return new r(t*Math.cos(e.im)-1,t*Math.sin(e.im))},BigNumber:function(e){return e.exp().minus(1)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3Y="fix",dependencies$3Y=["typed","Complex","matrix","ceil","floor","equalScalar","zeros","DenseMatrix"],createFixNumber=factory(name$3Y,["typed","ceil","floor"],(e=>{var{typed:t,ceil:r,floor:n}=e;return t(name$3Y,{number:function(e){return e>0?n(e):r(e)},"number, number":function(e,t){return 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Matrix":function(e){return deepMap(e,this)},"Array | Matrix, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(n(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return o(e,0)?s(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3X="floor",dependencies$3X=["typed","config","round","matrix","equalScalar","zeros","DenseMatrix"],createFloorNumber=factory(name$3X,["typed","config","round"],(e=>{var{typed:t,config:r,round:n}=e;return t(name$3X,{number:function(e){return nearlyEqual$1(e,n(e),r.epsilon)?n(e):Math.floor(e)},"number, number":function(e,t){if(nearlyEqual$1(e,n(e,t),r.epsilon))return n(e,t);var[i,a]="".concat(e,"e").split("e"),o=Math.floor(Number("".concat(i,"e").concat(Number(a)+t)));return[i,a]="".concat(o,"e").split("e"),Number("".concat(i,"e").concat(Number(a)-t))}})})),createFloor=factory(name$3X,dependencies$3X,(e=>{var{typed:t,config:r,round:n,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}=e,u=createAlgorithm11({typed:t,equalScalar:a}),c=createAlgorithm12({typed:t,DenseMatrix:s}),l=createAlgorithm14({typed:t}),f=createFloorNumber({typed:t,config:r,round:n});return t("floor",{number:f.signatures.number,"number,number":f.signatures["number,number"],Complex:function(e){return e.floor()},"Complex, number":function(e,t){return e.floor(t)},"Complex, BigNumber":function(e,t){return e.floor(t.toNumber())},BigNumber:function(e){return nearlyEqual(e,n(e),r.epsilon)?n(e):e.floor()},"BigNumber, BigNumber":function(e,t){return nearlyEqual(e,n(e,t),r.epsilon)?n(e,t):e.toDecimalPlaces(t.toNumber(),Decimal.ROUND_FLOOR)},Fraction:function(e){return e.floor()},"Fraction, number":function(e,t){return e.floor(t)},"Fraction, BigNumber":function(e,t){return e.floor(t.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},"Array, number | BigNumber":function(e,t){return deepMap(e,(e=>this(e,t)))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | Complex | Fraction | BigNumber, Array":function(e,t){return l(i(t),e,this,!0).valueOf()},"number | Complex | Fraction | BigNumber, Matrix":function(e,t){return a(e,0)?o(t.size(),t.storage()):"dense"===t.storage()?l(t,e,this,!0):c(t,e,this,!0)}})})),name$3W="algorithm01",dependencies$3W=["typed"],createAlgorithm01=factory(name$3W,dependencies$3W,(e=>{var{typed:t}=e;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,l=r._ptr,f=r._size,p=r._datatype;if(o.length!==f.length)throw new DimensionError(o.length,f.length);if(o[0]!==f[0]||o[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+f+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,d,h=o[0],y=o[1],g="string"==typeof s&&s===p?s:void 0,v=g?t.find(n,[g,g]):n,x=[];for(m=0;m{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A,M=a&&l?[]:void 0,S=[],E=[],T=a&&l?[]:void 0,O=a&&l?[]:void 0,C=[],k=[];for(w=0;w{var{typed:t,DenseMatrix:r}=e;return function(e,n,i,a){var o=e._values,s=e._index,u=e._ptr,c=e._size,l=e._datatype;if(!o)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var f,p=c[0],m=c[1],d=i;"string"==typeof l&&(f=l,n=t.convert(n,f),d=t.find(i,[f,f]));for(var h=[],y=[],g=[],v=0;v{var{typed:t}=e;return function(e,n,i){var a,o=e._data,s=e._size,u=e._datatype,c=n._data,l=n._size,f=n._datatype,p=[];if(s.length!==l.length)throw new DimensionError(s.length,l.length);for(var m=0;m0?r(d,0,p,p[0],o,c):[];return e.createDenseMatrix({data:h,size:p,datatype:a})};function r(e,t,n,i,a,o){var s=[];if(t===n.length-1)for(var u=0;u{var{typed:t,matrix:r,equalScalar:n,BigNumber:i,DenseMatrix:a}=e,o=createAlgorithm01({typed:t}),s=createAlgorithm04({typed:t,equalScalar:n}),u=createAlgorithm10({typed:t,DenseMatrix:a}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t});return t(name$3S,{"number, number":gcdNumber,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function gcd must be integer numbers");var r=new i(0);for(;!t.isZero();){var n=e.mod(t);e=t,t=n}return e.lt(r)?e.neg():e},"Fraction, Fraction":function(e,t){return e.gcd(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return u(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return l(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return l(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i{var{typed:t,equalScalar:r}=e;return function(e,n,i,a){var o=e._data,s=e._size,u=e._datatype,c=n._values,l=n._index,f=n._ptr,p=n._size,m=n._datatype;if(s.length!==p.length)throw new DimensionError(s.length,p.length);if(s[0]!==p[0]||s[1]!==p[1])throw new RangeError("Dimension mismatch. Matrix A ("+s+") must match Matrix B ("+p+")");if(!c)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var d,h=s[0],y=s[1],g=r,v=0,x=i;"string"==typeof u&&u===m&&(d=u,g=t.find(r,[d,d]),v=t.convert(0,d),x=t.find(i,[d,d]));for(var b=[],_=[],w=[],N=0;N{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._size,s=e._datatype,u=n._values,c=n._size,l=n._datatype;if(o.length!==c.length)throw new DimensionError(o.length,c.length);if(o[0]!==c[0]||o[1]!==c[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+c+")");var f,p=o[0],m=o[1],d=r,h=0,y=i;"string"==typeof s&&s===l&&(f=s,d=t.find(r,[f,f]),h=t.convert(0,f),y=t.find(i,[f,f]));for(var g=a&&u?[]:void 0,v=[],x=[],b=g?[]:void 0,_=[],w=[],N=0;N{var{typed:t,matrix:r,equalScalar:n}=e,i=createAlgorithm02({typed:t,equalScalar:n}),a=createAlgorithm06({typed:t,equalScalar:n}),o=createAlgorithm11({typed:t,equalScalar:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3P,{"number, number":lcmNumber,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function lcm must be integer numbers");if(e.isZero())return e;if(t.isZero())return t;var r=e.times(t);for(;!t.isZero();){var n=t;t=e.mod(n),e=n}return r.div(e).abs()},"Fraction, Fraction":function(e,t){return e.lcm(t)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return o(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return o(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return u(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return u(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i{var{typed:t,config:r,Complex:n}=e;return t(name$3O,{number:function(e){return e>=0||r.predictable?log10Number(e):new n(e,0).log().div(Math.LN10)},Complex:function(e){return new n(e).log().div(Math.LN10)},BigNumber:function(e){return!e.isNegative()||r.predictable?e.log():new n(e.toNumber(),0).log().div(Math.LN10)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3N="log2",dependencies$3N=["typed","config","Complex"],createLog2=factory(name$3N,dependencies$3N,(e=>{var{typed:t,config:r,Complex:n}=e;return t(name$3N,{number:function(e){return e>=0||r.predictable?log2Number(e):i(new n(e,0))},Complex:i,BigNumber:function(e){return!e.isNegative()||r.predictable?e.log(2):i(new n(e.toNumber(),0))},"Array | Matrix":function(e){return deepMap(e,this)}});function i(e){var t=Math.sqrt(e.re*e.re+e.im*e.im);return new n(Math.log2?Math.log2(t):Math.log(t)/Math.LN2,Math.atan2(e.im,e.re)/Math.LN2)}})),name$3M="algorithm03",dependencies$3M=["typed"],createAlgorithm03=factory(name$3M,dependencies$3M,(e=>{var{typed:t}=e;return function(e,r,n,i){var a=e._data,o=e._size,s=e._datatype,u=r._values,c=r._index,l=r._ptr,f=r._size,p=r._datatype;if(o.length!==f.length)throw new DimensionError(o.length,f.length);if(o[0]!==f[0]||o[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+f+")");if(!u)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var m,d=o[0],h=o[1],y=0,g=n;"string"==typeof s&&s===p&&(m=s,y=t.convert(0,m),g=t.find(n,[m,m]));for(var v=[],x=0;x{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A=a&&l?[]:void 0,M=[],S=[],E=A?[]:void 0,T=A?[]:void 0,O=[],C=[];for(w=0;w{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm02({typed:t,equalScalar:n}),o=createAlgorithm03({typed:t}),s=createAlgorithm05({typed:t,equalScalar:n}),u=createAlgorithm11({typed:t,equalScalar:n}),c=createAlgorithm12({typed:t,DenseMatrix:i}),l=createAlgorithm13({typed:t}),f=createAlgorithm14({typed:t});return t(name$3K,{"number, number":modNumber,"BigNumber, BigNumber":function(e,t){if(t.isNeg())throw new Error("Cannot calculate mod for a negative divisor");return t.isZero()?e:e.mod(t)},"Fraction, Fraction":function(e,t){if(t.compare(0)<0)throw new Error("Cannot calculate mod for a negative divisor");return e.compare(0)>=0?e.mod(t):e.mod(t).add(t).mod(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return l(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return u(e,t,this,!1)},"DenseMatrix, any":function(e,t){return f(e,t,this,!1)},"any, SparseMatrix":function(e,t){return c(t,e,this,!0)},"any, DenseMatrix":function(e,t){return f(t,e,this,!0)},"Array, any":function(e,t){return f(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return f(r(t),e,this,!0).valueOf()}})})),name$3J="multiplyScalar",dependencies$3J=["typed"],createMultiplyScalar=factory(name$3J,dependencies$3J,(e=>{var{typed:t}=e;return t("multiplyScalar",{"number, number":multiplyNumber,"Complex, Complex":function(e,t){return e.mul(t)},"BigNumber, BigNumber":function(e,t){return e.times(t)},"Fraction, Fraction":function(e,t){return e.mul(t)},"number | Fraction | BigNumber | Complex, Unit":function(e,t){var r=t.clone();return r.value=null===r.value?r._normalize(e):this(r.value,e),r},"Unit, number | Fraction | BigNumber | Complex":function(e,t){var r=e.clone();return r.value=null===r.value?r._normalize(t):this(r.value,t),r},"Unit, Unit":function(e,t){return e.multiply(t)}})})),name$3I="multiply",dependencies$3I=["typed","matrix","addScalar","multiplyScalar","equalScalar","dot"],createMultiply=factory(name$3I,dependencies$3I,(e=>{var{typed:t,matrix:r,addScalar:n,multiplyScalar:i,equalScalar:a,dot:o}=e,s=createAlgorithm11({typed:t,equalScalar:a}),u=createAlgorithm14({typed:t});function c(e,t){switch(e.length){case 1:switch(t.length){case 1:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vectors must have the same length");break;case 2:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Vector length ("+e[0]+") must match Matrix rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;case 2:switch(t.length){case 1:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix columns ("+e[1]+") must match Vector length ("+t[0]+")");break;case 2:if(e[1]!==t[0])throw new RangeError("Dimension mismatch in multiplication. Matrix A columns ("+e[1]+") must match Matrix B rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix A has "+e.length+" dimensions)")}}function l(e,r){if("dense"!==r.storage())throw new Error("Support for SparseMatrix not implemented");return function(e,r){var a,o=e._data,s=e._size,u=e._datatype,c=r._data,l=r._size,f=r._datatype,p=s[0],m=l[1],d=n,h=i;u&&f&&u===f&&"string"==typeof u&&(a=u,d=t.find(n,[a,a]),h=t.find(i,[a,a]));for(var y=[],g=0;gM)for(var E=0,T=0;T{var{typed:t,matrix:r,equalScalar:n,BigNumber:i}=e,a=createAlgorithm01({typed:t}),o=createAlgorithm02({typed:t,equalScalar:n}),s=createAlgorithm06({typed:t,equalScalar:n}),u=createAlgorithm11({typed:t,equalScalar:n}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t}),f="Complex number not supported in function nthRoot. Use nthRoots instead.";return t(name$3H,{number:nthRootNumber,"number, number":nthRootNumber,BigNumber:function(e){return p(e,new i(2))},Complex:function(e){throw new Error(f)},"Complex, number":function(e,t){throw new Error(f)},"BigNumber, BigNumber":p,"Array | Matrix":function(e){return this(e,2)},"SparseMatrix, SparseMatrix":function(e,t){if(1===t.density())return s(e,t,this);throw new Error("Root must be non-zero")},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){if(1===t.density())return a(e,t,this,!1);throw new Error("Root must be non-zero")},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return l(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){if(1===t.density())return u(t,e,this,!0);throw new Error("Root must be non-zero")},"number | BigNumber, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return this(r(e),t).valueOf()},"number | BigNumber, Array":function(e,t){return this(e,r(t)).valueOf()}});function p(e,t){var r=i.precision,n=i.clone({precision:r+2}),a=new i(0),o=new n(1),s=t.isNegative();if(s&&(t=t.neg()),t.isZero())throw new Error("Root must be non-zero");if(e.isNegative()&&!t.abs().mod(2).equals(1))throw new Error("Root must be odd when a is negative.");if(e.isZero())return s?new n(1/0):0;if(!e.isFinite())return s?a:e;var u=e.abs().pow(o.div(t));return u=e.isNeg()?u.neg():u,new i((s?o.div(u):u).toPrecision(r))}})),name$3G="sign",dependencies$3G=["typed","BigNumber","Fraction","complex"],createSign=factory(name$3G,dependencies$3G,(e=>{var{typed:t,BigNumber:r,complex:n,Fraction:i}=e;return t(name$3G,{number:signNumber,Complex:function(e){return 0===e.im?n(signNumber(e.re)):e.sign()},BigNumber:function(e){return new r(e.cmp(0))},Fraction:function(e){return new i(e.s,1)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){if(!e._isDerived()&&0!==e.units[0].unit.offset)throw new TypeError("sign is ambiguous for units with offset");return this(e.value)}})})),name$3F="sqrt",dependencies$3F=["config","typed","Complex"],createSqrt=factory(name$3F,dependencies$3F,(e=>{var{config:t,typed:r,Complex:n}=e;return r("sqrt",{number:i,Complex:function(e){return e.sqrt()},BigNumber:function(e){return!e.isNegative()||t.predictable?e.sqrt():i(e.toNumber())},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(.5)}});function i(e){return isNaN(e)?NaN:e>=0||t.predictable?Math.sqrt(e):new n(e,0).sqrt()}})),name$3E="square",dependencies$3E=["typed"],createSquare=factory(name$3E,dependencies$3E,(e=>{var{typed:t}=e;return t(name$3E,{number:squareNumber,Complex:function(e){return e.mul(e)},BigNumber:function(e){return e.times(e)},Fraction:function(e){return e.mul(e)},"Array | Matrix":function(e){return deepMap(e,this)},Unit:function(e){return e.pow(2)}})})),name$3D="subtract",dependencies$3D=["typed","matrix","equalScalar","addScalar","unaryMinus","DenseMatrix"],createSubtract=factory(name$3D,dependencies$3D,(e=>{var{typed:t,matrix:r,equalScalar:n,addScalar:i,unaryMinus:a,DenseMatrix:o}=e,s=createAlgorithm01({typed:t}),u=createAlgorithm03({typed:t}),c=createAlgorithm05({typed:t,equalScalar:n}),l=createAlgorithm10({typed:t,DenseMatrix:o}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$3D,{"number, number":function(e,t){return e-t},"Complex, Complex":function(e,t){return e.sub(t)},"BigNumber, BigNumber":function(e,t){return e.minus(t)},"Fraction, Fraction":function(e,t){return e.sub(t)},"Unit, Unit":function(e,t){if(null===e.value)throw new Error("Parameter x contains a unit with undefined value");if(null===t.value)throw new Error("Parameter y contains a unit with undefined value");if(!e.equalBase(t))throw new Error("Units do not match");var r=e.clone();return r.value=this(r.value,t.value),r.fixPrefix=!1,r},"SparseMatrix, SparseMatrix":function(e,t){return checkEqualDimensions(e,t),c(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return checkEqualDimensions(e,t),u(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return checkEqualDimensions(e,t),s(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return checkEqualDimensions(e,t),f(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return l(e,a(t),i)},"DenseMatrix, any":function(e,t){return p(e,t,this)},"any, SparseMatrix":function(e,t){return l(t,e,this,!0)},"any, DenseMatrix":function(e,t){return p(t,e,this,!0)},"Array, any":function(e,t){return p(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return p(r(t),e,this,!0).valueOf()}})}));function checkEqualDimensions(e,t){var r=e.size(),n=t.size();if(r.length!==n.length)throw new DimensionError(r.length,n.length)}var name$3C="xgcd",dependencies$3C=["typed","config","matrix","BigNumber"],createXgcd=factory(name$3C,dependencies$3C,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t(name$3C,{"number, number":function(e,t){var i=xgcdNumber(e,t);return"Array"===r.matrix?i:n(i)},"BigNumber, BigNumber":function(e,t){var a,o,s,u,c=new i(0),l=new i(1),f=c,p=l,m=l,d=c;if(!e.isInt()||!t.isInt())throw new Error("Parameters in function xgcd must be integer numbers");for(;!t.isZero();)o=e.div(t).floor(),s=e.mod(t),a=f,f=p.minus(o.times(f)),p=a,a=m,m=d.minus(o.times(m)),d=a,e=t,t=s;u=e.lt(c)?[e.neg(),p.neg(),d.neg()]:[e,e.isZero()?0:p,d];return"Array"===r.matrix?u:n(u)}})})),name$3B="invmod",dependencies$3B=["typed","config","BigNumber","xgcd","equal","smaller","mod","add","isInteger"],createInvmod=factory(name$3B,dependencies$3B,(e=>{var{typed:t,config:r,BigNumber:n,xgcd:i,equal:a,smaller:o,mod:s,add:u,isInteger:c}=e;return t(name$3B,{"number, number":l,"BigNumber, BigNumber":l});function l(e,t){if(!c(e)||!c(t))throw new Error("Parameters in function invmod must be integer numbers");if(e=s(e,t),a(t,0))throw new Error("Divisor must be non zero");var r=i(e,t);r=r.valueOf();var[l,f]=r;return a(l,n(1))?(f=s(f,t),o(f,n(0))&&(f=u(f,t)),f):NaN}})),name$3A="algorithm09",dependencies$3A=["typed","equalScalar"],createAlgorithm09=factory(name$3A,dependencies$3A,(e=>{var{typed:t,equalScalar:r}=e;return function(e,n,i){var a=e._values,o=e._index,s=e._ptr,u=e._size,c=e._datatype,l=n._values,f=n._index,p=n._ptr,m=n._size,d=n._datatype;if(u.length!==m.length)throw new DimensionError(u.length,m.length);if(u[0]!==m[0]||u[1]!==m[1])throw new RangeError("Dimension mismatch. Matrix A ("+u+") must match Matrix B ("+m+")");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));var _,w,N,$,A,M=a&&l?[]:void 0,S=[],E=[],T=M?[]:void 0,O=[];for(w=0;w{var{typed:t,matrix:r,equalScalar:n,multiplyScalar:i}=e,a=createAlgorithm02({typed:t,equalScalar:n}),o=createAlgorithm09({typed:t,equalScalar:n}),s=createAlgorithm11({typed:t,equalScalar:n}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3z,{"any, any":i,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,i,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,i,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,i,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,i)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,i,!1)},"DenseMatrix, any":function(e,t){return c(e,t,i,!1)},"any, SparseMatrix":function(e,t){return s(t,e,i,!0)},"any, DenseMatrix":function(e,t){return c(t,e,i,!0)},"Array, any":function(e,t){return c(r(e),t,i,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,i,!0).valueOf()}})}));function bitAndBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitAnd");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero()||t.eq(-1)||e.eq(t))return e;if(t.isZero()||e.eq(-1))return t;if(!e.isFinite()||!t.isFinite()){if(!e.isFinite()&&!t.isFinite())return e.isNegative()===t.isNegative()?e:new r(0);if(!e.isFinite())return t.isNegative()?e:e.isNegative()?new r(0):t;if(!t.isFinite())return e.isNegative()?t:t.isNegative()?new r(0):e}return bitwise(e,t,(function(e,t){return e&t}))}function bitNotBigNumber(e){if(e.isFinite()&&!e.isInteger())throw new Error("Integer expected in function bitNot");var t=e.constructor,r=t.precision;t.config({precision:1e9});var n=e.plus(new t(1));return n.s=-n.s||null,t.config({precision:r}),n}function bitOrBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitOr");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);var n=new r(-1);return e.isZero()||t.eq(n)||e.eq(t)?t:t.isZero()||e.eq(n)?e:e.isFinite()&&t.isFinite()?bitwise(e,t,(function(e,t){return e|t})):!e.isFinite()&&!e.isNegative()&&t.isNegative()||e.isNegative()&&!t.isNegative()&&!t.isFinite()?n:e.isNegative()&&t.isNegative()?e.isFinite()?e:t:e.isFinite()?t:e}function bitwise(e,t,r){var n,i,a,o,s,u=e.constructor,c=+(e.s<0),l=+(t.s<0);if(c){n=decCoefficientToBinaryString(bitNotBigNumber(e));for(var f=0;f0;)r(a[--m],o[--d])===h&&(y=y.plus(g)),g=g.times(v);for(;d>0;)r(s,o[--d])===h&&(y=y.plus(g)),g=g.times(v);return u.config({precision:x}),0===h&&(y.s=-y.s),y}function decCoefficientToBinaryString(e){for(var t=e.d,r=t[0]+"",n=1;n0)if(++s>c)for(s-=c;s--;)u+="0";else s1&&(null!==l[m+1]&&void 0!==l[m+1]||(l[m+1]=0),l[m+1]+=l[m]>>1,l[m]&=1)}return l.reverse()}function bitXor$1(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function bitXor");var r=e.constructor;if(e.isNaN()||t.isNaN())return new r(NaN);if(e.isZero())return t;if(t.isZero())return e;if(e.eq(t))return new r(0);var n=new r(-1);return e.eq(n)?bitNotBigNumber(t):t.eq(n)?bitNotBigNumber(e):e.isFinite()&&t.isFinite()?bitwise(e,t,(function(e,t){return e^t})):e.isFinite()||t.isFinite()?new r(e.isNegative()===t.isNegative()?1/0:-1/0):n}function leftShiftBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function leftShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:e.isFinite()||t.isFinite()?t.lt(55)?e.times(Math.pow(2,t.toNumber())+""):e.times(new r(2).pow(t)):new r(NaN)}function rightArithShiftBigNumber(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw new Error("Integers expected in function rightArithShift");var r=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new r(NaN):e.isZero()||t.isZero()?e:t.isFinite()?t.lt(55)?e.div(Math.pow(2,t.toNumber())+"").floor():e.div(new r(2).pow(t)).floor():e.isNegative()?new r(-1):e.isFinite()?new r(0):new r(NaN)}var name$3y="bitAnd",dependencies$3y=["typed","matrix","equalScalar"],createBitAnd=factory(name$3y,dependencies$3y,(e=>{var{typed:t,matrix:r,equalScalar:n}=e,i=createAlgorithm02({typed:t,equalScalar:n}),a=createAlgorithm06({typed:t,equalScalar:n}),o=createAlgorithm11({typed:t,equalScalar:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3y,{"number, number":bitAndNumber,"BigNumber, BigNumber":bitAndBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3x="bitNot",dependencies$3x=["typed"],createBitNot=factory(name$3x,dependencies$3x,(e=>{var{typed:t}=e;return t(name$3x,{number:bitNotNumber,BigNumber:bitNotBigNumber,"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3w="bitOr",dependencies$3w=["typed","matrix","equalScalar","DenseMatrix"],createBitOr=factory(name$3w,dependencies$3w,(e=>{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm01({typed:t}),o=createAlgorithm04({typed:t,equalScalar:n}),s=createAlgorithm10({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3w,{"number, number":bitOrNumber,"BigNumber, BigNumber":bitOrBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$3v="algorithm07",dependencies$3v=["typed","DenseMatrix"],createAlgorithm07=factory(name$3v,dependencies$3v,(e=>{var{typed:t,DenseMatrix:r}=e;return function(e,i,a){var o=e._size,s=e._datatype,u=i._size,c=i._datatype;if(o.length!==u.length)throw new DimensionError(o.length,u.length);if(o[0]!==u[0]||o[1]!==u[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+u+")");var l,f,p,m=o[0],d=o[1],h=0,y=a;"string"==typeof s&&s===c&&(l=s,h=t.convert(0,l),y=t.find(a,[l,l]));var g=[];for(f=0;f{var{typed:t,matrix:r,DenseMatrix:n}=e,i=createAlgorithm03({typed:t}),a=createAlgorithm07({typed:t,DenseMatrix:n}),o=createAlgorithm12({typed:t,DenseMatrix:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3u,{"number, number":bitXorNumber,"BigNumber, BigNumber":bitXor$1,"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3t="arg",dependencies$3t=["typed"],createArg=factory(name$3t,dependencies$3t,(e=>{var{typed:t}=e;return t(name$3t,{number:function(e){return Math.atan2(0,e)},BigNumber:function(e){return e.constructor.atan2(0,e)},Complex:function(e){return e.arg()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3s="conj",dependencies$3s=["typed"],createConj=factory(name$3s,dependencies$3s,(e=>{var{typed:t}=e;return t(name$3s,{number:function(e){return e},BigNumber:function(e){return e},Complex:function(e){return e.conjugate()},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3r="im",dependencies$3r=["typed"],createIm=factory(name$3r,dependencies$3r,(e=>{var{typed:t}=e;return t(name$3r,{number:function(e){return 0},BigNumber:function(e){return e.mul(0)},Fraction:function(e){return e.mul(0)},Complex:function(e){return e.im},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3q="re",dependencies$3q=["typed"],createRe=factory(name$3q,dependencies$3q,(e=>{var{typed:t}=e;return t(name$3q,{number:function(e){return e},BigNumber:function(e){return e},Fraction:function(e){return e},Complex:function(e){return e.re},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3p="not",dependencies$3p=["typed"],createNot=factory(name$3p,dependencies$3p,(e=>{var{typed:t}=e;return t(name$3p,{number:notNumber,Complex:function(e){return 0===e.re&&0===e.im},BigNumber:function(e){return e.isZero()||e.isNaN()},Unit:function(e){return null===e.value||this(e.value)},"Array | Matrix":function(e){return deepMap(e,this)}})})),name$3o="or",dependencies$3o=["typed","matrix","equalScalar","DenseMatrix"],createOr=factory(name$3o,dependencies$3o,(e=>{var{typed:t,matrix:r,equalScalar:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm05({typed:t,equalScalar:n}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$3o,{"number, number":orNumber,"Complex, Complex":function(e,t){return 0!==e.re||0!==e.im||0!==t.re||0!==t.im},"BigNumber, BigNumber":function(e,t){return!e.isZero()&&!e.isNaN()||!t.isZero()&&!t.isNaN()},"Unit, Unit":function(e,t){return this(e.value||0,t.value||0)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(r(t),e,this,!0).valueOf()}})})),name$3n="xor",dependencies$3n=["typed","matrix","DenseMatrix"],createXor=factory(name$3n,dependencies$3n,(e=>{var{typed:t,matrix:r,DenseMatrix:n}=e,i=createAlgorithm03({typed:t}),a=createAlgorithm07({typed:t,DenseMatrix:n}),o=createAlgorithm12({typed:t,DenseMatrix:n}),s=createAlgorithm13({typed:t}),u=createAlgorithm14({typed:t});return t(name$3n,{"number, number":xorNumber,"Complex, Complex":function(e,t){return(0!==e.re||0!==e.im)!=(0!==t.re||0!==t.im)},"BigNumber, BigNumber":function(e,t){return(!e.isZero()&&!e.isNaN())!=(!t.isZero()&&!t.isNaN())},"Unit, Unit":function(e,t){return this(e.value||0,t.value||0)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return o(e,t,this,!1)},"DenseMatrix, any":function(e,t){return u(e,t,this,!1)},"any, SparseMatrix":function(e,t){return o(t,e,this,!0)},"any, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, any":function(e,t){return u(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return u(r(t),e,this,!0).valueOf()}})})),name$3m="concat",dependencies$3m=["typed","matrix","isInteger"],createConcat=factory(name$3m,dependencies$3m,(e=>{var{typed:t,matrix:r,isInteger:n}=e;return t(name$3m,{"...Array | Matrix | number | BigNumber":function(e){var t,i,a=e.length,o=-1,s=!1,u=[];for(t=0;t0&&o>i)throw new IndexError(o,i+1)}else{var l=clone$3(c).valueOf(),f=arraySize(l);if(u[t]=l,i=o,o=f.length-1,t>0&&o!==i)throw new DimensionError(i+1,o+1)}}if(0===u.length)throw new SyntaxError("At least one matrix expected");for(var p=u.shift();u.length;)p=_concat(p,u.shift(),o,0);return s?r(p):p},"...string":function(e){return e.join("")}})}));function _concat(e,t,r,n){if(n{var{typed:t,Index:r,matrix:n,range:i}=e;return t(name$3l,{"Matrix, number":a,"Array, number":function(e,t){return a(n(clone$3(e)),t).valueOf()}});function a(e,t){if(2!==e.size().length)throw new Error("Only two dimensional matrix is supported");validateIndex(t,e.size()[1]);var n=i(0,e.size()[0]),a=new r(n,t);return e.subset(a)}})),name$3k="count",dependencies$3k=["typed","size","prod"],createCount=factory(name$3k,dependencies$3k,(e=>{var{typed:t,size:r,prod:n}=e;return t(name$3k,{string:function(e){return e.length},"Matrix | Array":function(e){return n(r(e))}})})),name$3j="cross",dependencies$3j=["typed","matrix","subtract","multiply"],createCross=factory(name$3j,dependencies$3j,(e=>{var{typed:t,matrix:r,subtract:n,multiply:i}=e;return t(name$3j,{"Matrix, Matrix":function(e,t){return r(a(e.toArray(),t.toArray()))},"Matrix, Array":function(e,t){return r(a(e.toArray(),t))},"Array, Matrix":function(e,t){return r(a(e,t.toArray()))},"Array, Array":a});function a(e,t){var r=Math.max(arraySize(e).length,arraySize(t).length);e=squeeze$1(e),t=squeeze$1(t);var a=arraySize(e),o=arraySize(t);if(1!==a.length||1!==o.length||3!==a[0]||3!==o[0])throw new RangeError("Vectors with length 3 expected (Size A = ["+a.join(", ")+"], B = ["+o.join(", ")+"])");var s=[n(i(e[1],t[2]),i(e[2],t[1])),n(i(e[2],t[0]),i(e[0],t[2])),n(i(e[0],t[1]),i(e[1],t[0]))];return r>1?[s]:s}})),name$3i="diag",dependencies$3i=["typed","matrix","DenseMatrix","SparseMatrix"],createDiag=factory(name$3i,dependencies$3i,(e=>{var{typed:t,matrix:r,DenseMatrix:n,SparseMatrix:i}=e;return t(name$3i,{Array:function(e){return a(e,0,arraySize(e),null)},"Array, number":function(e,t){return a(e,t,arraySize(e),null)},"Array, BigNumber":function(e,t){return a(e,t.toNumber(),arraySize(e),null)},"Array, string":function(e,t){return a(e,0,arraySize(e),t)},"Array, number, string":function(e,t,r){return a(e,t,arraySize(e),r)},"Array, BigNumber, string":function(e,t,r){return a(e,t.toNumber(),arraySize(e),r)},Matrix:function(e){return a(e,0,e.size(),e.storage())},"Matrix, number":function(e,t){return a(e,t,e.size(),e.storage())},"Matrix, BigNumber":function(e,t){return a(e,t.toNumber(),e.size(),e.storage())},"Matrix, string":function(e,t){return a(e,0,e.size(),t)},"Matrix, number, string":function(e,t,r){return a(e,t,e.size(),r)},"Matrix, BigNumber, string":function(e,t,r){return a(e,t.toNumber(),e.size(),r)}});function a(e,t,a,o){if(!isInteger$1(t))throw new TypeError("Second parameter in function diag must be an integer");var s=t>0?t:0,u=t<0?-t:0;switch(a.length){case 1:return function(e,t,r,a,o,s){var u=[a+o,a+s];if(r&&"sparse"!==r&&"dense"!==r)throw new TypeError("Unknown matrix type ".concat(r,'"'));var c="sparse"===r?i.diagonal(u,e,t):n.diagonal(u,e,t);return null!==r?c:c.valueOf()}(e,t,o,a[0],u,s);case 2:return function(e,t,n,i,a,o){if(isMatrix(e)){var s=e.diagonal(t);return null!==n?n!==s.storage()?r(s,n):s:s.valueOf()}for(var u=Math.min(i[0]-a,i[1]-o),c=[],l=0;l1&&void 0!==arguments[1]?arguments[1]:{};return r=null==r?Number.POSITIVE_INFINITY:r,t=null==t?JSON.stringify:t,function n(){"object"!=typeof n.cache&&(n.cache={values:new Map,lru:lruQueue(r||Number.POSITIVE_INFINITY)});for(var i=[],a=0;a{var{typed:t}=e;return t("filter",{"Array, function":_filterCallback,"Matrix, function":function(e,t){return e.create(_filterCallback(e.toArray(),t))},"Array, RegExp":filterRegExp,"Matrix, RegExp":function(e,t){return e.create(filterRegExp(e.toArray(),t))}})}));function _filterCallback(e,t){var r=maxArgumentCount(t);return filter$2(e,(function(e,n,i){return 1===r?t(e):2===r?t(e,[n]):t(e,[n],i)}))}var name$3g="flatten",dependencies$3g=["typed","matrix"],createFlatten=factory(name$3g,dependencies$3g,(e=>{var{typed:t,matrix:r}=e;return t(name$3g,{Array:function(e){return flatten$4(clone$3(e))},Matrix:function(e){var t=flatten$4(clone$3(e.toArray()));return r(t)}})})),name$3f="forEach",dependencies$3f=["typed"],createForEach=factory(name$3f,dependencies$3f,(e=>{var{typed:t}=e;return t(name$3f,{"Array, function":_forEach,"Matrix, function":function(e,t){return e.forEach(t)}})}));function _forEach(e,t){var r=maxArgumentCount(t);!function n(i,a){Array.isArray(i)?forEach$1(i,(function(e,t){n(e,a.concat(t))})):1===r?t(i):2===r?t(i,a):t(i,a,e)}(e,[])}var name$3e="getMatrixDataType",dependencies$3e=["typed"],createGetMatrixDataType=factory(name$3e,dependencies$3e,(e=>{var{typed:t}=e;return t(name$3e,{Array:function(e){return getArrayDataType(e,typeOf$1)},Matrix:function(e){return e.getDataType()}})})),name$3d="identity",dependencies$3d=["typed","config","matrix","BigNumber","DenseMatrix","SparseMatrix"],createIdentity=factory(name$3d,dependencies$3d,(e=>{var{typed:t,config:r,matrix:n,BigNumber:i,DenseMatrix:a,SparseMatrix:o}=e;return t(name$3d,{"":function(){return"Matrix"===r.matrix?n([]):[]},string:function(e){return n(e)},"number | BigNumber":function(e){return u(e,e,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber, string":function(e,t){return u(e,e,t)},"number | BigNumber, number | BigNumber":function(e,t){return u(e,t,"Matrix"===r.matrix?"dense":void 0)},"number | BigNumber, number | BigNumber, string":function(e,t,r){return u(e,t,r)},Array:function(e){return s(e)},"Array, string":function(e,t){return s(e,t)},Matrix:function(e){return s(e.valueOf(),e.storage())},"Matrix, string":function(e,t){return s(e.valueOf(),t)}});function s(e,t){switch(e.length){case 0:return t?n(t):[];case 1:return u(e[0],e[0],t);case 2:return u(e[0],e[1],t);default:throw new Error("Vector containing two values expected")}}function u(e,t,r){var n=isBigNumber(e)||isBigNumber(t)?i:null;if(isBigNumber(e)&&(e=e.toNumber()),isBigNumber(t)&&(t=t.toNumber()),!isInteger$1(e)||e<1)throw new Error("Parameters in function identity must be positive integers");if(!isInteger$1(t)||t<1)throw new Error("Parameters in function identity must be positive integers");var s=n?new i(1):1,u=n?new n(0):0,c=[e,t];if(r){if("sparse"===r)return o.diagonal(c,s,0,u);if("dense"===r)return a.diagonal(c,s,0,u);throw new TypeError('Unknown matrix type "'.concat(r,'"'))}for(var l=resize$1([],c,u),f=e{var{typed:t,matrix:r,multiplyScalar:n}=e;return t(name$3c,{"Matrix, Matrix":function(e,t){return r(i(e.toArray(),t.toArray()))},"Matrix, Array":function(e,t){return r(i(e.toArray(),t))},"Array, Matrix":function(e,t){return r(i(e,t.toArray()))},"Array, Array":i});function i(e,t){if(1===arraySize(e).length&&(e=[e]),1===arraySize(t).length&&(t=[t]),arraySize(e).length>2||arraySize(t).length>2)throw new RangeError("Vectors with dimensions greater then 2 are not supported expected (Size x = "+JSON.stringify(e.length)+", y = "+JSON.stringify(t.length)+")");var r=[],i=[];return e.map((function(e){return t.map((function(t){return i=[],r.push(i),e.map((function(e){return t.map((function(t){return i.push(n(e,t))}))}))}))}))&&r}})),name$3b="map",dependencies$3b=["typed"],createMap=factory(name$3b,dependencies$3b,(e=>{var{typed:t}=e;return t(name$3b,{"Array, function":_map$1,"Matrix, function":function(e,t){return e.map(t)}})}));function _map$1(e,t){var r=maxArgumentCount(t);return function n(i,a){if(Array.isArray(i))return i.map((function(e,t){return n(e,a.concat(t))}));try{return 1===r?t(i):2===r?t(i,a):t(i,a,e)}catch(t){if(t instanceof TypeError&&"data"in t&&"wrongType"===t.data.category){var o="map attempted to call '".concat(t.data.fn,"(").concat(i),s=JSON.stringify(a);throw 2===r?o+=","+s:1!==r&&(o+=",".concat(s,",").concat(e)),o+=")' but argument ".concat(t.data.index+1," of type "),o+="".concat(t.data.actual," does not match expected type "),o+=t.data.expected.join(" or "),new TypeError(o)}throw t}}(e,[])}var name$3a="diff",dependencies$3a=["typed","matrix","subtract","number"],createDiff=factory(name$3a,dependencies$3a,(e=>{var{typed:t,matrix:r,subtract:n,number:i}=e;return t(name$3a,{"Array | Matrix":function(e){return isMatrix(e)?r(o(e.toArray())):o(e)},"Array | Matrix, number":function(e,t){if(!isInteger$1(t))throw new RangeError("Dimension must be a whole number");return isMatrix(e)?r(a(e.toArray(),t)):a(e,t)},"Array | Matrix, BigNumber":function(e,t){return this(e,i(t))}});function a(e,t){if(isMatrix(e)&&(e=e.toArray()),!Array.isArray(e))throw RangeError("Array/Matrix does not have that many dimensions");if(t>0){var r=[];return e.forEach((e=>{r.push(a(e,t-1))})),r}if(0===t)return o(e);throw RangeError("Cannot have negative dimension")}function o(e){var t=[],r=e.length;if(r<2)return e;for(var n=1;n{var{typed:t,config:r,matrix:n,BigNumber:i}=e;return t("ones",{"":function(){return"Array"===r.matrix?a([]):a([],"default")},"...number | BigNumber | string":function(e){if("string"==typeof e[e.length-1]){var t=e.pop();return a(e,t)}return"Array"===r.matrix?a(e):a(e,"default")},Array:a,Matrix:function(e){var t=e.storage();return a(e.valueOf(),t)},"Array | Matrix, string":function(e,t){return a(e.valueOf(),t)}});function a(e,t){var r=function(e){var t=!1;return e.forEach((function(e,r,n){isBigNumber(e)&&(t=!0,n[r]=e.toNumber())})),t}(e),a=r?new i(1):1;if(function(e){e.forEach((function(e){if("number"!=typeof e||!isInteger$1(e)||e<0)throw new Error("Parameters in function ones must be positive integers")}))}(e),t){var o=n(t);return e.length>0?o.resize(e,a):o}var s=[];return e.length>0?resize$1(s,e,a):s}}));function noBignumber(){throw new Error('No "bignumber" implementation available')}function noFraction(){throw new Error('No "fraction" implementation available')}function noMatrix(){throw new Error('No "matrix" implementation available')}var name$38="range",dependencies$38=["typed","config","?matrix","?bignumber","smaller","smallerEq","larger","largerEq"],createRange=factory(name$38,dependencies$38,(e=>{var{typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u}=e;return t(name$38,{string:l,"string, boolean":l,"number, number":function(e,t){return c(f(e,t,1))},"number, number, number":function(e,t,r){return c(f(e,t,r))},"number, number, boolean":function(e,t,r){return c(r?p(e,t,1):f(e,t,1))},"number, number, number, boolean":function(e,t,r,n){return c(n?p(e,t,r):f(e,t,r))},"BigNumber, BigNumber":function(e,t){return c(m(e,t,new(0,e.constructor)(1)))},"BigNumber, BigNumber, BigNumber":function(e,t,r){return c(m(e,t,r))},"BigNumber, BigNumber, boolean":function(e,t,r){var n=e.constructor;return c(r?d(e,t,new n(1)):m(e,t,new n(1)))},"BigNumber, BigNumber, BigNumber, boolean":function(e,t,r,n){return c(n?d(e,t,r):m(e,t,r))}});function c(e){return"Matrix"===r.matrix?n?n(e):noMatrix():e}function l(e,t){var n=function(e){var t=e.split(":"),r=t.map((function(e){return Number(e)}));if(r.some((function(e){return isNaN(e)})))return null;switch(r.length){case 2:return{start:r[0],end:r[1],step:1};case 3:return{start:r[0],end:r[2],step:r[1]};default:return null}}(e);if(!n)throw new SyntaxError('String "'+e+'" is no valid range');return"BigNumber"===r.number?(void 0===i&&noBignumber(),c((t?d:m)(i(n.start),i(n.end),i(n.step)))):c((t?p:f)(n.start,n.end,n.step))}function f(e,t,r){var n=[],i=e;if(r>0)for(;a(i,t);)n.push(i),i+=r;else if(r<0)for(;s(i,t);)n.push(i),i+=r;return n}function p(e,t,r){var n=[],i=e;if(r>0)for(;o(i,t);)n.push(i),i+=r;else if(r<0)for(;u(i,t);)n.push(i),i+=r;return n}function m(e,t,r){var n=i(0),o=[],u=e;if(r.gt(n))for(;a(u,t);)o.push(u),u=u.plus(r);else if(r.lt(n))for(;s(u,t);)o.push(u),u=u.plus(r);return o}function d(e,t,r){var n=i(0),a=[],s=e;if(r.gt(n))for(;o(s,t);)a.push(s),s=s.plus(r);else if(r.lt(n))for(;u(s,t);)a.push(s),s=s.plus(r);return a}})),name$37="reshape",dependencies$37=["typed","isInteger","matrix"],createReshape=factory(name$37,dependencies$37,(e=>{var{typed:t,isInteger:r}=e;return t(name$37,{"Matrix, Array":function(e,t){return e.reshape(t)},"Array, Array":function(e,t){return t.forEach((function(e){if(!r(e))throw new TypeError("Invalid size for dimension: "+e)})),reshape$1(e,t)}})}));function ArgumentsError(e,t,r,n){if(!(this instanceof ArgumentsError))throw new SyntaxError("Constructor must be called with the new operator");this.fn=e,this.count=t,this.min=r,this.max=n,this.message="Wrong number of arguments in function "+e+" ("+t+" provided, "+r+(null!=n?"-"+n:"")+" expected)",this.stack=(new Error).stack}ArgumentsError.prototype=new Error,ArgumentsError.prototype.constructor=Error,ArgumentsError.prototype.name="ArgumentsError",ArgumentsError.prototype.isArgumentsError=!0;var name$36="resize",dependencies$36=["config","matrix"],createResize=factory(name$36,dependencies$36,(e=>{var{config:t,matrix:r}=e;return function(e,n,i){if(2!==arguments.length&&3!==arguments.length)throw new ArgumentsError("resize",arguments.length,2,3);if(isMatrix(n)&&(n=n.valueOf()),isBigNumber(n[0])&&(n=n.map((function(e){return isBigNumber(e)?e.toNumber():e}))),isMatrix(e))return e.resize(n,i,!0);if("string"==typeof e)return function(e,t,r){if(void 0!==r){if("string"!=typeof r||1!==r.length)throw new TypeError("Single character expected as defaultValue")}else r=" ";if(1!==t.length)throw new DimensionError(t.length,1);var n=t[0];if("number"!=typeof n||!isInteger$1(n))throw new TypeError("Invalid size, must contain positive integers (size: "+format$1(t)+")");if(e.length>n)return e.substring(0,n);if(e.length{var{typed:t,multiply:r,rotationMatrix:n}=e;return t(name$35,{"Array , number | BigNumber | Complex | Unit":function(e,t){return i(e,2),r(n(t),e).toArray()},"Matrix , number | BigNumber | Complex | Unit":function(e,t){return i(e,2),r(n(t),e)},"Array, number | BigNumber | Complex | Unit, Array | Matrix":function(e,t,a){return i(e,3),r(n(t,a),e)},"Matrix, number | BigNumber | Complex | Unit, Array | Matrix":function(e,t,a){return i(e,3),r(n(t,a),e)}});function i(e,t){var r=Array.isArray(e)?arraySize(e):e.size();if(r.length>2)throw new RangeError("Vector must be of dimensions 1x".concat(t));if(2===r.length&&1!==r[1])throw new RangeError("Vector must be of dimensions 1x".concat(t));if(r[0]!==t)throw new RangeError("Vector must be of dimensions 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Matrix A ("+u+") must match Matrix B ("+m+")");if(!a||!l)throw new Error("Cannot perform operation on Pattern Sparse Matrices");var h,y=u[0],g=u[1],v=r,x=0,b=i;"string"==typeof c&&c===d&&(h=c,v=t.find(r,[h,h]),x=t.convert(0,h),b=t.find(i,[h,h]));for(var _,w,N,$,A=[],M=[],S=[],E=[],T=[],O=0;O{var{typed:t,matrix:r,equalScalar:n,zeros:i,DenseMatrix:a}=e,o=createAlgorithm01({typed:t}),s=createAlgorithm02({typed:t,equalScalar:n}),u=createAlgorithm08({typed:t,equalScalar:n}),c=createAlgorithm10({typed:t,DenseMatrix:a}),l=createAlgorithm11({typed:t,equalScalar:n}),f=createAlgorithm13({typed:t}),p=createAlgorithm14({typed:t});return t(name$2y,{"number, number":leftShiftNumber,"BigNumber, BigNumber":leftShiftBigNumber,"SparseMatrix, SparseMatrix":function(e,t){return u(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return s(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return f(e,t,this)},"Array, 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name$2q="equalText",dependencies$2q=["typed","compareText","isZero"],createEqualText=factory(name$2q,dependencies$2q,(e=>{var{typed:t,compareText:r,isZero:n}=e;return t(name$2q,{"any, any":function(e,t){return n(r(e,t))}})})),name$2p="smaller",dependencies$2p=["typed","config","matrix","DenseMatrix"],createSmaller=factory(name$2p,dependencies$2p,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2p,{"boolean, boolean":function(e,t){return e{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2o,{"boolean, boolean":function(e,t){return e<=t},"number, number":function(e,t){return e<=t||nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.lte(t)||nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return 1!==e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2n="larger",dependencies$2n=["typed","config","matrix","DenseMatrix"],createLarger=factory(name$2n,dependencies$2n,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2n,{"boolean, boolean":function(e,t){return e>t},"number, number":function(e,t){return e>t&&!nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.gt(t)&&!nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return 1===e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return a(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return u(e,t,this)},"Array, Array":function(e,t){return this(n(e),n(t)).valueOf()},"Array, Matrix":function(e,t){return this(n(e),t)},"Matrix, Array":function(e,t){return this(e,n(t))},"SparseMatrix, any":function(e,t){return s(e,t,this,!1)},"DenseMatrix, any":function(e,t){return c(e,t,this,!1)},"any, SparseMatrix":function(e,t){return s(t,e,this,!0)},"any, DenseMatrix":function(e,t){return c(t,e,this,!0)},"Array, any":function(e,t){return c(n(e),t,this,!1).valueOf()},"any, Array":function(e,t){return c(n(t),e,this,!0).valueOf()}})})),name$2m="largerEq",dependencies$2m=["typed","config","matrix","DenseMatrix"],createLargerEq=factory(name$2m,dependencies$2m,(e=>{var{typed:t,config:r,matrix:n,DenseMatrix:i}=e,a=createAlgorithm03({typed:t}),o=createAlgorithm07({typed:t,DenseMatrix:i}),s=createAlgorithm12({typed:t,DenseMatrix:i}),u=createAlgorithm13({typed:t}),c=createAlgorithm14({typed:t});return t(name$2m,{"boolean, boolean":function(e,t){return e>=t},"number, number":function(e,t){return e>=t||nearlyEqual$1(e,t,r.epsilon)},"BigNumber, BigNumber":function(e,t){return e.gte(t)||nearlyEqual(e,t,r.epsilon)},"Fraction, Fraction":function(e,t){return-1!==e.compare(t)},"Complex, Complex":function(){throw new TypeError("No ordering relation is defined for complex numbers")},"Unit, Unit":function(e,t){if(!e.equalBase(t))throw new Error("Cannot compare units with different base");return this(e.value,t.value)},"SparseMatrix, SparseMatrix":function(e,t){return o(e,t,this)},"SparseMatrix, 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i=e.length;if(i!==t.length)return!1;for(var a=0;a{var{typed:t,config:r,equalScalar:n,matrix:i,DenseMatrix:a}=e,o=createAlgorithm03({typed:t}),s=createAlgorithm07({typed:t,DenseMatrix:a}),u=createAlgorithm12({typed:t,DenseMatrix:a}),c=createAlgorithm13({typed:t}),l=createAlgorithm14({typed:t});return t("unequal",{"any, any":function(e,t){return null===e?null!==t:null===t?null!==e:void 0===e?void 0!==t:void 0===t?void 0!==e:f(e,t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,f)},"SparseMatrix, DenseMatrix":function(e,t){return o(t,e,f,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,f,!1)},"DenseMatrix, DenseMatrix":function(e,t){return c(e,t,f)},"Array, Array":function(e,t){return this(i(e),i(t)).valueOf()},"Array, Matrix":function(e,t){return this(i(e),t)},"Matrix, Array":function(e,t){return this(e,i(t))},"SparseMatrix, any":function(e,t){return u(e,t,f,!1)},"DenseMatrix, any":function(e,t){return l(e,t,f,!1)},"any, SparseMatrix":function(e,t){return u(t,e,f,!0)},"any, DenseMatrix":function(e,t){return l(t,e,f,!0)},"Array, any":function(e,t){return l(i(e),t,f,!1).valueOf()},"any, Array":function(e,t){return l(i(t),e,f,!0).valueOf()}});function f(e,t){return!n(e,t)}}));factory(name$2k,["typed","equalScalar"],(e=>{var{typed:t,equalScalar:r}=e;return t(name$2k,{"any, any":function(e,t){return null===e?null!==t:null===t?null!==e:void 0===e?void 0!==t:void 0===t?void 0!==e:!r(e,t)}})}));var name$2j="partitionSelect",dependencies$2j=["typed","isNumeric","isNaN","compare"],createPartitionSelect=factory(name$2j,dependencies$2j,(e=>{var{typed:t,isNumeric:r,isNaN:n,compare:i}=e,a=i,o=(e,t)=>-i(e,t);return t(name$2j,{"Array | Matrix, number":function(e,t){return s(e,t,a)},"Array | Matrix, number, string":function(e,t,r){if("asc"===r)return s(e,t,a);if("desc"===r)return s(e,t,o);throw new Error('Compare string must be "asc" or "desc"')},"Array | Matrix, number, function":s});function s(e,t,r){if(!isInteger$1(t)||t<0)throw new Error("k must be a non-negative integer");if(isMatrix(e)){if(e.size().length>1)throw new Error("Only one dimensional matrices supported");return u(e.valueOf(),t,r)}if(Array.isArray(e))return u(e,t,r)}function u(e,t,i){if(t>=e.length)throw new Error("k out of bounds");for(var a=0;a=0){var f=e[c];e[c]=e[u],e[u]=f,--c}else++u;i(e[u],l)>0&&--u,t<=u?s=u:o=u+1}return e[t]}})),name$2i="sort",dependencies$2i=["typed","matrix","compare","compareNatural"],createSort=factory(name$2i,dependencies$2i,(e=>{var{typed:t,matrix:r,compare:n,compareNatural:i}=e,a=n,o=(e,t)=>-n(e,t);return t(name$2i,{Array:function(e){return u(e),e.sort(a)},Matrix:function(e){return c(e),r(e.toArray().sort(a),e.storage())},"Array, function":function(e,t){return u(e),e.sort(t)},"Matrix, function":function(e,t){return c(e),r(e.toArray().sort(t),e.storage())},"Array, string":function(e,t){return u(e),e.sort(s(t))},"Matrix, string":function(e,t){return c(e),r(e.toArray().sort(s(t)),e.storage())}});function s(e){if("asc"===e)return a;if("desc"===e)return o;if("natural"===e)return i;throw new Error('String "asc", "desc", or "natural" expected')}function u(e){if(1!==arraySize(e).length)throw new Error("One dimensional array expected")}function c(e){if(1!==e.size().length)throw new Error("One dimensional matrix expected")}})),name$2h="max",dependencies$2h=["typed","config","numeric","larger"],createMax=factory(name$2h,dependencies$2h,(e=>{var{typed:t,config:r,numeric:n,larger:i}=e;return t(name$2h,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return reduce$2(e,t.valueOf(),a)},"...":function(e){if(containsCollections(e))throw new TypeError("Scalar values expected in function max");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw improveErrorMessage(e,"max",t)}}function o(e){var t;if(deepForEach(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw improveErrorMessage(t,"max",e)}})),void 0===t)throw new Error("Cannot calculate max of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),name$2g="min",dependencies$2g=["typed","config","numeric","smaller"],createMin=factory(name$2g,dependencies$2g,(e=>{var{typed:t,config:r,numeric:n,smaller:i}=e;return t(name$2g,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){return reduce$2(e,t.valueOf(),a)},"...":function(e){if(containsCollections(e))throw new TypeError("Scalar values expected in function min");return o(e)}});function a(e,t){try{return i(e,t)?e:t}catch(e){throw improveErrorMessage(e,"min",t)}}function o(e){var t;if(deepForEach(e,(function(e){try{isNaN(e)&&"number"==typeof e?t=NaN:(void 0===t||i(e,t))&&(t=e)}catch(t){throw improveErrorMessage(t,"min",e)}})),void 0===t)throw new Error("Cannot calculate min of an empty array");return"string"==typeof t&&(t=n(t,r.number)),t}})),name$2f="ImmutableDenseMatrix",dependencies$2f=["smaller","DenseMatrix"],createImmutableDenseMatrixClass=factory(name$2f,dependencies$2f,(e=>{var{smaller:t,DenseMatrix:r}=e;function n(e,t){if(!(this instanceof n))throw new SyntaxError("Constructor must be called with the new operator");if(t&&!isString$1(t))throw new Error("Invalid datatype: "+t);if(isMatrix(e)||isArray$1(e)){var i=new r(e,t);this._data=i._data,this._size=i._size,this._datatype=i._datatype,this._min=null,this._max=null}else if(e&&isArray$1(e.data)&&isArray$1(e.size))this._data=e.data,this._size=e.size,this._datatype=e.datatype,this._min=void 0!==e.min?e.min:null,this._max=void 0!==e.max?e.max:null;else{if(e)throw new TypeError("Unsupported type of data ("+typeOf$1(e)+")");this._data=[],this._size=[0],this._datatype=t,this._min=null,this._max=null}}return n.prototype=new r,n.prototype.type="ImmutableDenseMatrix",n.prototype.isImmutableDenseMatrix=!0,n.prototype.subset=function(e){switch(arguments.length){case 1:var t=r.prototype.subset.call(this,e);return isMatrix(t)?new n({data:t._data,size:t._size,datatype:t._datatype}):t;case 2:case 3:throw new Error("Cannot invoke set subset on an Immutable Matrix instance");default:throw new SyntaxError("Wrong number of arguments")}},n.prototype.set=function(){throw new Error("Cannot invoke set on an Immutable Matrix instance")},n.prototype.resize=function(){throw new Error("Cannot invoke resize on an Immutable Matrix instance")},n.prototype.reshape=function(){throw new Error("Cannot invoke reshape on an Immutable Matrix instance")},n.prototype.clone=function(){return new n({data:clone$3(this._data),size:clone$3(this._size),datatype:this._datatype})},n.prototype.toJSON=function(){return{mathjs:"ImmutableDenseMatrix",data:this._data,size:this._size,datatype:this._datatype}},n.fromJSON=function(e){return new n(e)},n.prototype.swapRows=function(){throw new Error("Cannot invoke swapRows on an Immutable Matrix instance")},n.prototype.min=function(){if(null===this._min){var e=null;this.forEach((function(r){(null===e||t(r,e))&&(e=r)})),this._min=null!==e?e:void 0}return this._min},n.prototype.max=function(){if(null===this._max){var e=null;this.forEach((function(r){(null===e||t(e,r))&&(e=r)})),this._max=null!==e?e:void 0}return this._max},n}),{isClass:!0}),name$2e="Index",dependencies$2e=["ImmutableDenseMatrix"],createIndexClass=factory(name$2e,dependencies$2e,(e=>{var{ImmutableDenseMatrix:t}=e;function r(e){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");this._dimensions=[],this._isScalar=!0;for(var t=0,i=arguments.length;t{var{smaller:t,larger:r}=e,n=1/Math.log((1+Math.sqrt(5))/2);function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._minimum=null,this._size=0}function a(e,t,r){t.left.right=t.right,t.right.left=t.left,r.degree--,r.child===t&&(r.child=t.right),0===r.degree&&(r.child=null),t.left=e,t.right=e.right,e.right=t,t.right.left=t,t.parent=null,t.mark=!1}function o(e,t){var r=t.parent;r&&(t.mark?(a(e,t,r),o(r)):t.mark=!0)}i.prototype.type="FibonacciHeap",i.prototype.isFibonacciHeap=!0,i.prototype.insert=function(e,r){var n={key:e,value:r,degree:0};if(this._minimum){var i=this._minimum;n.left=i,n.right=i.right,i.right=n,n.right.left=n,t(e,i.key)&&(this._minimum=n)}else n.left=n,n.right=n,this._minimum=n;return this._size++,n},i.prototype.size=function(){return this._size},i.prototype.clear=function(){this._minimum=null,this._size=0},i.prototype.isEmpty=function(){return 0===this._size},i.prototype.extractMinimum=function(){var e=this._minimum;if(null===e)return e;for(var i=this._minimum,a=e.degree,o=e.child;a>0;){var u=o.right;o.left.right=o.right,o.right.left=o.left,o.left=i,o.right=i.right,i.right=o,o.right.left=o,o.parent=null,o=u,a--}return e.left.right=e.right,e.right.left=e.left,i=e===e.right?null:function(e,i){var a,o=Math.floor(Math.log(i)*n)+1,u=new Array(o),c=0,l=e;if(l)for(c++,l=l.right;l!==e;)c++,l=l.right;for(;c>0;){for(var f=l.degree,p=l.right;a=u[f];){if(r(l.key,a.key)){var m=a;a=l,l=m}s(a,l),u[f]=null,f++}u[f]=l,l=p,c--}e=null;for(var d=0;d{var{addScalar:t,equalScalar:r,FibonacciHeap:n}=e;function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._values=[],this._heap=new n}return i.prototype.type="Spa",i.prototype.isSpa=!0,i.prototype.set=function(e,t){if(this._values[e])this._values[e].value=t;else{var r=this._heap.insert(e,t);this._values[e]=r}},i.prototype.get=function(e){var t=this._values[e];return t?t.value:0},i.prototype.accumulate=function(e,r){var n=this._values[e];n?n.value=t(n.value,r):(n=this._heap.insert(e,r),this._values[e]=n)},i.prototype.forEach=function(e,t,n){var 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e.equalBase(I.NONE)&&null!==e.value&&!a.predictable?e.value:e}w.isValuelessUnit=function(e){return null!==O(e)},w.prototype.hasBase=function(e){if("string"==typeof e&&(e=I[e]),!e)return!1;for(var t=0;t1e-12)return!1;return!0},w.prototype.equalBase=function(e){for(var t=0;t1e-12)return!1;return!0},w.prototype.equals=function(e){return this.equalBase(e)&&d(this.value,e.value)},w.prototype.multiply=function(e){for(var t=this.clone(),r=0;r1e-12&&(hasOwnProperty$2(F,s)?n.push({unit:F[s].unit,prefix:F[s].prefix,power:r.dimensions[o]||0}):a=!0)}n.length1e-12){if(!hasOwnProperty$2(L.si,n))throw new Error("Cannot express custom unit "+n+" in SI units");t.push({unit:L.si[n].unit,prefix:L.si[n].prefix,power:e.dimensions[r]||0})}}return e.units=t,e.fixPrefix=!0,e.skipAutomaticSimplification=!0,e},w.prototype.formatUnits=function(){for(var e="",t="",r=0,n=0,i=0;i0?(r++,e+=" 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0!==t.value&&null!==t.value&&isComplex(t.value)&&(r=Math.abs(t.value.re)<1e-14),t.units)hasOwnProperty$2(t.units,n)&&t.units[n].unit&&("VA"===t.units[n].unit.name&&r?t.units[n].unit=R.VAR:"VAR"!==t.units[n].unit.name||r||(t.units[n].unit=R.VA));1!==t.units.length||t.fixPrefix||Math.abs(t.units[0].power-Math.round(t.units[0].power))<1e-14&&(t.units[0].prefix=t._bestPrefix());var i=t._denormalize(t.value),a=null!==t.value?y(i,e||{}):"",o=t.formatUnits();return t.value&&isComplex(t.value)&&(a="("+a+")"),o.length>0&&a.length>0&&(a+=" "),a+=o},w.prototype._bestPrefix=function(){if(1!==this.units.length)throw new Error("Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!");if(Math.abs(this.units[0].power-Math.round(this.units[0].power))>=1e-14)throw new Error("Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!");var e=null!==this.value?f(this.value):0,t=f(this.units[0].unit.value),r=this.units[0].prefix;if(0===e)return r;var n=this.units[0].power,i=Math.log(e/Math.pow(r.value*t,n))/Math.LN10-1.2;if(i>-2.200001&&i<1.800001)return r;i=Math.abs(i);var a=this.units[0].unit.prefixes;for(var o in a)if(hasOwnProperty$2(a,o)){var s=a[o];if(s.scientific){var 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this.properties)hasOwnProperty$2(this.properties,t)&&(e[t]=this.properties[t]);return new r(e)},r.prototype._toString=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push(stringify(r)+": "+this.properties[r].toString(e));return"{"+t.join(", ")+"}"},r.prototype.toJSON=function(){return{mathjs:"ObjectNode",properties:this.properties}},r.fromJSON=function(e){return new r(e.properties)},r.prototype.toHTML=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push(''+escape$1(r)+':'+this.properties[r].toHTML(e));return'{'+t.join(',')+'}'},r.prototype._toTex=function(e){var t=[];for(var r in this.properties)hasOwnProperty$2(this.properties,r)&&t.push("\\mathbf{"+r+":} & 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n.map((function(e){switch(e.getContent().type){case"ArrayNode":case"ConstantNode":case"SymbolNode":case"ParenthesisNode":return!1;default:return!0}}));switch(n.length){case 0:a=[];break;case 1:var u=getPrecedence(n[0],t);if(i&&null!==u){var c,l;if("keep"===t?(c=n[0].getIdentifier(),l=e.getIdentifier()):(c=n[0].getContent().getIdentifier(),l=e.getContent().getIdentifier()),!1===properties[o][l].latexLeftParens){a=[!1];break}if(!1===properties[u][c].latexParens){a=[!1];break}}if(null===u){a=[!1];break}if(u<=o){a=[!0];break}a=[!1];break;case 2:var f,p,m=getPrecedence(n[0],t),d=isAssociativeWith(e,n[0],t);f=null!==m&&(m===o&&"right"===s&&!d||m=2&&"OperatorNode:multiply"===e.getIdentifier()&&e.implicit&&"auto"===t&&"hide"===r&&(a=n.map((function(e,t){var r="ParenthesisNode"===e.getIdentifier();return!(!a[t]&&!r)}))),a}return r.prototype=new t,r.prototype.type="OperatorNode",r.prototype.isOperatorNode=!0,r.prototype._compile=function(e,t){if("string"!=typeof this.fn||!isSafeMethod(e,this.fn))throw e[this.fn]?new Error('No access to function "'+this.fn+'"'):new Error("Function "+this.fn+' missing in provided namespace "math"');var r=getSafeProperty(e,this.fn),n=map$2(this.args,(function(r){return r._compile(e,t)}));if(1===n.length){var i=n[0];return function(e,t,n){return r(i(e,t,n))}}if(2===n.length){var a=n[0],o=n[1];return function(e,t,n){return r(a(e,t,n),o(e,t,n))}}return function(e,t,i){return r.apply(null,map$2(n,(function(r){return r(e,t,i)})))}},r.prototype.forEach=function(e){for(var t=0;t2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())){var f=i.map((function(t,r){return t=t.toString(e),a[r]&&(t="("+t+")"),t}));return this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?f.join(" "):f.join(" "+this.op+" ")}return this.fn+"("+this.args.join(", 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i.length>2&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())?this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===r?l.join(''):l.join(''+escape$1(this.op)+""):''+escape$1(this.fn)+'('+l.join(',')+')'},r.prototype._toTex=function(e){var t=e&&e.parenthesis?e.parenthesis:"keep",r=e&&e.implicit?e.implicit:"hide",i=this.args,a=n(this,t,r,i,!0),o=latexOperators[this.fn];if(o=void 0===o?this.op:o,1===i.length){var s=getAssociativity(this,t),u=i[0].toTex(e);return a[0]&&(u="\\left(".concat(u,"\\right)")),"right"===s?o+u:u+o}if(2===i.length){var c=i[0],l=c.toTex(e);a[0]&&(l="\\left(".concat(l,"\\right)"));var f,p=i[1].toTex(e);switch(a[1]&&(p="\\left(".concat(p,"\\right)")),f="keep"===t?c.getIdentifier():c.getContent().getIdentifier(),this.getIdentifier()){case"OperatorNode:divide":return 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If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]},log10Docs={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]},log1pDocs={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]},log2Docs={name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]},modDocs={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]},multiplyDocs={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]},normDocs={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']},nthRootDocs={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]},nthRootsDocs={name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]},powDocs={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)","math.pow([[1, 2], [4, 3]], 2)","math.pow([[1, 2], [4, 3]], -1)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]},roundDocs={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)"],seealso:["ceil","floor","fix"]},signDocs={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]},sqrtDocs={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]},sqrtmDocs={name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[1, 2], [3, 4]])"],seealso:["sqrt","abs","square","multiply"]},squareDocs={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]},subtractDocs={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]},unaryMinusDocs={name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]},unaryPlusDocs={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]},xgcdDocs={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]},bitAndDocs={name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitNotDocs={name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitOrDocs={name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]},bitXorDocs={name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]},leftShiftDocs={name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]},rightArithShiftDocs={name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]},rightLogShiftDocs={name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]},bellNumbersDocs={name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]},catalanDocs={name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]},compositionDocs={name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]},stirlingS2Docs={name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]},argDocs={name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]},conjDocs={name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]},imDocs={name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]},reDocs={name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]},evaluateDocs={name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(" + 4 + ")")'],seealso:[]},helpDocs={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]},distanceDocs={name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]},intersectDocs={name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])"],seealso:[]},andDocs={name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]},notDocs={name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]},orDocs={name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]},xorDocs={name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]},columnDocs={name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row","matrixFromColumns"]},concatDocs={name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},countDocs={name:"count",category:"Matrix",syntax:["count(x)"],description:"Count the number of elements of a matrix, array or string.",examples:["a = [1, 2; 3, 4; 5, 6]","count(a)","size(a)",'count("hello world")'],seealso:["size"]},crossDocs={name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0], [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4], [5, 6, 7])"],seealso:["multiply","dot"]},ctransposeDocs={name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},detDocs={name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diagDocs={name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diffDocs={name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["diff([1, 2, 4, 7, 0])","diff([1, 2, 4, 7, 0], 0)","diff(matrix([1, 2, 4, 7, 0]))","diff([[1, 2], [3, 4]])","diff([[1, 2], [3, 4]], 0)","diff([[1, 2], [3, 4]], 1)","diff([[1, 2], [3, 4]], bignumber(1))","diff(matrix([[1, 2], [3, 4]]), 1)","diff([[1, 2], matrix([3, 4])], 1)"],seealso:["subtract","partitionSelect"]},dotDocs={name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]},eigsDocs={name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and eigenvectors of a real symmetric matrix",examples:["eigs([[5, 2.3], [2.3, 1]])"],seealso:["inv"]},filterDocs={name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]},flattenDocs={name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]},forEachDocs={name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["numberOfPets = {}","addPet(n) = numberOfPets[n] = (numberOfPets[n] ? numberOfPets[n]:0 ) + 1;",'forEach(["Dog","Cat","Cat"], addPet)',"numberOfPets"],seealso:["map","sort","filter"]},getMatrixDataTypeDocs={name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeOf"]},identityDocs={name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},invDocs={name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]},pinvDocs={name:"pinv",category:"Matrix",syntax:["pinv(x)"],description:"Calculate the Moore–Penrose inverse of a matrix",examples:["pinv([1, 2; 3, 4])","pinv([[1, 0], [0, 1], [0, 1]])","pinv(4)"],seealso:["inv"]},kronDocs={name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]},mapDocs={name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]},matrixFromColumnsDocs={name:"matrixFromColumns",category:"Matrix",syntax:["math.matrixFromColumns(...arr)","math.matrixFromColumns(row1, row2)","math.matrixFromColumns(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual columns.",examples:["matrixFromColumns([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromRows","matrixFromFunction","zeros"]},matrixFromFunctionDocs={name:"matrixFromFunction",category:"Matrix",syntax:["math.matrixFromFunction(size, fn)","math.matrixFromFunction(size, fn, format)","math.matrixFromFunction(size, fn, format, datatype)","math.matrixFromFunction(size, format, fn)","math.matrixFromFunction(size, format, datatype, fn)"],description:"Create a matrix by evaluating a generating function at each index.",examples:["f(I) = I[1] - I[2]","matrixFromFunction([3,3], f)","g(I) = I[1] - I[2] == 1 ? 4 : 0",'matrixFromFunction([100, 100], "sparse", g)',"matrixFromFunction([5], random)"],seealso:["matrix","matrixFromRows","matrixFromColumns","zeros"]},matrixFromRowsDocs={name:"matrixFromRows",category:"Matrix",syntax:["math.matrixFromRows(...arr)","math.matrixFromRows(row1, row2)","math.matrixFromRows(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual rows.",examples:["matrixFromRows([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromColumns","matrixFromFunction","zeros"]},onesDocs={name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]},partitionSelectDocs={name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1)'],seealso:["sort"]},rangeDocs={name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]},reshapeDocs={name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])"],seealso:["size","squeeze","resize"]},resizeDocs={name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]},rotateDocs={name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], math.pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]},rotationMatrixDocs={name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]},rowDocs={name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column","matrixFromRows"]},sizeDocs={name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","count","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]},sortDocs={name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"])',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]},squeezeDocs={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]},subsetDocs={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of the entries of a matrix or characters of a string. Indexes are one-based. There should be one index specification for each dimension of the target. Each specification can be a single index, a list of indices, or a range in colon notation `l:u`. In a range, both the lower bound l and upper bound u are included; and if a bound is omitted it defaults to the most extreme valid value. The cartesian product of the indices specified in each dimension determines the target of the operation.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]","f[[1,2], [1,3]] = [9, 10; 11, 12]","f"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]},traceDocs={name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]},transposeDocs={name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},zerosDocs={name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]},fftDocs={name:"fft",category:"Matrix",syntax:["fft(x)"],description:"Calculate N-dimensional fourier transform",examples:["fft([[1, 0], [1, 0]])"],seealso:["ifft"]},ifftDocs={name:"ifft",category:"Matrix",syntax:["ifft(x)"],description:"Calculate N-dimensional inverse fourier transform",examples:["ifft([[2, 2], [0, 0]])"],seealso:["fft"]},combinationsDocs={name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]},combinationsWithRepDocs={name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]},factorialDocs={name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]},gammaDocs={name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]},lgammaDocs={name:"lgamma",category:"Probability",syntax:["lgamma(n)"],description:"Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers.",examples:["lgamma(4)","lgamma(1/2)","lgamma(math.i)","lgamma(complex(1.1, 2))"],seealso:["gamma"]},kldivergenceDocs={name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]},multinomialDocs={name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]},permutationsDocs={name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]},pickRandomDocs={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]},randomDocs={name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]},randomIntDocs={name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]},compareDocs={name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]},compareNaturalDocs={name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]},compareTextDocs={name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]},deepEqualDocs={name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]},equalDocs={name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]},equalTextDocs={name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]},largerDocs={name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]},largerEqDocs={name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]},smallerDocs={name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]},smallerEqDocs={name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]},unequalDocs={name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]},setCartesianDocs={name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]},setDifferenceDocs={name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]},setDistinctDocs={name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]},setIntersectDocs={name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]},setIsSubsetDocs={name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]},setMultiplicityDocs={name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]},setPowersetDocs={name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]},setSizeDocs={name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]},setSymDifferenceDocs={name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]},setUnionDocs={name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]},erfDocs={name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]},madDocs={name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]},maxDocs={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]},meanDocs={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]},medianDocs={name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]},minDocs={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]},modeDocs={name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]},prodDocs={name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]},quantileSeqDocs={name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.",examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","variance"]},stdDocs={name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","prod","sum","variance"]},cumSumDocs={name:"cumsum",category:"Statistics",syntax:["cumsum(a, b, c, ...)","cumsum(A)"],description:"Compute the cumulative sum of all values.",examples:["cumsum(2, 3, 4, 1)","cumsum([2, 3, 4, 1])","cumsum([1, 2; 3, 4])","cumsum([1, 2; 3, 4], 1)","cumsum([1, 2; 3, 4], 2)"],seealso:["max","mean","median","min","prod","std","sum","variance"]},sumDocs={name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","variance"]},varianceDocs={name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, normalization)"],description:'Compute the variance of all values. 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u(e(h.object,y),e(h.index,y));if(isIndexNode(h))return new p(h.dimensions.map((t=>e(t,y))));if(isObjectNode(h)){var O={};for(var C in h.properties)O[C]=e(h.properties[C],y);return new m(O)}}return h}})),name$n="resolve",dependencies$n=["parse","ConstantNode","FunctionNode","OperatorNode","ParenthesisNode"],createResolve=factory(name$n,dependencies$n,(e=>{var{parse:t,ConstantNode:r,FunctionNode:n,OperatorNode:i,ParenthesisNode:a}=e;return function e(o,s){var u=arguments.length>2&&void 0!==arguments[2]?arguments[2]:new Set;if(!s)return o;if(isMap$1(s)||(s=createMap$1(s)),isSymbolNode(o)){if(u.has(o.name)){var c=Array.from(u).join(", ");throw new ReferenceError("recursive loop of variable definitions among {".concat(c,"}"))}var l=s.get(o.name);if(isNode(l)){var f=new Set(u);return f.add(o.name),e(l,s,f)}return"number"==typeof l?t(String(l)):void 0!==l?new r(l):o}if(isOperatorNode(o)){var p=o.args.map((function(t){return e(t,s,u)}));return new 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m})),name$k="rationalize",dependencies$k=["config","typed","equal","isZero","add","subtract","multiply","divide","pow","parse","simplifyCore","simplify","?bignumber","?fraction","mathWithTransform","matrix","AccessorNode","ArrayNode","ConstantNode","FunctionNode","IndexNode","ObjectNode","OperatorNode","SymbolNode","ParenthesisNode"],createRationalize=factory(name$k,dependencies$k,(e=>{var{config:t,typed:r,equal:n,isZero:i,add:a,subtract:o,multiply:s,divide:u,pow:c,parse:l,simplifyCore:f,simplify:p,fraction:m,bignumber:d,mathWithTransform:h,matrix:y,AccessorNode:g,ArrayNode:v,ConstantNode:x,FunctionNode:b,IndexNode:_,ObjectNode:w,OperatorNode:N,SymbolNode:$,ParenthesisNode:A}=e,M=createSimplifyConstant({typed:r,config:t,mathWithTransform:h,matrix:y,fraction:m,bignumber:d,AccessorNode:g,ArrayNode:v,ConstantNode:x,FunctionNode:b,IndexNode:_,ObjectNode:w,OperatorNode:N,SymbolNode:$});return r(name$k,{string:function(e){return this(l(e),{},!1)},"string, boolean":function(e,t){return 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i.firstRules=e.concat(t,n),i.distrDivRules=r,i.sucDivRules=n,i.firstRulesAgain=e.concat(t),i.finalRules=[f,{l:"n*-n",r:"-n^2"},{l:"n*n",r:"n^2"},M,{l:"n*-n^n1",r:"-n^(n1+1)"},{l:"n*n^n1",r:"n^(n1+1)"},{l:"n^n1*-n^n2",r:"-n^(n1+n2)"},{l:"n^n1*n^n2",r:"n^(n1+n2)"},{l:"n^n1*-n",r:"-n^(n1+1)"},{l:"n^n1*n",r:"n^(n1+1)"},{l:"n^n1/-n",r:"-n^(n1-1)"},{l:"n^n1/n",r:"n^(n1-1)"},{l:"n/-n^n1",r:"-n^(1-n1)"},{l:"n/n^n1",r:"n^(1-n1)"},{l:"n^n1/-n^n2",r:"n^(n1-n2)"},{l:"n^n1/n^n2",r:"n^(n1-n2)"},{l:"n1+(-n2*n3)",r:"n1-n2*n3"},{l:"v*(-c)",r:"-c*v"},{l:"n1+-n2",r:"n1-n2"},{l:"v*c",r:"c*v"},{l:"(n1^n2)^n3",r:"(n1^(n2*n3))"}],i}(),i=function(e,t,r,n){var i=[],a=p(e,n,t,{exactFractions:!1}),o="+-*"+((r=!!r)?"/":"");u(a);var s={};return s.expression=a,s.variables=i,s;function u(e){var t=e.type;if("FunctionNode"===t)throw new Error("There is an unsolved function call");if("OperatorNode"===t)if("^"===e.op){if("ConstantNode"!==e.args[1].type||!isInteger$1(parseFloat(e.args[1].value)))throw new Error("There is 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N("^","pow",[e.args[0].cloneDeep(),new x(a-1)]);e=new N("*","multiply",[s,u])}else e=new N("*","multiply",[e.args[0],e.args[0].cloneDeep()]);i&&("content"===r?t.content=e:t.args[r]=e)}}if("ParenthesisNode"===n)S(e.content,e,"content");else if("ConstantNode"!==n&&"SymbolNode"!==n)for(var c=0;cn&&(t[c]=0),t[c]+=o.cte*("+"===o.oper?1:-1),void(n=Math.max(c,n))}o.cte=c,""===o.fire&&(t[0]+=o.cte*("+"===o.oper?1:-1))}}(e,null,r);for(var a,o=!0,s=n=t.length-1;s>=0;s--)if(0!==t[s]){var u=new x(o?t[s]:Math.abs(t[s])),c=t[s]<0?"-":"+";if(s>0){var l=new $(i);if(s>1){var f=new x(s);l=new N("^","pow",[l,f])}u=-1===t[s]&&o?new N("-","unaryMinus",[l]):1===Math.abs(t[s])?l:new N("*","multiply",[u,l])}a=o?u:"+"===c?new N("+","add",[a,u]):new N("-","subtract",[a,u]),o=!1}return o?new x(0):a}})),name$j="reviver",dependencies$j=["classes"],createReviver=factory(name$j,dependencies$j,(e=>{var{classes:t}=e;return function(e,r){var n=t[r&&r.mathjs];return n&&"function"==typeof n.fromJSON?n.fromJSON(r):r}})),name$i="replacer",dependencies$i=[],createReplacer=factory(name$i,dependencies$i,(()=>function(e,t){return"number"!=typeof t||isFinite(t)&&!isNaN(t)?t:{mathjs:"number",value:String(t)}})),version$2="10.6.4",createTrue=factory("true",[],(()=>!0)),createFalse=factory("false",[],(()=>!1)),createNull=factory("null",[],(()=>null)),createInfinity=recreateFactory("Infinity",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1/0):1/0})),createNaN=recreateFactory("NaN",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(NaN):NaN})),createPi=recreateFactory("pi",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberPi(r):pi$1})),createTau=recreateFactory("tau",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberTau(r):tau$1})),createE=recreateFactory("e",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberE(r):e$1})),createPhi=recreateFactory("phi",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?createBigNumberPhi(r):phi$1})),createLN2=recreateFactory("LN2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(2).ln():Math.LN2})),createLN10=recreateFactory("LN10",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(10).ln():Math.LN10})),createLOG2E=recreateFactory("LOG2E",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1).div(new r(2).ln()):Math.LOG2E})),createLOG10E=recreateFactory("LOG10E",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(1).div(new r(10).ln()):Math.LOG10E})),createSQRT1_2=recreateFactory("SQRT1_2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r("0.5").sqrt():Math.SQRT1_2})),createSQRT2=recreateFactory("SQRT2",["config","?BigNumber"],(e=>{var{config:t,BigNumber:r}=e;return"BigNumber"===t.number?new r(2).sqrt():Math.SQRT2})),createI=recreateFactory("i",["Complex"],(e=>{var{Complex:t}=e;return t.I})),createUppercasePi=factory("PI",["pi"],(e=>{var{pi:t}=e;return t})),createUppercaseE=factory("E",["e"],(e=>{var{e:t}=e;return t})),createVersion=factory("version",[],(()=>version$2));function recreateFactory(e,t,r){return factory(e,t,r,{recreateOnConfigChange:!0})}var createSpeedOfLight=unitFactory("speedOfLight","299792458","m s^-1"),createGravitationConstant=unitFactory("gravitationConstant","6.67430e-11","m^3 kg^-1 s^-2"),createPlanckConstant=unitFactory("planckConstant","6.62607015e-34","J s"),createReducedPlanckConstant=unitFactory("reducedPlanckConstant","1.0545718176461565e-34","J s"),createMagneticConstant=unitFactory("magneticConstant","1.25663706212e-6","N A^-2"),createElectricConstant=unitFactory("electricConstant","8.8541878128e-12","F m^-1"),createVacuumImpedance=unitFactory("vacuumImpedance","376.730313667","ohm"),createCoulomb=unitFactory("coulomb","8.987551792261171e9","N m^2 C^-2"),createElementaryCharge=unitFactory("elementaryCharge","1.602176634e-19","C"),createBohrMagneton=unitFactory("bohrMagneton","9.2740100783e-24","J T^-1"),createConductanceQuantum=unitFactory("conductanceQuantum","7.748091729863649e-5","S"),createInverseConductanceQuantum=unitFactory("inverseConductanceQuantum","12906.403729652257","ohm"),createMagneticFluxQuantum=unitFactory("magneticFluxQuantum","2.0678338484619295e-15","Wb"),createNuclearMagneton=unitFactory("nuclearMagneton","5.0507837461e-27","J T^-1"),createKlitzing=unitFactory("klitzing","25812.807459304513","ohm"),createBohrRadius=unitFactory("bohrRadius","5.29177210903e-11","m"),createClassicalElectronRadius=unitFactory("classicalElectronRadius","2.8179403262e-15","m"),createElectronMass=unitFactory("electronMass","9.1093837015e-31","kg"),createFermiCoupling=unitFactory("fermiCoupling","1.1663787e-5","GeV^-2"),createFineStructure=numberFactory("fineStructure",.0072973525693),createHartreeEnergy=unitFactory("hartreeEnergy","4.3597447222071e-18","J"),createProtonMass=unitFactory("protonMass","1.67262192369e-27","kg"),createDeuteronMass=unitFactory("deuteronMass","3.3435830926e-27","kg"),createNeutronMass=unitFactory("neutronMass","1.6749271613e-27","kg"),createQuantumOfCirculation=unitFactory("quantumOfCirculation","3.6369475516e-4","m^2 s^-1"),createRydberg=unitFactory("rydberg","10973731.568160","m^-1"),createThomsonCrossSection=unitFactory("thomsonCrossSection","6.6524587321e-29","m^2"),createWeakMixingAngle=numberFactory("weakMixingAngle",.2229),createEfimovFactor=numberFactory("efimovFactor",22.7),createAtomicMass=unitFactory("atomicMass","1.66053906660e-27","kg"),createAvogadro=unitFactory("avogadro","6.02214076e23","mol^-1"),createBoltzmann=unitFactory("boltzmann","1.380649e-23","J K^-1"),createFaraday=unitFactory("faraday","96485.33212331001","C mol^-1"),createFirstRadiation=unitFactory("firstRadiation","3.7417718521927573e-16","W m^2"),createLoschmidt=unitFactory("loschmidt","2.686780111798444e25","m^-3"),createGasConstant=unitFactory("gasConstant","8.31446261815324","J K^-1 mol^-1"),createMolarPlanckConstant=unitFactory("molarPlanckConstant","3.990312712893431e-10","J s mol^-1"),createMolarVolume=unitFactory("molarVolume","0.022413969545014137","m^3 mol^-1"),createSackurTetrode=numberFactory("sackurTetrode",-1.16487052358),createSecondRadiation=unitFactory("secondRadiation","0.014387768775039337","m K"),createStefanBoltzmann=unitFactory("stefanBoltzmann","5.67037441918443e-8","W m^-2 K^-4"),createWienDisplacement=unitFactory("wienDisplacement","2.897771955e-3","m K"),createMolarMass=unitFactory("molarMass","0.99999999965e-3","kg mol^-1"),createMolarMassC12=unitFactory("molarMassC12","11.9999999958e-3","kg mol^-1"),createGravity=unitFactory("gravity","9.80665","m s^-2"),createPlanckLength=unitFactory("planckLength","1.616255e-35","m"),createPlanckMass=unitFactory("planckMass","2.176435e-8","kg"),createPlanckTime=unitFactory("planckTime","5.391245e-44","s"),createPlanckCharge=unitFactory("planckCharge","1.87554603778e-18","C"),createPlanckTemperature=unitFactory("planckTemperature","1.416785e+32","K");function unitFactory(e,t,r){return factory(e,["config","Unit","BigNumber"],(e=>{var{config:n,Unit:i,BigNumber:a}=e,o=new i("BigNumber"===n.number?new a(t):parseFloat(t),r);return o.fixPrefix=!0,o}))}function numberFactory(e,t){return factory(e,["config","BigNumber"],(e=>{var{config:r,BigNumber:n}=e;return"BigNumber"===r.number?new n(t):t}))}var name$h="apply",dependencies$h=["typed","isInteger"],createApplyTransform=factory(name$h,dependencies$h,(e=>{var{typed:t,isInteger:r}=e,n=createApply({typed:t,isInteger:r});return t("apply",{"...any":function(e){var t=e[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1));try{return n.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$g="column",dependencies$g=["typed","Index","matrix","range"],createColumnTransform=factory(name$g,dependencies$g,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e,a=createColumn({typed:t,Index:r,matrix:n,range:i});return t("column",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)&&(e[t]=r-1);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0});function compileInlineExpression(e,t,r){var n=e.filter((function(e){return isSymbolNode(e)&&!(e.name in t)&&!r.has(e.name)}))[0];if(!n)throw new Error('No undefined variable found in inline expression "'+e+'"');var i=n.name,a=createSubScope(r),o=e.compile();return function(e){return a.set(i,e),o.evaluate(a)}}var name$f="filter",dependencies$f=["typed"],createFilterTransform=factory(name$f,dependencies$f,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("filter",{"Array, function":_filter,"Matrix, function":function(e,t){return e.create(_filter(e.toArray(),t))},"Array, RegExp":filterRegExp,"Matrix, RegExp":function(e,t){return e.create(filterRegExp(e.toArray(),t))}});return r}),{isTransformFunction:!0});function _filter(e,t){var r=maxArgumentCount(t);return filter$2(e,(function(e,n,i){return 1===r?t(e):2===r?t(e,[n+1]):t(e,[n+1],i)}))}var name$e="forEach",dependencies$e=["typed"],createForEachTransform=factory(name$e,dependencies$e,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("forEach",{"Array | Matrix, function":function(e,t){var r=maxArgumentCount(t);!function n(i,a){Array.isArray(i)?forEach$1(i,(function(e,t){n(e,a.concat(t+1))})):1===r?t(i):2===r?t(i,a):t(i,a,e)}(e.valueOf(),[])}});return r}),{isTransformFunction:!0}),name$d="index",dependencies$d=["Index"],createIndexTransform=factory(name$d,dependencies$d,(e=>{var{Index:t}=e;return function(){for(var e=[],r=0,n=arguments.length;r0?0:2;else if(i&&!0===i.isSet)i=i.map((function(e){return e-1}));else if(isArray$1(i)||isMatrix(i))i=i.map((function(e){return e-1}));else if(isNumber$1(i))i--;else if(isBigNumber(i))i=i.toNumber()-1;else if("string"!=typeof i)throw new TypeError("Dimension must be an Array, Matrix, number, string, or Range");e[r]=i}var a=new t;return t.apply(a,e),a}}),{isTransformFunction:!0}),name$c="map",dependencies$c=["typed"],createMapTransform=factory(name$c,dependencies$c,(e=>{var{typed:t}=e;function r(e,t,r){var i,a;return e[0]&&(i=e[0].compile().evaluate(r)),e[1]&&(a=isSymbolNode(e[1])||isFunctionAssignmentNode(e[1])?e[1].compile().evaluate(r):compileInlineExpression(e[1],t,r)),n(i,a)}r.rawArgs=!0;var n=t("map",{"Array, function":function(e,t){return _map(e,t,e)},"Matrix, function":function(e,t){return e.create(_map(e.valueOf(),t,e))}});return r}),{isTransformFunction:!0});function _map(e,t,r){var n=maxArgumentCount(t);return function e(i,a){return Array.isArray(i)?map$2(i,(function(t,r){return e(t,a.concat(r+1))})):1===n?t(i):2===n?t(i,a):t(i,a,r)}(e,[])}function lastDimToZeroBase(e){if(2===e.length&&isCollection(e[0])){var t=(e=e.slice())[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1))}return e}var name$b="max",dependencies$b=["typed","config","numeric","larger"],createMaxTransform=factory(name$b,dependencies$b,(e=>{var{typed:t,config:r,numeric:n,larger:i}=e,a=createMax({typed:t,config:r,numeric:n,larger:i});return t("max",{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$a="mean",dependencies$a=["typed","add","divide"],createMeanTransform=factory(name$a,dependencies$a,(e=>{var{typed:t,add:r,divide:n}=e,i=createMean({typed:t,add:r,divide:n});return t("mean",{"...any":function(e){e=lastDimToZeroBase(e);try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$9="min",dependencies$9=["typed","config","numeric","smaller"],createMinTransform=factory(name$9,dependencies$9,(e=>{var{typed:t,config:r,numeric:n,smaller:i}=e,a=createMin({typed:t,config:r,numeric:n,smaller:i});return t("min",{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$8="range",dependencies$8=["typed","config","?matrix","?bignumber","smaller","smallerEq","larger","largerEq"],createRangeTransform=factory(name$8,dependencies$8,(e=>{var{typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u}=e,c=createRange({typed:t,config:r,matrix:n,bignumber:i,smaller:a,smallerEq:o,larger:s,largerEq:u});return t("range",{"...any":function(e){return"boolean"!=typeof e[e.length-1]&&e.push(!0),c.apply(null,e)}})}),{isTransformFunction:!0}),name$7="row",dependencies$7=["typed","Index","matrix","range"],createRowTransform=factory(name$7,dependencies$7,(e=>{var{typed:t,Index:r,matrix:n,range:i}=e,a=createRow({typed:t,Index:r,matrix:n,range:i});return t("row",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)&&(e[t]=r-1);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$6="subset",dependencies$6=["typed","matrix"],createSubsetTransform=factory(name$6,dependencies$6,(e=>{var{typed:t,matrix:r}=e,n=createSubset({typed:t,matrix:r});return t("subset",{"...any":function(e){try{return n.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$5="concat",dependencies$5=["typed","matrix","isInteger"],createConcatTransform=factory(name$5,dependencies$5,(e=>{var{typed:t,matrix:r,isInteger:n}=e,i=createConcat({typed:t,matrix:r,isInteger:n});return t("concat",{"...any":function(e){var t=e.length-1,r=e[t];isNumber$1(r)?e[t]=r-1:isBigNumber(r)&&(e[t]=r.minus(1));try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$4="diff",dependencies$4=["typed","matrix","subtract","number","bignumber"],createDiffTransform=factory(name$4,dependencies$4,(e=>{var{typed:t,matrix:r,subtract:n,number:i,bignumber:a}=e,o=createDiff({typed:t,matrix:r,subtract:n,number:i,bignumber:a});return t(name$4,{"...any":function(e){e=lastDimToZeroBase(e);try{return o.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$3="std",dependencies$3=["typed","sqrt","variance"],createStdTransform=factory(name$3,dependencies$3,(e=>{var{typed:t,sqrt:r,variance:n}=e,i=createStd({typed:t,sqrt:r,variance:n});return t("std",{"...any":function(e){e=lastDimToZeroBase(e);try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$2="sum",dependencies$2=["typed","config","add","numeric"],createSumTransform=factory(name$2,dependencies$2,(e=>{var{typed:t,config:r,add:n,numeric:i}=e,a=createSum({typed:t,config:r,add:n,numeric:i});return t(name$2,{"...any":function(e){e=lastDimToZeroBase(e);try{return a.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name$1="cumsum",dependencies$1=["typed","add","unaryPlus"],createCumSumTransform=factory(name$1,dependencies$1,(e=>{var{typed:t,add:r,unaryPlus:n}=e,i=createCumSum({typed:t,add:r,unaryPlus:n});return t(name$1,{"...any":function(e){if(2===e.length&&isCollection(e[0])){var t=e[1];isNumber$1(t)?e[1]=t-1:isBigNumber(t)&&(e[1]=t.minus(1))}try{return i.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),name="variance",dependencies=["typed","add","subtract","multiply","divide","apply","isNaN"],createVarianceTransform=factory(name,dependencies,(e=>{var{typed:t,add:r,subtract:n,multiply:i,divide:a,apply:o,isNaN:s}=e,u=createVariance({typed:t,add:r,subtract:n,multiply:i,divide:a,apply:o,isNaN:s});return t(name,{"...any":function(e){e=lastDimToZeroBase(e);try{return u.apply(null,e)}catch(e){throw errorTransform(e)}}})}),{isTransformFunction:!0}),allFactories=Object.freeze({__proto__:null,createTyped:createTyped,createResultSet:createResultSet,createBigNumberClass:createBigNumberClass,createComplexClass:createComplexClass,createFractionClass:createFractionClass,createRangeClass:createRangeClass,createMatrixClass:createMatrixClass,createDenseMatrixClass:createDenseMatrixClass,createClone:createClone,createIsInteger:createIsInteger,createIsNegative:createIsNegative,createIsNumeric:createIsNumeric,createHasNumericValue:createHasNumericValue,createIsPositive:createIsPositive,createIsZero:createIsZero,createIsNaN:createIsNaN,createTypeOf:createTypeOf,createEqualScalar:createEqualScalar,createSparseMatrixClass:createSparseMatrixClass,createNumber:createNumber,createString:createString,createBoolean:createBoolean,createBignumber:createBignumber,createComplex:createComplex,createFraction:createFraction,createMatrix:createMatrix,createMatrixFromFunction:createMatrixFromFunction,createMatrixFromRows:createMatrixFromRows,createMatrixFromColumns:createMatrixFromColumns,createSplitUnit:createSplitUnit,createUnaryMinus:createUnaryMinus,createUnaryPlus:createUnaryPlus,createAbs:createAbs,createApply:createApply,createAddScalar:createAddScalar,createCbrt:createCbrt,createCeil:createCeil,createCube:createCube,createExp:createExp,createExpm1:createExpm1,createFix:createFix,createFloor:createFloor,createGcd:createGcd,createLcm:createLcm,createLog10:createLog10,createLog2:createLog2,createMod:createMod,createMultiplyScalar:createMultiplyScalar,createMultiply:createMultiply,createNthRoot:createNthRoot,createSign:createSign,createSqrt:createSqrt,createSquare:createSquare,createSubtract:createSubtract,createXgcd:createXgcd,createInvmod:createInvmod,createDotMultiply:createDotMultiply,createBitAnd:createBitAnd,createBitNot:createBitNot,createBitOr:createBitOr,createBitXor:createBitXor,createArg:createArg,createConj:createConj,createIm:createIm,createRe:createRe,createNot:createNot,createOr:createOr,createXor:createXor,createConcat:createConcat,createColumn:createColumn,createCount:createCount,createCross:createCross,createDiag:createDiag,createFilter:createFilter,createFlatten:createFlatten,createForEach:createForEach,createGetMatrixDataType:createGetMatrixDataType,createIdentity:createIdentity,createKron:createKron,createMap:createMap,createDiff:createDiff,createOnes:createOnes,createRange:createRange,createReshape:createReshape,createResize:createResize,createRotate:createRotate,createRotationMatrix:createRotationMatrix,createRow:createRow,createSize:createSize,createSqueeze:createSqueeze,createSubset:createSubset,createTranspose:createTranspose,createCtranspose:createCtranspose,createZeros:createZeros,createFft:createFft,createIfft:createIfft,createErf:createErf,createMode:createMode,createProd:createProd,createFormat:createFormat,createBin:createBin,createOct:createOct,createHex:createHex,createPrint:createPrint,createTo:createTo,createIsPrime:createIsPrime,createNumeric:createNumeric,createDivideScalar:createDivideScalar,createPow:createPow,createRound:createRound,createLog:createLog,createLog1p:createLog1p,createNthRoots:createNthRoots,createDotPow:createDotPow,createDotDivide:createDotDivide,createLsolve:createLsolve,createUsolve:createUsolve,createLsolveAll:createLsolveAll,createUsolveAll:createUsolveAll,createLeftShift:createLeftShift,createRightArithShift:createRightArithShift,createRightLogShift:createRightLogShift,createAnd:createAnd,createCompare:createCompare,createCompareNatural:createCompareNatural,createCompareText:createCompareText,createEqual:createEqual,createEqualText:createEqualText,createSmaller:createSmaller,createSmallerEq:createSmallerEq,createLarger:createLarger,createLargerEq:createLargerEq,createDeepEqual:createDeepEqual,createUnequal:createUnequal,createPartitionSelect:createPartitionSelect,createSort:createSort,createMax:createMax,createMin:createMin,createImmutableDenseMatrixClass:createImmutableDenseMatrixClass,createIndexClass:createIndexClass,createFibonacciHeapClass:createFibonacciHeapClass,createSpaClass:createSpaClass,createUnitClass:createUnitClass,createUnitFunction:createUnitFunction,createSparse:createSparse,createCreateUnit:createCreateUnit,createAcos:createAcos,createAcosh:createAcosh,createAcot:createAcot,createAcoth:createAcoth,createAcsc:createAcsc,createAcsch:createAcsch,createAsec:createAsec,createAsech:createAsech,createAsin:createAsin,createAsinh:createAsinh,createAtan:createAtan,createAtan2:createAtan2,createAtanh:createAtanh,createCos:createCos,createCosh:createCosh,createCot:createCot,createCoth:createCoth,createCsc:createCsc,createCsch:createCsch,createSec:createSec,createSech:createSech,createSin:createSin,createSinh:createSinh,createTan:createTan,createTanh:createTanh,createSetCartesian:createSetCartesian,createSetDifference:createSetDifference,createSetDistinct:createSetDistinct,createSetIntersect:createSetIntersect,createSetIsSubset:createSetIsSubset,createSetMultiplicity:createSetMultiplicity,createSetPowerset:createSetPowerset,createSetSize:createSetSize,createSetSymDifference:createSetSymDifference,createSetUnion:createSetUnion,createAdd:createAdd,createHypot:createHypot,createNorm:createNorm,createDot:createDot,createTrace:createTrace,createIndex:createIndex,createNode:createNode,createAccessorNode:createAccessorNode,createArrayNode:createArrayNode,createAssignmentNode:createAssignmentNode,createBlockNode:createBlockNode,createConditionalNode:createConditionalNode,createConstantNode:createConstantNode,createFunctionAssignmentNode:createFunctionAssignmentNode,createIndexNode:createIndexNode,createObjectNode:createObjectNode,createOperatorNode:createOperatorNode,createParenthesisNode:createParenthesisNode,createRangeNode:createRangeNode,createRelationalNode:createRelationalNode,createSymbolNode:createSymbolNode,createFunctionNode:createFunctionNode,createParse:createParse,createCompile:createCompile,createEvaluate:createEvaluate,createParserClass:createParserClass,createParser:createParser,createLup:createLup,createQr:createQr,createSlu:createSlu,createLusolve:createLusolve,createHelpClass:createHelpClass,createChainClass:createChainClass,createHelp:createHelp,createChain:createChain,createDet:createDet,createInv:createInv,createPinv:createPinv,createEigs:createEigs,createExpm:createExpm,createSqrtm:createSqrtm,createDivide:createDivide,createDistance:createDistance,createIntersect:createIntersect,createSum:createSum,createCumSum:createCumSum,createMean:createMean,createMedian:createMedian,createMad:createMad,createVariance:createVariance,createQuantileSeq:createQuantileSeq,createStd:createStd,createCombinations:createCombinations,createCombinationsWithRep:createCombinationsWithRep,createGamma:createGamma,createLgamma:createLgamma,createFactorial:createFactorial,createKldivergence:createKldivergence,createMultinomial:createMultinomial,createPermutations:createPermutations,createPickRandom:createPickRandom,createRandom:createRandom,createRandomInt:createRandomInt,createStirlingS2:createStirlingS2,createBellNumbers:createBellNumbers,createCatalan:createCatalan,createComposition:createComposition,createLeafCount:createLeafCount,createSimplify:createSimplify,createSimplifyCore:createSimplifyCore,createResolve:createResolve,createSymbolicEqual:createSymbolicEqual,createDerivative:createDerivative,createRationalize:createRationalize,createReviver:createReviver,createReplacer:createReplacer,createE:createE,createUppercaseE:createUppercaseE,createFalse:createFalse,createI:createI,createInfinity:createInfinity,createLN10:createLN10,createLN2:createLN2,createLOG10E:createLOG10E,createLOG2E:createLOG2E,createNaN:createNaN,createNull:createNull,createPhi:createPhi,createPi:createPi,createUppercasePi:createUppercasePi,createSQRT1_2:createSQRT1_2,createSQRT2:createSQRT2,createTau:createTau,createTrue:createTrue,createVersion:createVersion,createAtomicMass:createAtomicMass,createAvogadro:createAvogadro,createBohrMagneton:createBohrMagneton,createBohrRadius:createBohrRadius,createBoltzmann:createBoltzmann,createClassicalElectronRadius:createClassicalElectronRadius,createConductanceQuantum:createConductanceQuantum,createCoulomb:createCoulomb,createDeuteronMass:createDeuteronMass,createEfimovFactor:createEfimovFactor,createElectricConstant:createElectricConstant,createElectronMass:createElectronMass,createElementaryCharge:createElementaryCharge,createFaraday:createFaraday,createFermiCoupling:createFermiCoupling,createFineStructure:createFineStructure,createFirstRadiation:createFirstRadiation,createGasConstant:createGasConstant,createGravitationConstant:createGravitationConstant,createGravity:createGravity,createHartreeEnergy:createHartreeEnergy,createInverseConductanceQuantum:createInverseConductanceQuantum,createKlitzing:createKlitzing,createLoschmidt:createLoschmidt,createMagneticConstant:createMagneticConstant,createMagneticFluxQuantum:createMagneticFluxQuantum,createMolarMass:createMolarMass,createMolarMassC12:createMolarMassC12,createMolarPlanckConstant:createMolarPlanckConstant,createMolarVolume:createMolarVolume,createNeutronMass:createNeutronMass,createNuclearMagneton:createNuclearMagneton,createPlanckCharge:createPlanckCharge,createPlanckConstant:createPlanckConstant,createPlanckLength:createPlanckLength,createPlanckMass:createPlanckMass,createPlanckTemperature:createPlanckTemperature,createPlanckTime:createPlanckTime,createProtonMass:createProtonMass,createQuantumOfCirculation:createQuantumOfCirculation,createReducedPlanckConstant:createReducedPlanckConstant,createRydberg:createRydberg,createSackurTetrode:createSackurTetrode,createSecondRadiation:createSecondRadiation,createSpeedOfLight:createSpeedOfLight,createStefanBoltzmann:createStefanBoltzmann,createThomsonCrossSection:createThomsonCrossSection,createVacuumImpedance:createVacuumImpedance,createWeakMixingAngle:createWeakMixingAngle,createWienDisplacement:createWienDisplacement,createApplyTransform:createApplyTransform,createColumnTransform:createColumnTransform,createFilterTransform:createFilterTransform,createForEachTransform:createForEachTransform,createIndexTransform:createIndexTransform,createMapTransform:createMapTransform,createMaxTransform:createMaxTransform,createMeanTransform:createMeanTransform,createMinTransform:createMinTransform,createRangeTransform:createRangeTransform,createRowTransform:createRowTransform,createSubsetTransform:createSubsetTransform,createConcatTransform:createConcatTransform,createDiffTransform:createDiffTransform,createStdTransform:createStdTransform,createSumTransform:createSumTransform,createCumSumTransform:createCumSumTransform,createVarianceTransform:createVarianceTransform}),BigNumber=createBigNumberClass({config:config$2}),Complex=createComplexClass({}),e=createE({BigNumber:BigNumber,config:config$2}),_false=createFalse({}),fineStructure=createFineStructure({BigNumber:BigNumber,config:config$2}),Fraction=createFractionClass({}),i=createI({Complex:Complex}),_Infinity=createInfinity({BigNumber:BigNumber,config:config$2}),LN10=createLN10({BigNumber:BigNumber,config:config$2}),LOG10E=createLOG10E({BigNumber:BigNumber,config:config$2}),Matrix=createMatrixClass({}),_NaN=createNaN({BigNumber:BigNumber,config:config$2}),_null=createNull({}),phi=createPhi({BigNumber:BigNumber,config:config$2}),Range=createRangeClass({}),ResultSet=createResultSet({}),SQRT1_2=createSQRT1_2({BigNumber:BigNumber,config:config$2}),sackurTetrode=createSackurTetrode({BigNumber:BigNumber,config:config$2}),tau=createTau({BigNumber:BigNumber,config:config$2}),_true=createTrue({}),version$1=createVersion({}),DenseMatrix=createDenseMatrixClass({Matrix:Matrix}),efimovFactor=createEfimovFactor({BigNumber:BigNumber,config:config$2}),LN2=createLN2({BigNumber:BigNumber,config:config$2}),pi=createPi({BigNumber:BigNumber,config:config$2}),replacer=createReplacer({}),SQRT2=createSQRT2({BigNumber:BigNumber,config:config$2}),typed=createTyped({BigNumber:BigNumber,Complex:Complex,DenseMatrix:DenseMatrix,Fraction:Fraction}),unaryPlus=createUnaryPlus({BigNumber:BigNumber,config:config$2,typed:typed}),weakMixingAngle=createWeakMixingAngle({BigNumber:BigNumber,config:config$2}),abs$1=createAbs({typed:typed}),acos$1=createAcos({Complex:Complex,config:config$2,typed:typed}),acot$1=createAcot({BigNumber:BigNumber,typed:typed}),acsc$1=createAcsc({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),addScalar=createAddScalar({typed:typed}),arg=createArg({typed:typed}),asech$1=createAsech({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),asinh$1=createAsinh({typed:typed}),atan$1=createAtan({typed:typed}),atanh$1=createAtanh({Complex:Complex,config:config$2,typed:typed}),bignumber=createBignumber({BigNumber:BigNumber,typed:typed}),bitNot=createBitNot({typed:typed}),boolean=createBoolean({typed:typed}),clone$1=createClone({typed:typed}),combinations=createCombinations({typed:typed}),complex=createComplex({Complex:Complex,typed:typed}),conj$1=createConj({typed:typed}),cosh$1=createCosh({typed:typed}),coth$1=createCoth({BigNumber:BigNumber,typed:typed}),csc$1=createCsc({BigNumber:BigNumber,typed:typed}),cube=createCube({typed:typed}),equalScalar=createEqualScalar({config:config$2,typed:typed}),erf$1=createErf({typed:typed}),exp$1=createExp({typed:typed}),expm1=createExpm1({Complex:Complex,typed:typed}),filter$1=createFilter({typed:typed}),forEach=createForEach({typed:typed}),format=createFormat({typed:typed}),getMatrixDataType=createGetMatrixDataType({typed:typed}),hex=createHex({format:format,typed:typed}),im$1=createIm({typed:typed}),isInteger=createIsInteger({typed:typed}),isNegative=createIsNegative({typed:typed}),isPositive=createIsPositive({typed:typed}),isZero=createIsZero({typed:typed}),LOG2E=createLOG2E({BigNumber:BigNumber,config:config$2}),lgamma=createLgamma({Complex:Complex,typed:typed}),log10$1=createLog10({Complex:Complex,config:config$2,typed:typed}),log2=createLog2({Complex:Complex,config:config$2,typed:typed}),map$1=createMap({typed:typed}),multiplyScalar=createMultiplyScalar({typed:typed}),not=createNot({typed:typed}),number=createNumber({typed:typed}),oct=createOct({format:format,typed:typed}),pickRandom=createPickRandom({config:config$2,typed:typed}),print=createPrint({typed:typed}),random$1=createRandom({config:config$2,typed:typed}),re$1=createRe({typed:typed}),sec$1=createSec({BigNumber:BigNumber,typed:typed}),sign$1=createSign({BigNumber:BigNumber,Fraction:Fraction,complex:complex,typed:typed}),sin$1=createSin({typed:typed}),SparseMatrix=createSparseMatrixClass({Matrix:Matrix,equalScalar:equalScalar,typed:typed}),splitUnit=createSplitUnit({typed:typed}),square=createSquare({typed:typed}),string=createString({typed:typed}),tan$1=createTan({typed:typed}),typeOf=createTypeOf({typed:typed}),acosh$1=createAcosh({Complex:Complex,config:config$2,typed:typed}),acsch$1=createAcsch({BigNumber:BigNumber,typed:typed}),apply=createApply({isInteger:isInteger,typed:typed}),asec$1=createAsec({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),bin=createBin({format:format,typed:typed}),combinationsWithRep=createCombinationsWithRep({typed:typed}),cos$1=createCos({typed:typed}),csch$1=createCsch({BigNumber:BigNumber,typed:typed}),isNaN$2=createIsNaN({typed:typed}),isPrime=createIsPrime({typed:typed}),randomInt=createRandomInt({config:config$2,typed:typed}),sech$1=createSech({BigNumber:BigNumber,typed:typed}),sinh$1=createSinh({typed:typed}),sparse=createSparse({SparseMatrix:SparseMatrix,typed:typed}),sqrt$1=createSqrt({Complex:Complex,config:config$2,typed:typed}),tanh$1=createTanh({typed:typed}),unaryMinus=createUnaryMinus({typed:typed}),acoth$1=createAcoth({BigNumber:BigNumber,Complex:Complex,config:config$2,typed:typed}),cot$1=createCot({BigNumber:BigNumber,typed:typed}),fraction=createFraction({Fraction:Fraction,typed:typed}),isNumeric=createIsNumeric({typed:typed}),matrix$2=createMatrix({DenseMatrix:DenseMatrix,Matrix:Matrix,SparseMatrix:SparseMatrix,typed:typed}),matrixFromFunction=createMatrixFromFunction({isZero:isZero,matrix:matrix$2,typed:typed}),mod$1=createMod({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),nthRoot=createNthRoot({BigNumber:BigNumber,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),numeric=createNumeric({bignumber:bignumber,fraction:fraction,number:number}),or=createOr({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),prod=createProd({config:config$2,multiplyScalar:multiplyScalar,numeric:numeric,typed:typed}),reshape=createReshape({isInteger:isInteger,matrix:matrix$2,typed:typed}),size$1=createSize({matrix:matrix$2,config:config$2,typed:typed}),smaller=createSmaller({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),squeeze=createSqueeze({matrix:matrix$2,typed:typed}),subset=createSubset({matrix:matrix$2,typed:typed}),subtract$1=createSubtract({DenseMatrix:DenseMatrix,addScalar:addScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed,unaryMinus:unaryMinus}),to=createTo({matrix:matrix$2,typed:typed}),transpose=createTranspose({matrix:matrix$2,typed:typed}),xgcd=createXgcd({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),zeros=createZeros({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),and=createAnd({equalScalar:equalScalar,matrix:matrix$2,not:not,typed:typed,zeros:zeros}),bitAnd=createBitAnd({equalScalar:equalScalar,matrix:matrix$2,typed:typed}),bitXor=createBitXor({DenseMatrix:DenseMatrix,matrix:matrix$2,typed:typed}),cbrt=createCbrt({BigNumber:BigNumber,Complex:Complex,Fraction:Fraction,config:config$2,isNegative:isNegative,matrix:matrix$2,typed:typed,unaryMinus:unaryMinus}),compare=createCompare({BigNumber:BigNumber,DenseMatrix:DenseMatrix,Fraction:Fraction,config:config$2,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),compareText=createCompareText({matrix:matrix$2,typed:typed}),concat=createConcat({isInteger:isInteger,matrix:matrix$2,typed:typed}),count=createCount({prod:prod,size:size$1,typed:typed}),ctranspose=createCtranspose({conj:conj$1,transpose:transpose,typed:typed}),diag=createDiag({DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,matrix:matrix$2,typed:typed}),divideScalar=createDivideScalar({numeric:numeric,typed:typed}),dotDivide=createDotDivide({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),equal$1=createEqual({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),fft=createFft({addScalar:addScalar,divideScalar:divideScalar,exp:exp$1,i:i,matrix:matrix$2,multiplyScalar:multiplyScalar,tau:tau,typed:typed}),flatten$3=createFlatten({matrix:matrix$2,typed:typed}),gcd=createGcd({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),hasNumericValue=createHasNumericValue({isNumeric:isNumeric,typed:typed}),hypot=createHypot({abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,isPositive:isPositive,multiplyScalar:multiplyScalar,smaller:smaller,sqrt:sqrt$1,typed:typed}),ifft=createIfft({conj:conj$1,dotDivide:dotDivide,fft:fft,typed:typed}),kron=createKron({matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),largerEq=createLargerEq({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),leftShift=createLeftShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),lsolve=createLsolve({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),matrixFromColumns=createMatrixFromColumns({flatten:flatten$3,matrix:matrix$2,size:size$1,typed:typed}),min$1=createMin({config:config$2,numeric:numeric,smaller:smaller,typed:typed}),mode=createMode({isNaN:isNaN$2,isNumeric:isNumeric,typed:typed}),nthRoots=createNthRoots({Complex:Complex,config:config$2,divideScalar:divideScalar,typed:typed}),ones=createOnes({BigNumber:BigNumber,config:config$2,matrix:matrix$2,typed:typed}),partitionSelect=createPartitionSelect({compare:compare,isNaN:isNaN$2,isNumeric:isNumeric,typed:typed}),resize=createResize({config:config$2,matrix:matrix$2}),rightArithShift=createRightArithShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),round$1=createRound({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),smallerEq=createSmallerEq({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),unequal=createUnequal({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),usolve=createUsolve({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),xor=createXor({DenseMatrix:DenseMatrix,matrix:matrix$2,typed:typed}),add$1=createAdd({DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,addScalar:addScalar,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),atan2$1=createAtan2({BigNumber:BigNumber,DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),bitOr=createBitOr({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed}),catalan=createCatalan({addScalar:addScalar,combinations:combinations,divideScalar:divideScalar,isInteger:isInteger,isNegative:isNegative,multiplyScalar:multiplyScalar,typed:typed}),compareNatural=createCompareNatural({compare:compare,typed:typed}),cumsum=createCumSum({add:add$1,typed:typed,unaryPlus:unaryPlus}),deepEqual=createDeepEqual({equal:equal$1,typed:typed}),diff=createDiff({matrix:matrix$2,number:number,subtract:subtract$1,typed:typed}),dot=createDot({addScalar:addScalar,conj:conj$1,multiplyScalar:multiplyScalar,size:size$1,typed:typed}),equalText=createEqualText({compareText:compareText,isZero:isZero,typed:typed}),floor=createFloor({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,round:round$1,typed:typed,zeros:zeros}),identity$1=createIdentity({BigNumber:BigNumber,DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,config:config$2,matrix:matrix$2,typed:typed}),invmod=createInvmod({BigNumber:BigNumber,add:add$1,config:config$2,equal:equal$1,isInteger:isInteger,mod:mod$1,smaller:smaller,typed:typed,xgcd:xgcd}),larger=createLarger({DenseMatrix:DenseMatrix,config:config$2,matrix:matrix$2,typed:typed}),log$1=createLog({Complex:Complex,config:config$2,divideScalar:divideScalar,typed:typed}),lsolveAll=createLsolveAll({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),matrixFromRows=createMatrixFromRows({flatten:flatten$3,matrix:matrix$2,size:size$1,typed:typed}),multiply$1=createMultiply({addScalar:addScalar,dot:dot,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),qr=createQr({addScalar:addScalar,complex:complex,conj:conj$1,divideScalar:divideScalar,equal:equal$1,identity:identity$1,isZero:isZero,matrix:matrix$2,multiplyScalar:multiplyScalar,sign:sign$1,sqrt:sqrt$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus,zeros:zeros}),range$1=createRange({bignumber:bignumber,matrix:matrix$2,config:config$2,larger:larger,largerEq:largerEq,smaller:smaller,smallerEq:smallerEq,typed:typed}),rightLogShift=createRightLogShift({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,typed:typed,zeros:zeros}),setSize=createSetSize({compareNatural:compareNatural,typed:typed}),slu=createSlu({SparseMatrix:SparseMatrix,abs:abs$1,add:add$1,divideScalar:divideScalar,larger:larger,largerEq:largerEq,multiply:multiply$1,subtract:subtract$1,transpose:transpose,typed:typed}),sum=createSum({add:add$1,config:config$2,numeric:numeric,typed:typed}),trace=createTrace({add:add$1,matrix:matrix$2,typed:typed}),usolveAll=createUsolveAll({DenseMatrix:DenseMatrix,divideScalar:divideScalar,equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed}),asin$1=createAsin({Complex:Complex,config:config$2,typed:typed}),ceil=createCeil({DenseMatrix:DenseMatrix,config:config$2,equalScalar:equalScalar,matrix:matrix$2,round:round$1,typed:typed,zeros:zeros}),composition=createComposition({addScalar:addScalar,combinations:combinations,isInteger:isInteger,isNegative:isNegative,isPositive:isPositive,larger:larger,typed:typed}),cross=createCross({matrix:matrix$2,multiply:multiply$1,subtract:subtract$1,typed:typed}),det=createDet({divideScalar:divideScalar,isZero:isZero,matrix:matrix$2,multiply:multiply$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),distance=createDistance({abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,multiplyScalar:multiplyScalar,sqrt:sqrt$1,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),dotMultiply=createDotMultiply({equalScalar:equalScalar,matrix:matrix$2,multiplyScalar:multiplyScalar,typed:typed}),FibonacciHeap=createFibonacciHeapClass({larger:larger,smaller:smaller}),fix=createFix({Complex:Complex,DenseMatrix:DenseMatrix,ceil:ceil,equalScalar:equalScalar,floor:floor,matrix:matrix$2,typed:typed,zeros:zeros}),ImmutableDenseMatrix=createImmutableDenseMatrixClass({DenseMatrix:DenseMatrix,smaller:smaller}),Index=createIndexClass({ImmutableDenseMatrix:ImmutableDenseMatrix}),intersect=createIntersect({abs:abs$1,add:add$1,addScalar:addScalar,config:config$2,divideScalar:divideScalar,equalScalar:equalScalar,flatten:flatten$3,isNumeric:isNumeric,isZero:isZero,matrix:matrix$2,multiply:multiply$1,multiplyScalar:multiplyScalar,smaller:smaller,subtract:subtract$1,typed:typed}),lcm=createLcm({equalScalar:equalScalar,matrix:matrix$2,typed:typed}),log1p=createLog1p({Complex:Complex,config:config$2,divideScalar:divideScalar,log:log$1,typed:typed}),max$1=createMax({config:config$2,larger:larger,numeric:numeric,typed:typed}),quantileSeq=createQuantileSeq({add:add$1,compare:compare,multiply:multiply$1,partitionSelect:partitionSelect,typed:typed}),row=createRow({Index:Index,matrix:matrix$2,range:range$1,typed:typed}),setCartesian=createSetCartesian({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setDistinct=createSetDistinct({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setIsSubset=createSetIsSubset({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setPowerset=createSetPowerset({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),sort=createSort({compare:compare,compareNatural:compareNatural,matrix:matrix$2,typed:typed}),column=createColumn({Index:Index,matrix:matrix$2,range:range$1,typed:typed}),index=createIndex({Index:Index,typed:typed}),inv=createInv({abs:abs$1,addScalar:addScalar,det:det,divideScalar:divideScalar,identity:identity$1,matrix:matrix$2,multiply:multiply$1,typed:typed,unaryMinus:unaryMinus}),pinv=createPinv({Complex:Complex,add:add$1,ctranspose:ctranspose,deepEqual:deepEqual,divideScalar:divideScalar,dot:dot,dotDivide:dotDivide,equal:equal$1,inv:inv,matrix:matrix$2,multiply:multiply$1,typed:typed}),pow$1=createPow({Complex:Complex,config:config$2,fraction:fraction,identity:identity$1,inv:inv,matrix:matrix$2,multiply:multiply$1,number:number,typed:typed}),setDifference=createSetDifference({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),setMultiplicity=createSetMultiplicity({Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),Spa=createSpaClass({FibonacciHeap:FibonacciHeap,addScalar:addScalar,equalScalar:equalScalar}),sqrtm=createSqrtm({abs:abs$1,add:add$1,identity:identity$1,inv:inv,max:max$1,multiply:multiply$1,size:size$1,sqrt:sqrt$1,subtract:subtract$1,typed:typed}),Unit=createUnitClass({BigNumber:BigNumber,Complex:Complex,Fraction:Fraction,abs:abs$1,addScalar:addScalar,config:config$2,divideScalar:divideScalar,equal:equal$1,fix:fix,format:format,isNumeric:isNumeric,multiplyScalar:multiplyScalar,number:number,pow:pow$1,round:round$1,subtract:subtract$1}),vacuumImpedance=createVacuumImpedance({BigNumber:BigNumber,Unit:Unit,config:config$2}),wienDisplacement=createWienDisplacement({BigNumber:BigNumber,Unit:Unit,config:config$2}),atomicMass=createAtomicMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),bohrMagneton=createBohrMagneton({BigNumber:BigNumber,Unit:Unit,config:config$2}),boltzmann=createBoltzmann({BigNumber:BigNumber,Unit:Unit,config:config$2}),conductanceQuantum=createConductanceQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),createUnit=createCreateUnit({Unit:Unit,typed:typed}),deuteronMass=createDeuteronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),dotPow=createDotPow({DenseMatrix:DenseMatrix,equalScalar:equalScalar,matrix:matrix$2,pow:pow$1,typed:typed}),electricConstant=createElectricConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),elementaryCharge=createElementaryCharge({BigNumber:BigNumber,Unit:Unit,config:config$2}),expm=createExpm({abs:abs$1,add:add$1,identity:identity$1,inv:inv,multiply:multiply$1,typed:typed}),faraday=createFaraday({BigNumber:BigNumber,Unit:Unit,config:config$2}),firstRadiation=createFirstRadiation({BigNumber:BigNumber,Unit:Unit,config:config$2}),gamma$1=createGamma({BigNumber:BigNumber,Complex:Complex,config:config$2,multiplyScalar:multiplyScalar,pow:pow$1,typed:typed}),gravitationConstant=createGravitationConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),hartreeEnergy=createHartreeEnergy({BigNumber:BigNumber,Unit:Unit,config:config$2}),klitzing=createKlitzing({BigNumber:BigNumber,Unit:Unit,config:config$2}),loschmidt=createLoschmidt({BigNumber:BigNumber,Unit:Unit,config:config$2}),magneticConstant=createMagneticConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarMass=createMolarMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarPlanckConstant=createMolarPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),neutronMass=createNeutronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),nuclearMagneton=createNuclearMagneton({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckCharge=createPlanckCharge({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckLength=createPlanckLength({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckTemperature=createPlanckTemperature({BigNumber:BigNumber,Unit:Unit,config:config$2}),protonMass=createProtonMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),reducedPlanckConstant=createReducedPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),rydberg=createRydberg({BigNumber:BigNumber,Unit:Unit,config:config$2}),setIntersect=createSetIntersect({DenseMatrix:DenseMatrix,Index:Index,compareNatural:compareNatural,size:size$1,subset:subset,typed:typed}),speedOfLight=createSpeedOfLight({BigNumber:BigNumber,Unit:Unit,config:config$2}),stefanBoltzmann=createStefanBoltzmann({BigNumber:BigNumber,Unit:Unit,config:config$2}),thomsonCrossSection=createThomsonCrossSection({BigNumber:BigNumber,Unit:Unit,config:config$2}),avogadro=createAvogadro({BigNumber:BigNumber,Unit:Unit,config:config$2}),bohrRadius=createBohrRadius({BigNumber:BigNumber,Unit:Unit,config:config$2}),coulomb=createCoulomb({BigNumber:BigNumber,Unit:Unit,config:config$2}),divide$1=createDivide({divideScalar:divideScalar,equalScalar:equalScalar,inv:inv,matrix:matrix$2,multiply:multiply$1,typed:typed}),electronMass=createElectronMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),factorial$1=createFactorial({gamma:gamma$1,typed:typed}),gravity=createGravity({BigNumber:BigNumber,Unit:Unit,config:config$2}),inverseConductanceQuantum=createInverseConductanceQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),lup=createLup({DenseMatrix:DenseMatrix,Spa:Spa,SparseMatrix:SparseMatrix,abs:abs$1,addScalar:addScalar,divideScalar:divideScalar,equalScalar:equalScalar,larger:larger,matrix:matrix$2,multiplyScalar:multiplyScalar,subtract:subtract$1,typed:typed,unaryMinus:unaryMinus}),magneticFluxQuantum=createMagneticFluxQuantum({BigNumber:BigNumber,Unit:Unit,config:config$2}),molarMassC12=createMolarMassC12({BigNumber:BigNumber,Unit:Unit,config:config$2}),multinomial=createMultinomial({add:add$1,divide:divide$1,factorial:factorial$1,isInteger:isInteger,isPositive:isPositive,multiply:multiply$1,typed:typed}),permutations=createPermutations({factorial:factorial$1,typed:typed}),planckMass=createPlanckMass({BigNumber:BigNumber,Unit:Unit,config:config$2}),quantumOfCirculation=createQuantumOfCirculation({BigNumber:BigNumber,Unit:Unit,config:config$2}),secondRadiation=createSecondRadiation({BigNumber:BigNumber,Unit:Unit,config:config$2}),stirlingS2=createStirlingS2({bignumber:bignumber,addScalar:addScalar,combinations:combinations,divideScalar:divideScalar,factorial:factorial$1,isInteger:isInteger,isNegative:isNegative,larger:larger,multiplyScalar:multiplyScalar,number:number,pow:pow$1,subtract:subtract$1,typed:typed}),unit=createUnitFunction({Unit:Unit,typed:typed}),bellNumbers=createBellNumbers({addScalar:addScalar,isInteger:isInteger,isNegative:isNegative,stirlingS2:stirlingS2,typed:typed}),eigs=createEigs({abs:abs$1,add:add$1,addScalar:addScalar,atan:atan$1,bignumber:bignumber,column:column,complex:complex,config:config$2,cos:cos$1,diag:diag,divideScalar:divideScalar,dot:dot,equal:equal$1,flatten:flatten$3,im:im$1,inv:inv,larger:larger,matrix:matrix$2,matrixFromColumns:matrixFromColumns,multiply:multiply$1,multiplyScalar:multiplyScalar,number:number,qr:qr,re:re$1,sin:sin$1,smaller:smaller,sqrt:sqrt$1,subtract:subtract$1,typed:typed,usolve:usolve,usolveAll:usolveAll}),fermiCoupling=createFermiCoupling({BigNumber:BigNumber,Unit:Unit,config:config$2}),mean=createMean({add:add$1,divide:divide$1,typed:typed}),molarVolume=createMolarVolume({BigNumber:BigNumber,Unit:Unit,config:config$2}),planckConstant=createPlanckConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),setSymDifference=createSetSymDifference({Index:Index,concat:concat,setDifference:setDifference,size:size$1,subset:subset,typed:typed}),classicalElectronRadius=createClassicalElectronRadius({BigNumber:BigNumber,Unit:Unit,config:config$2}),lusolve=createLusolve({DenseMatrix:DenseMatrix,lsolve:lsolve,lup:lup,matrix:matrix$2,slu:slu,typed:typed,usolve:usolve}),median=createMedian({add:add$1,compare:compare,divide:divide$1,partitionSelect:partitionSelect,typed:typed}),setUnion=createSetUnion({Index:Index,concat:concat,setIntersect:setIntersect,setSymDifference:setSymDifference,size:size$1,subset:subset,typed:typed}),variance=createVariance({add:add$1,apply:apply,divide:divide$1,isNaN:isNaN$2,multiply:multiply$1,subtract:subtract$1,typed:typed}),kldivergence=createKldivergence({divide:divide$1,dotDivide:dotDivide,isNumeric:isNumeric,log:log$1,matrix:matrix$2,multiply:multiply$1,sum:sum,typed:typed}),norm=createNorm({abs:abs$1,add:add$1,conj:conj$1,ctranspose:ctranspose,eigs:eigs,equalScalar:equalScalar,larger:larger,matrix:matrix$2,multiply:multiply$1,pow:pow$1,smaller:smaller,sqrt:sqrt$1,typed:typed}),planckTime=createPlanckTime({BigNumber:BigNumber,Unit:Unit,config:config$2}),rotationMatrix=createRotationMatrix({BigNumber:BigNumber,DenseMatrix:DenseMatrix,SparseMatrix:SparseMatrix,addScalar:addScalar,config:config$2,cos:cos$1,matrix:matrix$2,multiplyScalar:multiplyScalar,norm:norm,sin:sin$1,typed:typed,unaryMinus:unaryMinus}),gasConstant=createGasConstant({BigNumber:BigNumber,Unit:Unit,config:config$2}),std=createStd({sqrt:sqrt$1,typed:typed,variance:variance}),mad=createMad({abs:abs$1,map:map$1,median:median,subtract:subtract$1,typed:typed}),rotate=createRotate({multiply:multiply$1,rotationMatrix:rotationMatrix,typed:typed}),math$2={},mathWithTransform={},classes={},Chain=createChainClass({math:math$2}),Node=createNode({mathWithTransform:mathWithTransform}),ObjectNode=createObjectNode({Node:Node}),OperatorNode=createOperatorNode({Node:Node}),ParenthesisNode=createParenthesisNode({Node:Node}),RelationalNode=createRelationalNode({Node:Node}),ArrayNode=createArrayNode({Node:Node}),BlockNode=createBlockNode({Node:Node,ResultSet:ResultSet}),ConditionalNode=createConditionalNode({Node:Node}),ConstantNode=createConstantNode({Node:Node}),RangeNode=createRangeNode({Node:Node}),reviver=createReviver({classes:classes}),chain$1=createChain({Chain:Chain,typed:typed}),FunctionAssignmentNode=createFunctionAssignmentNode({Node:Node,typed:typed}),AccessorNode=createAccessorNode({Node:Node,subset:subset}),AssignmentNode=createAssignmentNode({matrix:matrix$2,Node:Node,subset:subset}),IndexNode=createIndexNode({Node:Node,size:size$1}),SymbolNode=createSymbolNode({Unit:Unit,Node:Node,math:math$2}),FunctionNode=createFunctionNode({Node:Node,SymbolNode:SymbolNode,math:math$2}),parse$2=createParse({AccessorNode:AccessorNode,ArrayNode:ArrayNode,AssignmentNode:AssignmentNode,BlockNode:BlockNode,ConditionalNode:ConditionalNode,ConstantNode:ConstantNode,FunctionAssignmentNode:FunctionAssignmentNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,RangeNode:RangeNode,RelationalNode:RelationalNode,SymbolNode:SymbolNode,config:config$2,numeric:numeric,typed:typed}),resolve=createResolve({ConstantNode:ConstantNode,FunctionNode:FunctionNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,parse:parse$2}),simplifyCore=createSimplifyCore({AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,divide:divide$1,equal:equal$1,isZero:isZero,multiply:multiply$1,pow:pow$1,subtract:subtract$1}),compile=createCompile({parse:parse$2,typed:typed}),Help=createHelpClass({parse:parse$2}),leafCount=createLeafCount({parse:parse$2,typed:typed}),simplify$2=createSimplify({bignumber:bignumber,fraction:fraction,AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,config:config$2,divide:divide$1,equal:equal$1,isZero:isZero,mathWithTransform:mathWithTransform,matrix:matrix$2,multiply:multiply$1,parse:parse$2,pow:pow$1,resolve:resolve,simplifyCore:simplifyCore,subtract:subtract$1,typed:typed}),symbolicEqual=createSymbolicEqual({OperatorNode:OperatorNode,parse:parse$2,simplify:simplify$2,typed:typed}),evaluate$1=createEvaluate({parse:parse$2,typed:typed}),help=createHelp({Help:Help,mathWithTransform:mathWithTransform,typed:typed}),Parser=createParserClass({evaluate:evaluate$1}),rationalize=createRationalize({bignumber:bignumber,fraction:fraction,AccessorNode:AccessorNode,ArrayNode:ArrayNode,ConstantNode:ConstantNode,FunctionNode:FunctionNode,IndexNode:IndexNode,ObjectNode:ObjectNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,add:add$1,config:config$2,divide:divide$1,equal:equal$1,isZero:isZero,mathWithTransform:mathWithTransform,matrix:matrix$2,multiply:multiply$1,parse:parse$2,pow:pow$1,simplify:simplify$2,simplifyCore:simplifyCore,subtract:subtract$1,typed:typed}),derivative$1=createDerivative({ConstantNode:ConstantNode,FunctionNode:FunctionNode,OperatorNode:OperatorNode,ParenthesisNode:ParenthesisNode,SymbolNode:SymbolNode,config:config$2,equal:equal$1,isZero:isZero,numeric:numeric,parse:parse$2,simplify:simplify$2,typed:typed}),parser=createParser({Parser:Parser,typed:typed});_extends$1(math$2,{e:e,false:_false,fineStructure:fineStructure,i:i,Infinity:_Infinity,LN10:LN10,LOG10E:LOG10E,NaN:_NaN,null:_null,phi:phi,SQRT1_2:SQRT1_2,sackurTetrode:sackurTetrode,tau:tau,true:_true,E:e,version:version$1,efimovFactor:efimovFactor,LN2:LN2,pi:pi,replacer:replacer,reviver:reviver,SQRT2:SQRT2,typed:typed,unaryPlus:unaryPlus,PI:pi,weakMixingAngle:weakMixingAngle,abs:abs$1,acos:acos$1,acot:acot$1,acsc:acsc$1,addScalar:addScalar,arg:arg,asech:asech$1,asinh:asinh$1,atan: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o=a.length,s=Array(o+1);for(s[0]=0,r=0;r=u){if(i[l]=m[c],0===c)return;++l,s=f[--c],u=p[c]}else 0===n[o=a[r[s]]]?(n[o]=1,f[c]=s,m[++c]=o,s=t[o],p[c]=u=t[o+1]):++s},numeric.ccsLPSolve=function(e,t,r,n,i,a,o){var s=e[0],u=e[1],c=e[2];s.length;var l,f,p,m,d,h,y,g,v,x=t[0],b=t[1],_=t[2];for(f=x[i],p=x[i+1],n.length=0,l=f;la&&(o=i,a=s);for(_(v[r])=c){if(i[f]=a[d[l]],0===l)return;++f,u=p[--l],c=m[l]}else 0===n[s=r[u]]?(n[s]=1,p[l]=u,d[++l]=s,u=t[s=a[s]],m[l]=c=t[s+1]):++u}},numeric.ccsLPSolve0=function(e,t,r,n,i,a,o,s){var u=e[0],c=e[1],l=e[2];u.length;var f,p,m,d,h,y,g,v,x,b=t[0],_=t[1],w=t[2];for(p=b[i],m=b[i+1],n.length=0,f=p;fa&&(o=i,a=s);for(_(v[w[r]])r[n]&&(r[n]=t.length),t)t.hasOwnProperty(i)&&e(t[i],r,n+1);return r},numeric.sclone=function e(t,r,n){void 0===r&&(r=0),void 0===n&&(n=numeric.sdim(t).length);var i,a=Array(t.length);if(r===n-1){for(i in t)t.hasOwnProperty(i)&&(a[i]=t[i]);return a}for(i in t)t.hasOwnProperty(i)&&(a[i]=e(t[i],r+1,n));return a},numeric.sdiag=function(e){var t,r,n=e.length,i=Array(n);for(t=n-1;t>=1;t-=2)r=t-1,i[t]=[],i[t][t]=e[t],i[r]=[],i[r][r]=e[r];return 0===t&&(i[0]=[],i[0][0]=e[t]),i},numeric.sidentity=function(e){return numeric.sdiag(numeric.rep([e],1))},numeric.stranspose=function(e){var t,r,n,i=[];for(t in e.length,e)if(e.hasOwnProperty(t))for(r in n=e[t])n.hasOwnProperty(r)&&("object"!=typeof i[r]&&(i[r]=[]),i[r][t]=n[r]);return i},numeric.sLUP=function(e,t){throw new Error("The function numeric.sLUP had a bug in it and has been removed. 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numeric.sdotMM(e,t);default:throw new Error("numeric.sdot not implemented for tensors of order "+r+" and "+n)}},numeric.sscatter=function(e){var t,r,n,i,a=e[0].length,o=e.length,s=[];for(r=a-1;r>=0;--r)if(e[o-1][r]){for(i=s,n=0;n=0;--a)r[a]=[];for(a=i;a>=0;--a)r[a].push(n[a]);r[i+1].push(o)}}else e(o,r,n);return n.length>i&&n.pop(),r},numeric.cLU=function(e){var t,r,n,i,a,o,s=e[0],u=e[1],c=e[2],l=s.length,f=0;for(t=0;tf&&(f=s[t]);f++;var p,m=Array(f),d=Array(f),h=numeric.rep([f],1/0),y=numeric.rep([f],-1/0);for(n=0;ny[t]&&(y[t]=r);for(t=0;ty[t+1]&&(y[t+1]=y[t]);for(t=f-1;t>=1;t--)h[t]=0;p--){for(;c[m]>p;)i[p]-=l[m]*i[c[m]],m--;i[p]/=l[m],m--}return i},numeric.cgrid=function(e,t){"number"==typeof e&&(e=[e,e]);var r,n,i,a=numeric.rep(e,-1);if("function"!=typeof t)if("L"===t)t=function(t,r){return t>=e[0]/2||ri&&(i=a[n]);for(i++,r=numeric.rep([i],0),n=0;n1;)i[n=o((t+r)/2)]<=e?t=n:r=n;return this._at(e,t)}a=e.length;var s,u=Array(a);for(s=a-1;-1!==s;--s)u[s]=this.at(e[s]);return u},numeric.Spline.prototype.diff=function(){var e,t,r,n=this.x,i=this.yl,a=this.yr,o=this.kl,s=this.kr,u=i.length,c=o,l=s,f=Array(u),p=Array(u),m=numeric.add,d=numeric.mul,h=numeric.div,y=numeric.sub;for(e=u-1;-1!==e;--e)t=n[e+1]-n[e],r=y(a[e+1],i[e]),f[e]=h(m(d(r,6),d(o[e],-4*t),d(s[e+1],-2*t)),t*t),p[e+1]=h(m(d(r,-6),d(o[e],2*t),d(s[e+1],4*t)),t*t);return new numeric.Spline(n,c,l,f,p)},numeric.Spline.prototype.roots=function(){function e(e){return e*e}var t=[],r=this.x,n=this.yl,i=this.yr,a=this.kl,o=this.kr;"number"==typeof n[0]&&(n=[n],i=[i],a=[a],o=[o]);var s,u,c,l,f,p,m,d,h,y,g,v,x,b,_,w,N,$,A,M,S,E,T,O=n.length,C=r.length-1,k=(t=Array(O),Math.sqrt);for(s=0;s!==O;++s){for(l=n[s],f=i[s],p=a[s],m=o[s],d=[],u=0;u!==C;u++){for(u>0&&f[u]*l[u]<0&&d.push(r[u]),w=r[u+1]-r[u],r[u],g=l[u],v=f[u+1],h=p[u]/w,x=(y=m[u+1]/w)+3*g+2*h-3*v,b=3*(y+h+2*(g-v)),(_=e(h-y+3*(g-v))+12*y*g)<=0?N=($=x/b)>r[u]&&$r[u]&&$r[u]&&A0)S=E,$=A;else{for(var D=0;!((T=($*E-A*S)/($-A))<=S||T>=E);)if((M=this._at(T,u))*A>0)E=T,A=M,-1===D&&($*=.5),D=-1;else{if(!(M*$>0))break;S=T,$=M,1===D&&(A*=.5),D=1}d.push(T),S=N[c+1],$=this._at(S,u)}else d.push(S),S=E,$=A;0===A&&d.push(E)}t[s]=d}return"number"==typeof this.yl[0]?t[0]:t},numeric.spline=function(e,t,r,n){var i,a=e.length,o=[],s=[],u=[],c=numeric.sub,l=numeric.mul,f=numeric.add;for(i=a-2;i>=0;i--)s[i]=e[i+1]-e[i],u[i]=c(t[i+1],t[i]);"string"!=typeof r&&"string"!=typeof n||(r=n="periodic");var p=[[],[],[]];switch(typeof r){case"undefined":o[0]=l(3/(s[0]*s[0]),u[0]),p[0].push(0,0),p[1].push(0,1),p[2].push(2/s[0],1/s[0]);break;case"string":o[0]=f(l(3/(s[a-2]*s[a-2]),u[a-2]),l(3/(s[0]*s[0]),u[0])),p[0].push(0,0,0),p[1].push(a-2,0,1),p[2].push(1/s[a-2],2/s[a-2]+2/s[0],1/s[0]);break;default:o[0]=r,p[0].push(0),p[1].push(0),p[2].push(1)}for(i=1;i20)throw new Error("Numerical gradient 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s,u,c,l,f,p,m,d,h,y,g,v,x,b=[e],_=[r],w=[n(e,r)],N=[],$=[3/40,9/40],A=[44/45,-56/15,32/9],M=[19372/6561,-25360/2187,64448/6561,-212/729],S=[9017/3168,-355/33,46732/5247,49/176,-5103/18656],E=[35/384,0,500/1113,125/192,-2187/6784,11/84],T=[.10013431883002395,0,.3918321794184259,-.02982460176594817,.05893268337240795,-.04497888809104361,5618549.5/235043384],O=[.2,.3,.8,8/9,1,1],C=[-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,1/40],k=0,D=(t-e)/10,I=0,B=numeric.add,z=numeric.mul,R=Math.min,P=Math.abs,q=numeric.norminf,L=Math.pow,F=numeric.any,j=numeric.lt,U=numeric.and;numeric.sub;var G=new numeric.Dopri(b,_,w,N,-1,"");for("function"==typeof o&&(g=o(e,r));et&&(D=t-e),s=n(e+O[0]*D,B(r,z(.2*D,w[k]))),u=n(e+O[1]*D,B(B(r,z($[0]*D,w[k])),z($[1]*D,s))),c=n(e+O[2]*D,B(B(B(r,z(A[0]*D,w[k])),z(A[1]*D,s)),z(A[2]*D,u))),l=n(e+O[3]*D,B(B(B(B(r,z(M[0]*D,w[k])),z(M[1]*D,s)),z(M[2]*D,u)),z(M[3]*D,c))),f=n(e+O[4]*D,B(B(B(B(B(r,z(S[0]*D,w[k])),z(S[1]*D,s)),z(S[2]*D,u)),z(S[3]*D,c)),z(S[4]*D,l))),p=n(e+D,h=B(B(B(B(B(r,z(w[k],D*E[0])),z(u,D*E[2])),z(c,D*E[3])),z(l,D*E[4])),z(f,D*E[5]))),(y="number"==typeof(m=B(B(B(B(B(z(w[k],D*C[0]),z(u,D*C[2])),z(c,D*C[3])),z(l,D*C[4])),z(f,D*C[5])),z(p,D*C[6])))?P(m):q(m))>i){if(e+(D=.2*D*L(i/y,.25))===e){G.msg="Step size became too small";break}}else{if(N[k]=B(B(B(B(B(B(r,z(w[k],D*T[0])),z(u,D*T[2])),z(c,D*T[3])),z(l,D*T[4])),z(f,D*T[5])),z(p,D*T[6])),b[++k]=e+D,_[k]=h,w[k]=p,"function"==typeof o){var V,Z,H=e,X=e+.5*D;if(v=o(X,N[k-1]),F(x=U(j(g,0),j(0,v)))||(H=X,g=v,v=o(X=e+D,h),x=U(j(g,0),j(0,v))),F(x)){for(var W,Q,Y=0,J=1,K=1;;){if("number"==typeof g)Z=(K*v*H-J*g*X)/(K*v-J*g);else 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t=e[0],r=e.slice(1);if("apply"===t){if("string"!=typeof r[0])throw Error("Non string functions not implemented for conversion to mathjs");if("factorial"===r[0])return new math.OperatorNode("!","factorial",[this.convert(r[1])]);let e=functionConverstions[r[0]];e||(e=r[0]);const t=new math.SymbolNode(e),n=r[1];let i;return i="tuple"===n[0]?n.slice(1).map(function(e,t){return this.convert(e)}.bind(this)):[this.convert(n)],new math.FunctionNode(t,i)}if("lts"===t||"gts"===t){const e=r[0],n=r[1];if("tuple"!==e[0]||"tuple"!==n[0])throw new Error("Badly formed ast");const i=e.slice(1).map(function(e,t){return this.convert(e)}.bind(this));let a=[];for(let r=1;r","larger",i.slice(r-1,r+1))):"lts"===t?a.push(new math.OperatorNode("<=","smallerEq",i.slice(r-1,r+1))):a.push(new math.OperatorNode(">=","largerEq",i.slice(r-1,r+1)));let o=new math.OperatorNode("and","and",a.slice(0,2));for(let e=2;e=","largerEq",[e,o])):u.push(new math.OperatorNode(">","larger",[e,o])),a[2]?u.push(new 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math.OperatorNode("and","and",p);return"notsubset"!==t&&"notsuperset"!==t||(m=new math.OperatorNode("not","not",[m])),m}if("matrix"===t){let e=r[0],t=e[1],n=e[2],i=r[1];if(!Number.isInteger(t)||!Number.isInteger(n))throw Error("Matrix must have integer dimensions");let a=[];for(let e=1;e<=t;e++){let t=[];for(let r=1;r<=n;r++)t.push(this.convert(i[e][r]));a.push(new math.ArrayNode(t))}return new math.ArrayNode(a)}if(t in operators$2)return operators$2[t](r.map(function(e,t){return this.convert(e)}.bind(this)));throw Error("Operator "+t+" not implemented for conversion to mathjs")}}var function_normalizations={ln:"log",arccos:"acos",arccosh:"acosh",arcsin:"asin",arcsinh:"asinh",arctan:"atan",arctanh:"atanh",arcsec:"asec",arcsech:"asech",arccsc:"acsc",arccsch:"acsch",arccot:"acot",arccoth:"acoth",cosec:"csc"},create_trig_inverses_for=["cos","cosh","sin","sinh","tan","tanh","sec","sech","csc","csch","cot","coth"],move_exponents_outside_for=["cos","cosh","sin","sinh","tan","tanh","sec","sech","csc","csch","cot","coth"];function normalize_function_names(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("apply"===r){if("sqrt"===n[0])return["^",normalize_function_names(n[1]),.5];var i=normalize_function_names_sub(n[0]);i=["apply",i];var a=n.slice(1).map((function(e){return normalize_function_names(e)}));return a=a.length>1?["tuple"].concat(a):a[0],i.push(a),i}return"^"===r&&"e"===n[0]&&math$1.define_e?["apply","exp",normalize_function_names(n[1])]:"binom"===r?["apply","nCr",["tuple",normalize_function_names(n[0]),normalize_function_names(n[1])]]:[r].concat(n.map((function(e){return normalize_function_names(e)})))}function normalize_function_names_sub(e){if("string"==typeof e)return e in function_normalizations?function_normalizations[e]:e;if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if("^"===t&&2===r.length&&-1===r[1]){let e=normalize_function_names_sub(r[0]);if(create_trig_inverses_for.includes(e))return"a"+e}return[t].concat(r.map((function(e){return normalize_function_names_sub(e)})))}function normalize_applied_functions(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("apply"===r){let e=n[0];if("^"===e[0]){let t=e[1],r=e[2];return-1!==r&&move_exponents_outside_for.includes(t)?["^",["apply",t,normalize_applied_functions(n[1])],r]:["apply",e,normalize_applied_functions(n[1])]}let t=0;for(;"prime"===e[0];)t+=1,e=e[1];let r=["apply",e,normalize_applied_functions(n[1])];for(let e=0;e2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_integer_ast(e,o[0],r),is_integer_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_integer_ast(a[0],n,r);if("*"===i){return!!a.every((function(e){return is_integer_ast(e,n,r)}))||void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!is_positive_ast(a[1],n,!0,r))return;if(!1===e)return!0}let t=is_integer_ast(a[0],n,r),i=is_integer_ast(a[1],n,r);if(!t)return t;if(!i)return;return!!is_positive_ast(a[1],n,!1,r)||void 0}if("+"===i){let e=0;for(let t=0;t0)return;e+=1}if(void 0===i)return}return 0===e}if("apply"===i)return!!(functions.C.Z&&functions.C.Z.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.Z&&functions.R.Z.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.Z&&functions.nonzeroC.Z.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.Z&&functions.nonneg.Z.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.Z&&functions.pos.Z.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("/"===i||"prime"===i)return;return!1}return!1}function is_real_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e)return Number.isFinite(e);var n=evaluate_to_constant(e,{remove_units_first:!1,nan_for_non_numeric:!1});if(null!==n)return"number"==typeof n&&Number.isFinite(n);if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}if("in"===a&&o[0]===e&&"R"===o[1])return negate_adjust(!0,s);if("notin"===a&&o[0]===e&&"R"===o[1])return negate_adjust(!1,s);if(!1===s){if("in"===a&&o[0]===e&&"Z"===o[1])return!0}else if("notin"===a&&o[0]===e&&"Z"===o[1])return!0;if("<"===a||"le"===a){let t=variables(n),r=functions$2(n);if(-1!==t.indexOf(e)&&0===r.length)return!0}if("="===a&&!s||"ne"===a&&s){let t=narrow_assumptions(i,r);if(o[0]===e)return is_real_ast(o[1],t);if(o[1]===e)return is_real_ast(o[0],t)}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_real_ast(e,o[0],r),is_real_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_real_ast(a[0],n,r);if("*"===i||"+"===i){if(a.length>2&&(a=(e=unflattenRight(e)).slice(1)),"*"===i&&(!1===is_nonzero_ast(a[0],n,r)||!1===is_nonzero_ast(a[1],n,r)))return!0;let t=is_real_ast(a[0],n,r),o=is_real_ast(a[1],n,r);return!(!t||!o)||!(t&&!1===o||o&&!1===t)&&void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r),t=is_positive_ast(a[1],n,!0,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!t)return;if(!1===e)return!0}let i=is_real_ast(a[0],n,r),o=is_real_ast(a[1],n,r);if(!i||!o)return;if(!is_positive_ast(a[0],n,!1,r)){return!!is_integer_ast(a[1],n,r)||void 0}return!!is_positive_ast(a[0],n,!0,r)||(!!t||void 0)}if("/"===i){if(!is_nonzero_ast(a[1],n,r))return;if(!1===is_nonzero_ast(a[0],n,r))return!0;if(!is_real_ast(a[0],n,r)||!is_real_ast(a[1],n,r))return;return!0}if("apply"===i)return!!(functions.C.R&&functions.C.R.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.R&&functions.R.R.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.R&&functions.nonzeroC.R.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.R&&functions.nonneg.R.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.R&&functions.pos.R.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("prime"===i)return;return!1}return!1}function is_complex_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e)return Number.isFinite(e);var n=evaluate_to_constant(e,{remove_units_first:!1,nan_for_non_numeric:!1});if(null!==n)return"number"==typeof n?Number.isFinite(n):!(void 0===n.re||!Number.isFinite(n.re)||void 0===n.im||!Number.isFinite(n.im));if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}if("in"===a&&o[0]===e&&"C"===o[1])return negate_adjust(!0,s);if("notin"===a&&o[0]===e&&"C"===o[1])return negate_adjust(!1,s);if(!1===s){if("in"===a){if(o[0]===e&&"Z"===o[1])return!0;if(o[0]===e&&"R"===o[1])return!0}}else if("notin"===a){if(o[0]===e&&"Z"===o[1])return!0;if(o[0]===e&&"R"===o[1])return!0}if("<"===a||"le"===a){let t=variables(n),r=functions$2(n);if(-1!==t.indexOf(e)&&0===r.length)return!0}if("="===a&&!s||"ne"===a&&s){let t=narrow_assumptions(i,r);if(o[0]===e)return is_complex_ast(o[1],t);if(o[1]===e)return is_complex_ast(o[0],t)}if("and"!==a&&"or"!==a)return;if(s)return;return o.length>2&&(n=unflattenRight(n),o=n.slice(1)),simple_assumption_combination(a,is_complex_ast(e,o[0],r),is_complex_ast(e,o[1],r))}if(Array.isArray(e)){let n;n=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let i=e[0],a=e.slice(1);if("-"===i)return is_complex_ast(a[0],n,r);if("*"===i||"+"===i){if("*"===i&&!a.every((e=>!1!==is_nonzero_ast(e,n,r))))return!0;return!!a.every((e=>is_complex_ast(e,n,r)))||void 0}if("^"===i){let e=is_nonzero_ast(a[0],n,r),t=is_positive_ast(a[1],n,!0,r);if(e){if(!1===is_nonzero_ast(a[1],n,r))return a[0]!==1/0&&a[0]!==-1/0}else{if(Number.isNaN(a[0]))return!1;if(!t)return;if(!1===e)return!0}let i=is_complex_ast(a[0],n,r),o=is_complex_ast(a[1],n,r);return!(!i||!o)||void 0}if("/"===i){if(!is_nonzero_ast(a[1],n,r))return;if(!1===is_nonzero_ast(a[0],n,r))return!0;if(!is_complex_ast(a[0],n,r)||!is_complex_ast(a[1],n,r))return;return!0}if("apply"===i)return!!(functions.C.C&&functions.C.C.includes(a[0])&&is_complex_ast(a[1],n,r))||(!!(functions.R.C&&functions.R.C.includes(a[0])&&is_real_ast(a[1],n,r))||(!!(functions.nonzeroC.C&&functions.nonzeroC.C.includes(a[0])&&is_nonzero_ast(a[1],n,r)&&is_complex_ast(a[1],n,r))||(!!(functions.nonneg.C&&functions.nonneg.C.includes(a[0])&&is_positive_ast(a[1],n,!1,r))||(!!(functions.pos.C&&functions.pos.C.includes(a[0])&&is_positive_ast(a[1],n,!0,r))||void 0))));if("prime"===i)return;return!1}return!1}function is_nonzero_ast(e,t,r){if("object"!=typeof t&&(t=[]),void 0===r&&(r=t),"number"==typeof e){if(Number.isFinite(e))return 0!==e;if(Number.isNaN(e))return;return!0}var n=evaluate_to_constant(e,{remove_units_first:!1,nan_for_non_numeric:!1});if(null!==n){if("number"==typeof n){if(Number.isFinite(n))return 0!==n;if(Number.isNaN(n))return;return!0}return void 0!==n.re&&void 0!==n.im&&(0!==n.re||0!==n.im)||void 0}if("string"==typeof e){let n;if(n=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(n))return;let i=n,a=n[0],o=n.slice(1),s=!1;for(;"not"===a;){if(s=!s,n=o[0],!Array.isArray(n))return;a=n[0],o=n.slice(1)}let u=narrow_assumptions(i,r);if("="===a&&!s||"ne"===a&&s){if(o[0]===e)return is_nonzero_ast(o[1],u);if(o[1]===e)return 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is_nonzero_ast(a[0],n,r);if("+"===i){if(a.length>2&&(a=(e=unflattenRight(e)).slice(1)),equal(a[0],simplify(["-",a[1]],r)))return!1;let t=is_nonzero_ast(a[0],n,r),i=is_nonzero_ast(a[1],n,r);if(!1===t)return i;if(!1===i)return t;let o=is_real_ast(a[0],n,r),s=is_real_ast(a[1],n,r);if(!o||!s)return!0===o?!1===s||void 0:!0===s&&!1===o||void 0;let u=is_positive_ast(a[0],n,!1,r),c=is_positive_ast(a[1],n,!1,r),l=is_positive_ast(a[0],n,!0,r),f=is_positive_ast(a[1],n,!0,r);return!!(u&&f||l&&c)||(!1===u&&!1===f||!1===l&&!1===c||void 0)}if("*"===i){let e=!0;for(let t=0;t0:e>=0);var i=is_real_ast(e,t,n);if(!i)return i;var a=evaluate_to_constant(e,{remove_units_first:!1,nan_for_non_numeric:!1});if(null!==a)return"number"==typeof a&&(!!Number.isFinite(a)&&(r?a>0:a>=0));if("string"==typeof e){let i;if(i=Array.isArray(t)?t:t.get_assumptions(e),!Array.isArray(i))return;let a=i,o=i[0],s=i.slice(1),u=!1;for(;"not"===o;){if(u=!u,i=s[0],!Array.isArray(i))return;o=i[0],s=i.slice(1)}let c=narrow_assumptions(a,n);if("="===o&&!u||"ne"===o&&u){if(s[0]===e)return is_positive_ast(s[1],c,r);if(s[1]===e)return is_positive_ast(s[0],c,r)}if("<"===o)if(u){if(s[0]===e&&is_positive_ast(s[1],c,r))return!0;if(s[1]===e&&is_negative_ast(s[0],c,!r))return!1}else{if(s[0]===e&&is_negative_ast(s[1],c,!1))return!1;if(s[1]===e&&is_positive_ast(s[0],c,!1))return!0}if("le"===o)if(u){if(s[0]===e&&is_positive_ast(s[1],c,!1))return!0;if(s[1]===e&&is_negative_ast(s[0],c,!1))return!1}else{if(s[0]===e&&is_negative_ast(s[1],c,!r))return!1;if(s[1]===e&&is_positive_ast(s[0],c,r))return!0}if("and"!==o&&"or"!==o)return;if(u)return;return s.length>2&&(i=unflattenRight(i),s=i.slice(1)),simple_assumption_combination(o,is_positive_ast(e,s[0],r,n),is_positive_ast(e,s[1],r,n))}if(Array.isArray(e)){let i;i=Array.isArray(t)?t:t.get_assumptions([variables(e)]);let a=e[0],o=e.slice(1);if("-"===a)return is_negative_ast(o[0],i,r,n);if("+"===a){o.length>2&&(o=(e=unflattenRight(e)).slice(1));let t=is_positive_ast(o[0],i,!1,n),a=is_positive_ast(o[1],i,!1,n),s=is_positive_ast(o[0],i,!0,n),u=is_positive_ast(o[1],i,!0,n);if(r){if(t&&u||s&&a)return!0}else if(t&&a)return!0;if(r){if(!1===s&&!1===u)return!1}else if(!1===t&&!1===u||!1===s&&!1===a)return!1;return}if("*"===a){if(!o.every((e=>!1!==is_nonzero_ast(e,i,n))))return!r;o.length>2&&(o=(e=unflattenRight(e)).slice(1));let t=is_real_ast(o[0],i,n),a=is_real_ast(o[1],i,n);if(void 0===t||void 0===a)return;if(!1===t)return!1===a&&void 0;if(!1===a)return!1;let s=is_positive_ast(o[0],i,!1,n),u=is_positive_ast(o[1],i,!1,n),c=is_positive_ast(o[0],i,!0,n),l=is_positive_ast(o[1],i,!0,n);if(r){if(c&&l||!1===s&&!1===u)return!0;if(!1===c&&u||s&&!1===l)return!1}else{if(s&&u||!1===c&&!1===l)return!0;if(c&&!1===u||!1===s&&l)return!1}return}if("/"===a){if(!is_nonzero_ast(o[1],i,n))return;if(!1===is_nonzero_ast(o[0],i,n))return!r;let e=is_positive_ast(o[1],i,!0,n);if(void 0===e)return;let t=e?r:!r,a=is_positive_ast(o[0],i,t,n);if(void 0===a)return;return!0===a?!0===e:!0!==e}if("^"===a){let e=is_nonzero_ast(o[0],i,n);if(e){if(!1===is_nonzero_ast(o[1],i,n)){if(o[0]===1/0||o[0]===-1/0)return;return!0}}else{if(!is_positive_ast(o[1],i,!0,n))return;if(!1===e)return!r;if(r)return}if(!0!==is_real_ast(o[0],i,n))return;if(!is_positive_ast(o[0],i,r,n)){return!!is_integer_ast(simplify(["/",o[1],2],n),i,n)||void 0}return!!is_real_ast(o[1],i,n)||void 0}if("apply"===a&&!r)return!!(functions.C.nonneg&&functions.C.nonneg.includes(o[0])&&is_complex_ast(o[1],i,n))||(!!(functions.R.nonneg&&functions.R.nonneg.includes(o[0])&&is_real_ast(o[1],i,n))||(!!(functions.nonzeroC.nonneg&&functions.nonzeroC.nonneg.includes(o[0])&&is_nonzero_ast(o[1],i,n)&&is_complex_ast(o[1],i,n))||(!!(functions.nonneg.nonneg&&functions.nonneg.nonneg.includes(o[0])&&is_positive_ast(o[1],i,!1,n))||(!!(functions.pos.nonneg&&functions.pos.nonneg.includes(o[0])&&is_positive_ast(o[1],i,!0,n))||void 0))));if("apply"===a&&r)return!!(functions.C.pos&&functions.C.pos.includes(o[0])&&is_complex_ast(o[1],i,n))||(!!(functions.R.pos&&functions.R.pos.includes(o[0])&&is_real_ast(o[1],i,n))||(!!(functions.nonzeroC.pos&&functions.nonzeroC.pos.includes(o[0])&&is_nonzero_ast(o[1],i,n)&&is_complex_ast(o[1],i,n))||(!!(functions.nonneg.pos&&functions.nonneg.pos.includes(o[0])&&is_positive_ast(o[1],i,!1,n))||(!!(functions.pos.pos&&functions.pos.pos.includes(o[0])&&is_positive_ast(o[1],i,!0,n))||void 0))));if("prime"===a)return;return!1}return!1}function is_negative_ast(e,t,r,n){void 0===r&&(r=!0);var i=is_real_ast(e,t,n);if(!0===i){let i=is_positive_ast(e,t,!r,n);return!1===i||!0!==i&&void 0}return i}function tuples_to_vectors(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("tuple"===r){return["vector"].concat(n.map((function(e,t){return tuples_to_vectors(e)})))}if("apply"===r){if("tuple"===n[1][0]){let e=tuples_to_vectors(n[0]),t=n[1].slice(1);return["apply",e,["tuple"].concat(t.map((function(e,t){return tuples_to_vectors(e)})))]}}else if("gts"===r||"lts"===r||"interval"===r){let e=n[0],t=n[1];if("tuple"!==e[0]||"tuple"!==t[0])throw new Error("Badly formed ast");return[r,["tuple"].concat(e.slice(1).map((function(e,t){return tuples_to_vectors(e)}))),t]}return[r].concat(n.map((function(e,t){return tuples_to_vectors(e)})))}function to_intervals(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("tuple"===r&&2===n.length){let e=["tuple"].concat(n.map((function(e,t){return to_intervals(e)})));return e=["interval",e,["tuple",!1,!1]],e}if("array"===r&&2===n.length){let e=["tuple"].concat(n.map((function(e,t){return to_intervals(e)})));return e=["interval",e,["tuple",!0,!0]],e}if("apply"===r){if("tuple"===n[1][0]){let e=to_intervals(n[0]),t=n[1].slice(1);return["apply",e,["tuple"].concat(t.map((function(e,t){return to_intervals(e)})))]}}else if("gts"===r||"lts"===r||"interval"===r){let e=n[0],t=n[1];if("tuple"!==e[0]||"tuple"!==t[0])throw new Error("Badly formed ast");return[r,["tuple"].concat(e.slice(1).map((function(e,t){return to_intervals(e)}))),t]}return[r].concat(n.map((function(e,t){return to_intervals(e)})))}function altvectors_to_vectors(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if("altvector"===r){return["vector"].concat(n.map((function(e,t){return altvectors_to_vectors(e)})))}return[r].concat(n.map((function(e,t){return altvectors_to_vectors(e)})))}function ParseError(e,t){this.name="ParseError",this.message=e||"Error parsing input",this.stack=(new Error).stack,this.location=t}functions.C.nonneg=["abs"],functions.C.nonzero=["exp"],functions.C.R=["abs","arg"],functions.C.C=["abs","arg","exp","sign","cos","cosh","sin","sinh","erf","sqrt","log","ln","log10"],functions.R.pos=["exp"],functions.R.nonneg=["abs","exp","arg"],functions.R.R=["abs","arg","exp","sign","cos","cosh","sin","sinh","erf"],functions.R.Z=["sign"],functions.nonzeroC.pos=["abs"],functions.nonneg.nonneg=["abs","exp","arg","sqrt","erf"],functions.nonzeroC.nonzero=["abs"],functions.nonneg.R=[...new Set(functions.R.R.concat(functions.nonneg.nonneg))],functions.pos.pos=["abs","exp","sqrt","erf"],functions.pos.nonneg=functions.pos.pos,functions.pos.nonzero=["abs","exp","sqrt","erf"],functions.pos.R=functions.nonneg.R.concat(["log","ln","log10"]),ParseError.prototype=Object.create(Error.prototype),ParseError.prototype.constructor=ParseError;class lexer{constructor(e,t="\\s"){this.input="",this.location=0,this.token_rules=[],this.initial_whitespace=new RegExp("^("+t+")+");for(let t of e)this.token_rules.push([new RegExp("^"+t[0])].concat(t.slice(1)))}set_input(e){if("string"!=typeof e)throw new Error("Input must be a string");this.input=e,this.location=0}return_state(){return{input:this.input,location:this.location}}set_state({input:e=null,location:t=0}={}){null!==e&&(this.input=e,this.location=t)}advance({remove_initial_space:e=!0}={}){let t=this.initial_whitespace.exec(this.input);if(t){let r=t[0].length;if(this.input=this.input.slice(r),this.location+=r,!e)return{token_type:"SPACE",token_text:t[0],original_text:t[0]}}if(0===this.input.length)return{token_type:"EOF",token_text:"",original_text:""};for(var r of(t=null,this.token_rules))if(t=r[0].exec(this.input),t){let e=t[0].length;this.input=this.input.slice(e),this.location+=e;break}return null===t?{token_type:"INVALID",token_text:this.input[0],original_text:this.input[0]}:r.length>2?{token_type:r[1],token_text:r[2],original_text:t[0]}:{token_type:r[1],token_text:t[0],original_text:t[0]}}unput(e){if("string"!=typeof e)throw new Error("Input must be a string");this.location-=e.length,this.input=e+this.input}}var is_associative={"+":!0,"*":!0,and:!0,or:!0,union:!0,intersect:!0};function flatten(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if(r=r.map((function(e,t){return flatten(e)})),is_associative[t]){for(var n=[],i=0;i2?n=n.concat(r[i].slice(1)):n.push(r[i]);r=n}return[t].concat(r)}const sci_notat_exp_regex$1="(E[+\\-]?[0-9]+\\s*($|(?=\\,|\\||\\)|\\}|\\])))?",number_rules_sci$1=[["[0-9]+(\\.[0-9]*)?"+sci_notat_exp_regex$1,"NUMBER"],["\\.[0-9]+"+sci_notat_exp_regex$1,"NUMBER"]],number_rules_non_sci$1=[["[0-9]+(\\.[0-9]*)?","NUMBER"],["\\.[0-9]+","NUMBER"]],base_text_rules=[["\\*\\*","^"],["\\*","*"],["\\xB7","*"],["·","*"],["•","*"],["⋅","*"],["×","*"],["/","/"],["-","-"],["֊","-"],["־","-"],["᠆","-"],["‐","-"],["‑","-"],["‒","-"],["–","-"],["—","-"],["―","-"],["⁻","-"],["₋","-"],["−","-"],["⸺","-"],["⸻","-"],["﹘","-"],["﹣","-"],["－","-"],["\\+","+"],["\\^","^"],["‸","^"],["ʌ","^"],["\\|","|"],["\\(","("],["\\)",")"],["\\[","["],["\\]","]"],["\\{","{"],["\\}","}"],["⟨","LANGLE"],["⟩","RANGLE"],["〈","LANGLE"],["〉","RANGLE"],[",",","],[":",":"],["α","VARMULTICHAR","alpha"],["β","VARMULTICHAR","beta"],["ϐ","VARMULTICHAR","beta"],["Γ","VARMULTICHAR","Gamma"],["γ","VARMULTICHAR","gamma"],["Δ","VARMULTICHAR","Delta"],["δ","VARMULTICHAR","delta"],["ε","VARMULTICHAR","epsilon"],["ϵ","VARMULTICHAR","epsilon"],["ζ","VARMULTICHAR","zeta"],["η","VARMULTICHAR","eta"],["Θ","VARMULTICHAR","Theta"],["ϴ","VARMULTICHAR","Theta"],["θ","VARMULTICHAR","theta"],["ᶿ","VARMULTICHAR","theta"],["ϑ","VARMULTICHAR","theta"],["ι","VARMULTICHAR","iota"],["κ","VARMULTICHAR","kappa"],["Λ","VARMULTICHAR","Lambda"],["λ","VARMULTICHAR","lambda"],["μ","VARMULTICHAR","mu"],["µ","VARMULTICHAR","mu"],["ν","VARMULTICHAR","nu"],["Ξ","VARMULTICHAR","Xi"],["ξ","VARMULTICHAR","xi"],["Π","VARMULTICHAR","Pi"],["π","VARMULTICHAR","pi"],["ϖ","VARMULTICHAR","pi"],["ρ","VARMULTICHAR","rho"],["ϱ","VARMULTICHAR","rho"],["Σ","VARMULTICHAR","Sigma"],["σ","VARMULTICHAR","sigma"],["ς","VARMULTICHAR","sigma"],["τ","VARMULTICHAR","tau"],["Υ","VARMULTICHAR","Upsilon"],["υ","VARMULTICHAR","upsilon"],["Φ","VARMULTICHAR","Phi"],["φ","VARMULTICHAR","phi"],["ϕ","VARMULTICHAR","phi"],["Ψ","VARMULTICHAR","Psi"],["ψ","VARMULTICHAR","psi"],["Ω","VARMULTICHAR","Omega"],["ω","VARMULTICHAR","omega"],["oo(?![a-zA-Z0-9])","INFINITY"],["OO(?![a-zA-Z0-9])","INFINITY"],["infty(?![a-zA-Z0-9])","INFINITY"],["infinity(?![a-zA-Z0-9])","INFINITY"],["Infinity(?![a-zA-Z0-9])","INFINITY"],["∞","INFINITY"],["ℯ","VAR","e"],["♠","VARMULTICHAR","spade"],["♡","VARMULTICHAR","heart"],["♢","VARMULTICHAR","diamond"],["♣","VARMULTICHAR","club"],["★","VARMULTICHAR","bigstar"],["◯","VARMULTICHAR","bigcirc"],["◊","VARMULTICHAR","lozenge"],["△","VARMULTICHAR","bigtriangleup"],["▽","VARMULTICHAR","bigtriangledown"],["⧫","VARMULTICHAR","blacklozenge"],["■","VARMULTICHAR","blacksquare"],["▲","VARMULTICHAR","blacktriangle"],["▼","VARMULTICHAR","blacktriangledown"],["◀","VARMULTICHAR","blacktriangleleft"],["▶","VARMULTICHAR","blacktriangleright"],["□","VARMULTICHAR","Box"],["∘","VARMULTICHAR","circ"],["⋆","VARMULTICHAR","star"],["and(?![a-zA-Z0-9])","AND"],["\\&\\&?","AND"],["∧","AND"],["or(?![a-zA-Z0-9])","OR"],["∨","OR"],["not(?![a-zA-Z0-9])","NOT"],["¬","NOT"],["=","="],["᐀","="],["゠","="],["!=","NE"],["≠","NE"],["<=","LE"],["≤","LE"],[">=","GE"],["≥","GE"],["<","<"],[">",">"],["forall(?![a-zA-Z0-9])","FORALL"],["∀","FORALL"],["exists(?![a-zA-Z0-9])","EXISTS"],["∃","EXISTS"],["elementof(?![a-zA-Z0-9])","IN"],["∈","IN"],["notelementof(?![a-zA-Z0-9])","NOTIN"],["∉","NOTIN"],["containselement(?![a-zA-Z0-9])","NI"],["∋","NI"],["notcontainselement(?![a-zA-Z0-9])","NOTNI"],["∌","NOTNI"],["subset(?![a-zA-Z0-9])","SUBSET"],["⊂","SUBSET"],["subseteq(?![a-zA-Z0-9])","SUBSETEQ"],["⊆","SUBSETEQ"],["notsubset(?![a-zA-Z0-9])","NOTSUBSET"],["⊄","NOTSUBSET"],["notsubseteq(?![a-zA-Z0-9])","NOTSUBSETEQ"],["⊈","NOTSUBSETEQ"],["superset(?![a-zA-Z0-9])","SUPERSET"],["⊃","SUPERSET"],["superseteq(?![a-zA-Z0-9])","SUPERSETEQ"],["⊇","SUPERSETEQ"],["notsuperset(?![a-zA-Z0-9])","NOTSUPERSET"],["⊅","NOTSUPERSET"],["notsuperseteq(?![a-zA-Z0-9])","NOTSUPERSETEQ"],["⊉","NOTSUPERSETEQ"],["union(?![a-zA-Z0-9])","UNION"],["∪","UNION"],["intersect(?![a-zA-Z0-9])","INTERSECT"],["∩","INTERSECT"],["perp(?![a-zA-Z0-9])","PERP"],["⟂","PERP"],["parallel(?![a-zA-Z0-9])","PARALLEL"],["∥","PARALLEL"],["angle(?![a-zA-Z0-9])","ANGLE"],["∠","ANGLE"],["int(?![a-zA-Z0-9])","INT"],["∫","INT"],["!","!"],["'","'"],["_","_"],["\\.\\.\\.","LDOTS"],["[a-zA-Z∂][a-zA-Z∂0-9]*","VAR"],["[＿$%]","VAR"]],allowSimplifiedFunctionApplicationDefault$1=!0,splitSymbolsDefault=!0,unsplitSymbolsDefault=["alpha","beta","gamma","Gamma","delta","Delta","epsilon","zeta","eta","theta","Theta","iota","kappa","lambda","Lambda","mu","nu","xi","Xi","pi","Pi","rho","sigma","Sigma","tau","Tau","upsilon","Upsilon","phi","Phi","chi","psi","Psi","omega","Omega","angle","deg"],appliedFunctionSymbolsDefault$1=["abs","exp","log","ln","log10","sign","sqrt","erf","cos","cosh","acos","acosh","arccos","arccosh","cot","coth","acot","acoth","arccot","arccoth","csc","csch","acsc","acsch","arccsc","arccsch","sec","sech","asec","asech","arcsec","arcsech","sin","sinh","asin","asinh","arcsin","arcsinh","tan","tanh","atan","atan2","atanh","arctan","arctanh","arg","conj","re","im","det"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textToAst$4{constructor({allowSimplifiedFunctionApplication:e=allowSimplifiedFunctionApplicationDefault$1,splitSymbols:t=splitSymbolsDefault,unsplitSymbols:r=unsplitSymbolsDefault,appliedFunctionSymbols:n=appliedFunctionSymbolsDefault$1,functionSymbols:i=functionSymbolsDefault$1,operatorSymbols:a=operatorSymbolsDefault$1,units:o=unitsDefault$1,parseLeibnizNotation:s=parseLeibnizNotationDefault$1,parseScientificNotation:u=!0}={}){this.allowSimplifiedFunctionApplication=e,this.splitSymbols=t,this.unsplitSymbols=r,this.appliedFunctionSymbols=n,this.functionSymbols=i,this.operatorSymbols=a,this.units=o,this.parseLeibnizNotation=s;let c=base_text_rules;c=u?[...number_rules_sci$1,...c]:[...number_rules_non_sci$1,...c],this.lexer=new lexer(c)}advance(e){if(this.token=this.lexer.advance(e),"INVALID"===this.token.token_type)throw new ParseError("Invalid symbol '"+this.token.original_text+"'",this.lexer.location)}return_state(){return{lexer_state:this.lexer.return_state(),token:Object.assign({},this.token)}}set_state(e){this.lexer.set_state(e.lexer_state),this.token=Object.assign({},e.token)}convert(e){this.lexer.set_input(e),this.advance();var t=this.statement_list();if("EOF"!==this.token.token_type)throw new ParseError("Invalid location of '"+this.token.original_text+"'",this.lexer.location);return flatten(t)}statement_list(){for(var e=[this.statement()];","===this.token.token_type;)this.advance(),e.push(this.statement());return e=e.length>1?["list"].concat(e):e[0]}statement({inside_absolute_value:e=0}={}){if("LDOTS"===this.token.token_type)return this.advance(),["ldots"];var t;try{t=this.return_state();let r=this.statement_a({inside_absolute_value:e});return":"!==this.token.token_type?r:(this.advance(),[":",r,this.statement_a()])}catch(e){try{this.set_state(t);let r=this.statement_a({parse_absolute_value:!1});if("|"!==this.token.token_type)throw e;return this.advance(),["|",r,this.statement_a({parse_absolute_value:!1})]}catch(t){throw e}}}statement_a({inside_absolute_value:e=0,parse_absolute_value:t=!0}={}){for(var r=this.statement_b({inside_absolute_value:e,parse_absolute_value:t});"OR"===this.token.token_type;){let n=this.token.token_type.toLowerCase();this.advance(),r=[n,r,this.statement_b({inside_absolute_value:e,parse_absolute_value:t})]}return r}statement_b(e){for(var t=this.relation(e);"AND"===this.token.token_type;){let r=this.token.token_type.toLowerCase();this.advance(),t=[r,t,this.relation(e)]}return t}relation(e){if("NOT"===this.token.token_type||"!"===this.token.token_type)return this.advance(),["not",this.relation(e)];if("FORALL"===this.token.token_type||"EXISTS"===this.token.token_type){let t=this.token.token_type.toLowerCase();return this.advance(),[t,this.relation(e)]}for(var t=this.expression(e);"="===this.token.token_type||"NE"===this.token.token_type||"<"===this.token.token_type||">"===this.token.token_type||"LE"===this.token.token_type||"GE"===this.token.token_type||"IN"===this.token.token_type||"NOTIN"===this.token.token_type||"NI"===this.token.token_type||"NOTNI"===this.token.token_type||"SUBSET"===this.token.token_type||"NOTSUBSET"===this.token.token_type||"SUBSETEQ"===this.token.token_type||"NOTSUBSETEQ"===this.token.token_type||"SUPERSET"===this.token.token_type||"NOTSUPERSET"===this.token.token_type||"SUPERSETEQ"===this.token.token_type||"NOTSUPERSETEQ"===this.token.token_type;){let r=this.token.token_type.toLowerCase(),n=0;"<"===this.token.token_type||"LE"===this.token.token_type?n=-1:">"!==this.token.token_type&&"GE"!==this.token.token_type||(n=1),this.advance();let i=this.expression(e);if(-1===n)if("<"===this.token.token_type||"LE"===this.token.token_type){let n=["tuple"];"<"===r?n.push(!0):n.push(!1);let a=["tuple",t,i];for(;"<"===this.token.token_type||"LE"===this.token.token_type;)"<"===this.token.token_type?n.push(!0):n.push(!1),this.advance(),a.push(this.expression(e));t=["lts",a,n]}else t=[r,t,i];else if(1===n)if(">"===this.token.token_type||"GE"===this.token.token_type){let n=["tuple"];">"===r?n.push(!0):n.push(!1);let a=["tuple",t,i];for(;">"===this.token.token_type||"GE"===this.token.token_type;)">"===this.token.token_type?n.push(!0):n.push(!1),this.advance(),a.push(this.expression(e));t=["gts",a,n]}else t=[r,t,i];else if("="===r)for(t=["=",t,i];"="===this.token.token_type;)this.advance(),t.push(this.expression(e));else t=[r,t,i]}return t}expression(e){let t=!1;"+"===this.token.token_type&&(t=!0,this.advance());let r=!1;"-"===this.token.token_type&&(r=!0,this.advance());var n=this.term(e);if(r||t){if(!1===n)return(t?"+":"")+(r?"-":"");if("string"==typeof n&&[...n].every((e=>["+","-"].includes(e))))return(t?"+":"")+(r?"-":"")+n}for(!1===n&&(n="＿"),r&&(n=n>0?-n:["-",n]),t&&(n=["+",n]);["+","-","UNION","INTERSECT","PERP","PARALLEL"].includes(this.token.token_type);){let t=this.token.token_type.toLowerCase(),r=!1,i=!1;"-"===this.token.token_type?(t="+",r=!0,this.advance()):(this.advance(),"+"===t&&"-"===this.token.token_type&&(r=!0,i=!0,this.advance()));let a=this.term(e);if("+"===t){if(!1===a&&("number"==typeof n||"string"==typeof n))return i?n+"+-":r?n+"-":n+"+";if("string"==typeof a&&[...a].every((e=>["+","-"].includes(e)))&&("number"==typeof n||"string"==typeof n))return i?n+"+-"+a:r?n+"-"+a:n+"+"+a}!1===a&&(a="＿"),r&&(a=a>0?-a:["-",a]),n=[t,n,a]}return n}term(e){var t=this.factor(e),r=!1;do{if(r=!1,"*"===this.token.token_type){this.advance(),!1===t&&(t="＿");let n=this.factor(e);!1===n&&(n="＿"),t=["*",t,n],r=!0}else if("/"===this.token.token_type){this.advance(),!1===t&&(t="＿");let n=this.factor(e);!1===n&&(n="＿"),t=["/",t,n],r=!0}else{let n=Object.assign({},e);n.allow_absolute_value_closing=!0;let i=this.nonMinusFactor(n);!1!==i&&(!1===t&&(t="＿"),t=["*",t,i],r=!0)}}while(r);return this.convert_units_in_term(flatten(t))}convert_units_in_term(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("*"===t){let t=r.length;for(let[e,n]of r.entries()){let i=this.units[n];if(i){if(i.prefix&&e0){let a,o=n;return i.substitute&&(o=i.substitute),a=1===e?["unit",r[0],o]:["unit",["*",...r.slice(0,e)],o],e===t-1?a:this.convert_units_in_term(["*",a,...r.slice(e+1)])}}}return e}return"/"===t?["/",this.convert_units_in_term(r[0]),this.convert_units_in_term(r[1])]:e}factor(e){if("+"===this.token.token_text){this.advance();let t=this.factor(e);return!1===t?"+":"string"==typeof t&&[...t].every((e=>["+","-"].includes(e)))?"+"+t:["+",t]}if("-"===this.token.token_type){this.advance();let t=this.factor(e);return t>0?-t:!1===t?"-":"string"==typeof t&&[...t].every((e=>["+","-"].includes(e)))?"-"+t:["-",t]}let t=this.nonMinusFactor(e);return!1===t&&"PERP"===this.token.token_type&&(t="perp",this.advance()),t}nonMinusFactor(e){for(var t=this.baseFactor(e);"^"===this.token.token_type||"!"===this.token.token_type||"'"===this.token.token_type;)if(!1===t&&(t="＿"),"^"===this.token.token_type){this.advance(),t=["^",t,this.get_subsuperscript(e)]}else"!"===this.token.token_type?(t=["apply","factorial",t],this.advance()):(t=["prime",t],this.advance());return t}get_subsuperscript({parse_absolute_value:e}){if(["+","-","PERP"].includes(this.token.token_type)){let e=this.token.token_type.toLowerCase();return this.advance(),e}{let t=this.baseFactor({parse_absolute_value:e,in_subsuperscript_with_no_delimiters:!0});return!1===t&&(t="＿"),t}}baseFactor({inside_absolute_value:e=0,parse_absolute_value:t=!0,allow_absolute_value_closing:r=!1,in_subsuperscript_with_no_delimiters:n=!1}={}){var i=!1;if("NUMBER"===this.token.token_type)i=parseFloat(this.token.token_text),this.advance();else if("INFINITY"===this.token.token_type)i=1/0,this.advance();else if("VAR"===this.token.token_type||"VARMULTICHAR"===this.token.token_type){if(i=this.token.token_text,this.appliedFunctionSymbols.includes(i)||this.functionSymbols.includes(i)){let e=!1;if(this.appliedFunctionSymbols.includes(i)&&(e=!0),this.advance(),"_"===this.token.token_type){this.advance();let e=this.get_subsuperscript({parse_absolute_value:t});i="log"===i&&10===e?"log10":["_",i,e]}if(n)e&&(i=["apply",i,"＿"]);else{for(;"'"===this.token.token_type;)i=["prime",i],this.advance();for(;"^"===this.token.token_type;){this.advance(),i=["^",i,this.get_subsuperscript({parse_absolute_value:t})]}if("("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),"list"===e[0]&&(e[0]="tuple"),i=["apply",i,e]}else if(e){if(!this.allowSimplifiedFunctionApplication)throw new ParseError("Expecting ( after function",this.lexer.location);let e=this.factor({parse_absolute_value:t});!1===e&&(e="＿"),i=["apply",i,e]}}return i}if(this.operatorSymbols.includes(i))if(this.advance(),"("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),i="list"===e[0]?[i,...e.slice(1)]:[i,e]}else{let e=this.factor({parse_absolute_value:t});!1===e&&(e="＿"),i=[i,e]}else{if(this.parseLeibnizNotation){let e=this.return_state(),t=this.leibniz_notation();if(t)return t;this.set_state(e)}let n=this.splitSymbols;if(n&&("VARMULTICHAR"===this.token.token_type||this.unsplitSymbols.includes(i)||1===i.length||i.match(/[\d]/g))&&(n=!1),n){for(let e=i.length-1;e>=0;e--)this.lexer.unput(" "),this.lexer.unput(i[e]);return this.advance(),this.baseFactor({inside_absolute_value:e,parse_absolute_value:t,allow_absolute_value_closing:r})}this.advance()}}else if("("===this.token.token_type||"["===this.token.token_type||"{"===this.token.token_type||"LANGLE"===this.token.token_type){let e,t,r=this.token.token_type;"("===this.token.token_type?(e=")",t="]"):"["===this.token.token_type?(e="]",t=")"):"{"===this.token.token_type?(e="}",t=null):(e="RANGLE",t=null),this.advance();let n=1;if("list"===(i=this.statement_list())[0]&&(n=i.length-1),this.token.token_type!==e){if(2!==n||null===t)throw new ParseError("Expecting "+e,this.lexer.location);if(this.token.token_type!==t)throw new ParseError("Expecting ) or ]",this.lexer.location);let a;i[0]="tuple",a="("===r?["tuple",!1,!0]:["tuple",!0,!1],(i=["interval",i]).push(a)}else n>=2?i[0]="("===r?"tuple":"["===r?"array":"{"===r?"set":"altvector":"{"===r&&(i=("|"===i[0]||i[0],["set",i]));this.advance()}else if("|"!==this.token.token_type||!t||0!==e&&r){if("ANGLE"===this.token.token_type)if(this.advance(),"("===this.token.token_type){this.advance();let e=this.statement_list();if(")"!==this.token.token_type)throw new ParseError("Expecting )",this.lexer.location);this.advance(),"list"===e[0]?i=["angle",...e.slice(1)]:"*"===e[0]&&(i=["angle",e])}else{let e=[],r=this.nonMinusFactor({parse_absolute_value:t});for(;!1!==r;)e.push(r),r=this.nonMinusFactor({parse_absolute_value:t});i=0===e.length?"angle":["angle",...e]}else if("INT"===this.token.token_type){this.advance();let e="int";if("_"===this.token.token_type){this.advance(),e=["_",e,this.get_subsuperscript({parse_absolute_value:t})]}if("^"===this.token.token_type){this.advance(),e=["^",e,this.get_subsuperscript({parse_absolute_value:t})]}let r=flatten(this.term({parse_absolute_value:t}));if(Array.isArray(r)&&"*"===r[0]){let e=[];for(let t=0;t2&&(this.lexer.unput(this.token.token_text.slice(2)),this.token.token_text=this.token.token_text.slice(0,2));let s=this.token.token_text;if(2===s.length){if(!/[a-zA-Z]/.exec(s[1]))return!1;i.push(s[1])}else{if(this.advance(),("VAR"!==this.token.token_type||this.token.token_text.includes("∂"))&&"VARMULTICHAR"!==this.token.token_type)return!1;i.push(this.token.token_text)}let u=1,c=!1;if(this.advance({remove_initial_space:!1}),"SPACE"===this.token.token_type&&(c=!0,this.advance()),"^"===this.token.token_type){if(this.advance(),"NUMBER"!==this.token.token_type)return!1;if(u=parseFloat(this.token.token_text),!Number.isInteger(u))return!1;c=!1,this.advance({remove_initial_space:!1}),"SPACE"===this.token.token_type&&(c=!0,this.advance())}if(a.push(u),o+=u,o>r)return!1;if(o===r){if(!c&&("VAR"===this.token.token_type||"VARMULTICHAR"===this.token.token_type))return!1;"SPACE"===this.token.token_type&&this.advance();let o="derivative_leibniz";"∂"===t&&(o="partial_"+o),e=[o],1===r?e.push(n):e.push(["tuple",n,r]);let s=[];for(let e=0;et[e+1]));if(t.length!==n||i.length!==n)return subtree;let a=["+",...t.map(((e,t)=>["*",e,i[t]]))];r.push(a)}s.push(r)}return{success:!0,newMatrix:["matrix",["tuple",r,i],s]}}function a(e,t){let r=e[1][1],n=e[1][2],i=e[2],a=["tuple"];for(let e=0;e=0;t--){let n=r[t][0];if("matrix"===n){let n=i(r[t],e);if(!n.success)break;e=n.newMatrix,r.pop()}else{if(["tuple","list","vector","altvector","interval","set","array"].includes(n))break;1!==r[t]&&(e=a(e,r[t])),r.pop()}}for(;n.length>0;){let t=n[0][0];if("matrix"===t){let t=i(e,n[0]);if(!t.success)break;e=t.newMatrix,n.splice(0,1)}else{if(["tuple","list","vector","altvector","interval","set","array"].includes(t))break;1!==n[0]&&(e=a(e,n[0])),n.splice(0,1)}}return r.length>0||n.length>0?["*",...r,e,...n]:e}return e})),(t||r)&&(o=["*",["matrix",["tuple","m","n"],"matrixData"],"b"],s={variables:{n:Number.isInteger,m:Number.isInteger,matrixData:!0,b:!0}},n=transform(n,(function(e){let n=match$2(e,o,s);if(n){let i,a=n.m,o=n.n,s=n.b,u=n.matrixData,c=[];t&&(c.push("vector"),c.push("altvector")),r&&c.push("tuple");let l=[];if(c.includes(s[0]))i=s;else{if(!Array.isArray(s)||"*"!==s[0]||!c.includes(s[1][0]))return e;i=s[1],l=s.slice(2)}let f=i.slice(1);if(f.length!==o)return e;let p=[i[0]];for(let e=0;e["*",e,f[t]]))];p.push(t)}return l.length>0?["*",p,...l]:p}return e}))),n}function perform_vector_scalar_multiplications(e,t=!0){var r=get_tree(e);let n=function(e,t){let r=["*","a",[t,"vectorData"],"b"],n={allow_implicit_identities:["a","b"]};return e=transform(e,(function(e){let i=match$2(e,r,n);if(i){if(1===i.a&&1===i.b)return e;let r=i.vectorData;r=Array.isArray(r)&&r[0]===t?r.slice(1):[r];let n=[],a=[];Array.isArray(i.a)&&"*"===i.a[0]?n.push(...i.a.slice(1)):n.push(i.a),Array.isArray(i.b)&&"*"===i.b[0]?a.push(...i.b.slice(1)):a.push(i.b);for(let e=n.length-1;e>=0;e--){let t=n[e][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t))break;1!==n[e]&&(r=r.map((t=>["*",t,n[e]]))),n.pop()}for(;a.length>0;){let e=a[0][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(e))break;1!==a[0]&&(r=r.map((e=>["*",e,a[0]]))),a.splice(0,1)}let o=[t,...r];return n.length>0||a.length>0?["*",...n,o,...a]:o}return e})),e};return r=n(r,"vector"),r=n(r,"altvector"),t&&(r=n(r,"tuple")),r}function perform_matrix_scalar_multiplications(e){var t=get_tree(e);let r=["*","a",["matrix","size","matrixData"],"b"],n={allow_implicit_identities:["a","b"]};return t=transform(t,(function(e){let t=match$2(e,r,n);if(t){if(1===t.a&&1===t.b)return e;let r=t.matrixData,n=[],i=[];Array.isArray(t.a)&&"*"===t.a[0]?n.push(...t.a.slice(1)):n.push(t.a),Array.isArray(t.b)&&"*"===t.b[0]?i.push(...t.b.slice(1)):i.push(t.b);for(let e=n.length-1;e>=0;e--){let t=n[e][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(t))break;1!==n[e]&&(r=r.map((t=>"tuple"===t?t:t.map((t=>"tuple"===t?t:["*",t,n[e]]))))),n.pop()}for(;i.length>0;){let e=i[0][0];if(["tuple","list","vector","altvector","interval","set","array","matrix"].includes(e))break;1!==i[0]&&(r=r.map((e=>"tuple"===e?e:e.map((e=>"tuple"===e?e:["*",e,i[0]]))))),i.splice(0,1)}let a=["matrix",t.size,r];return n.length>0||i.length>0?["*",...n,a,...i]:a}return e})),t}function expand_relations(e){var t=get_tree(e);return transform(t,expand_relations_transform)}function expand_relations_transform(e){if(!Array.isArray(e))return e;var t=e[0],r=e.slice(1);if("="===t){if(r.length<=2)return e;let t=["and"];for(let e=0;e":"lts"===t?"le":"ge",i.push([a,e[r],e[r+1]])}let a=["and",i[0],i[1]];for(let e=2;e",n,c]),s[2]?a?f.push([">",n,l]):f.push(["le",n,l]):a?f.push(["ge",n,l]):f.push(["<",n,l]),u=a?["or"].concat(f):["and"].concat(f),u}if("subset"===t||"notsubset"===t||"superset"===t||"notsuperset"===t){let n,i,a=!1;if("notsubset"!==t&&"notsuperset"!==t||(a=!0),"subset"===t||"notsubset"===t?(n=r[0],i=r[1]):(n=r[1],i=r[0]),n=to_intervals(n),i=to_intervals(i),"interval"!==n[0]||"interval"!==i[0])return e;let o=n[1],s=n[2],u=i[1],c=i[2];if("tuple"!==o[0]||"tuple"!==s[0]||"tuple"!==u[0]||"tuple"!==c[0])throw new Error("Badly formed ast");let l,f=o[1],p=o[2],m=u[1],d=u[2],h=[];return s[1]&&!c[1]?a?h.push(["le",f,m]):h.push([">",f,m]):a?h.push(["<",f,m]):h.push(["ge",f,m]),s[2]&&!c[2]?a?h.push(["ge",p,d]):h.push(["<",p,d]):a?h.push([">",p,d]):h.push(["le",p,d]),l=a?["or"].concat(h):["and"].concat(h),l}return e}function substitute(e,t){var r=get_tree(e),n={};for(let e in t)n[e]=get_tree(t[e]);return substitute$1(r,n)}function substitute_component(e,t,r){let n=get_tree(e);if(get_tree(r),"number"==typeof t)t=[t];else if(!Array.isArray(t))throw Error("Invalid substitute_component: "+t);let i=["list","tuple","vector","altvector","array"];return function e(t,n,a){if(0===n.length)return r;if(!Array.isArray(t))throw Error("Invalid substitute_component: expected list, tuple, vector, or array");let o=t[0],s=t.slice(1);if(!i.includes(o))throw Error("Invalid substitute_component: expected list, tuple, vector, or array");let u=n[0];if(u<0||u>s.length-1)throw Error("Invalid substitute_component: component out of range");let c=n.slice(1),l=e(s[u],c);return[o,...s.slice(0,u),l,...s.slice(u+1)]}(n,t)}function get_component(e,t){let r=get_tree(e);if("number"==typeof t)t=[t];else if(!Array.isArray(t))throw Error("Invalid get_component: "+t);let n=["list","tuple","vector","altvector","array"];return function e(t,r){if(0===r.length)return t;if(!Array.isArray(t))throw Error("Invalid get_component: expected list, tuple, vector, or array");let i=t[0],a=t.slice(1);if(!n.includes(i))throw Error("Invalid get_component: expected list, tuple, vector, or array");let o=r[0];if(o<0||o>a.length-1)throw Error("Invalid get_component: component out of range");let s=r.slice(1);return e(a[o],s)}(r,t)}var transformation=Object.freeze({__proto__:null,expand:expand,expand_relations:expand_relations,substitute:substitute,substitute_component:substitute_component,get_component:get_component,perform_vector_scalar_multiplications:perform_vector_scalar_multiplications,perform_matrix_scalar_multiplications:perform_matrix_scalar_multiplications,perform_matrix_multiplications:perform_matrix_multiplications});function clean(e){return flatten$5(get_tree(e))}function evalf(e,t){return parseFloat(math$1.format(e,{notation:"exponential",precision:t}))}function collapse_unary_minus(e){var t=get_tree(e);if(!Array.isArray(t))return t;var r=t[0],n=t.slice(1);if(n=n.map((e=>collapse_unary_minus(e))),"-"===r){if("number"==typeof n[0])return-n[0];if(Array.isArray(n[0])&&"*"===n[0][0]&&"number"==typeof n[0][1])return["*",-n[0][1]].concat(n[0].slice(2));if(Array.isArray(n[0])&&"/"===n[0][0]){if("number"==typeof n[0][1])return["/",-n[0][1],n[0][2]];if(Array.isArray(n[0][1])&&"*"===n[0][1][0]&&"number"==typeof n[0][1][1])return["/",["*",-n[0][1][1]].concat(n[0][1].slice(2)),n[0][2]]}}return[r].concat(n)}function simplify(e,t,r){var n=get_tree(e);return contains_blank(n)?n:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),n=evaluate_numbers(n,{assumptions:t,max_digits:r,evaluate_functions:!0}),Array.isArray(n)?n=collect_like_terms_factors(n=perform_vector_matrix_additions_scalar_multiplications(n=simplify_logical(n,t)),t,r):n)}function simplify_logical(e,t){var r=get_tree(e);if(contains_blank(r))return r;void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),r=evaluate_numbers(r,{assumptions:t}),r=unflattenRight(r);var n=[];return n.push([["not",["not","a"]],"a"]),n.push([["not",["and","a","b"]],["or",["not","a"],["not","b"]]]),n.push([["not",["or","a","b"]],["and",["not","a"],["not","b"]]]),n.push([["not",["=","a","b"]],["ne","a","b"]]),n.push([["not",["ne","a","b"]],["=","a","b"]]),n.push([["not",["<","a","b"]],["le","b","a"]]),n.push([["not",["le","a","b"]],["not",["le","a","b"]]]),n.push([["not",["in","a","b"]],["notin","a","b"]]),n.push([["not",["subset","a","b"]],["notsubset","a","b"]]),r=flatten$5(r=applyAllTransformations(r,n,20))}function perform_vector_matrix_additions_scalar_multiplications(e,t=!0){var r=get_tree(e);r=perform_vector_scalar_multiplications(r=perform_matrix_scalar_multiplications(r),t);let n=["+","a","b"];return r=transform(r,(function(e){let r=match$2(e,n,{allow_permutations:!0});if(r){let n=["vector","altvector"];t&&n.push("tuple");let i={},a={},o=[];if(n.includes(r.a[0])){let e=r.a.length-1;i[e]||(i[e]=[]),i[e].push(r.a)}else if("matrix"===r.a[0]){let e=r.a[1].slice(1).toString();a[e]||(a[e]=[]),a[e].push(r.a)}else o.push(r.a);if(n.includes(r.b[0])){let e=r.b.length-1;i[e]||(i[e]=[]),i[e].push(r.b)}else if("matrix"===r.b[0]){let e=r.b[1].slice(1).toString();a[e]||(a[e]=[]),a[e].push(r.b)}else if("+"===r.b[0])for(let e of r.b.slice(1))if(n.includes(e[0])){let t=e.length-1;i[t]||(i[t]=[]),i[t].push(e)}else if("matrix"===e[0]){let t=e[1].slice(1).toString();a[t]||(a[t]=[]),a[t].push(e)}else o.push(e);else o.push(r.b);if(Object.values(i).every((e=>e.length<2))&&Object.values(a).every((e=>e.length<2)))return e;let s=o;for(let e in i)if(i[e].length<2)s.push(...i[e]);else{let t,r=i[e].some((e=>"vector"===e[0])),n=i[e].some((e=>"tuple"===e[0])),a=i[e].some((e=>"altvector"===e[0]));t=r||n&&a?["vector"]:a?["altvector"]:["tuple"];for(let r=0;re[r+1]))]);s.push(t)}for(let e in a)if(a[e].length<2)s.push(...a[e]);else{let[t,r]=e.split(",").map(Number),n=["tuple"];for(let i=0;ie[2][i+1][n+1]))]);n.push(t)}let i=["matrix",["tuple",t,r],n];s.push(i)}return 1===s.length?s[0]:["+",...s]}return e})),r}function contains_decimal_number(e){return"string"!=typeof e&&("number"==typeof e?!(!Number.isFinite(e)||Number.isInteger(e)):!!Array.isArray(e)&&e.slice(1).some((e=>contains_decimal_number(e))))}function contains_only_numbers(e,{include_number_symbols:t=!1,evaluate_functions:r=!1}={}){if("string"==typeof e){if(t){if("e"===e&&math$1.define_e)return!0;if("pi"===e&&math$1.define_pi)return!0}return!("i"!==e||!math$1.define_i)}return"number"==typeof e||!!Array.isArray(e)&&(r&&"apply"===e[0]?e.slice(2).every((e=>contains_only_numbers(e,{include_number_symbols:t}))):e.slice(1).every((e=>contains_only_numbers(e,{include_number_symbols:t}))))}function try_evaluate_sum_of_numbers(e,t,r){if("number"==typeof e){if(0===e)return t;if("number"==typeof t)return e+t;if(Array.isArray(t)&&"+"===t[0]&&"number"==typeof t[1])return["+",e+t[1],t[2]];if(!r&&Array.isArray(t)&&"+"===t[0]&&"number"==typeof t[2])return["+",e+t[2],t[1]]}return"number"==typeof t&&0===t?e:null}function try_evaluate_negate_number(e){if("number"==typeof e)return-e;if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1])return["*",-e[1]].concat(e.slice(2));if(Array.isArray(e)&&"/"===e[0]){if("number"==typeof e[1])return["/",-e[1],e[2]];if(Array.isArray(e[1])&&"*"===e[1][0]&&"number"==typeof e[1][1])return["/",["*",-e[1][1]].concat(e[1].slice(2)),e[2]]}return null}function try_evaluate_product_of_numbers(e,t){if("number"==typeof e){if(isNaN(e))return NaN;if("number"==typeof t)return e*t;if(!isFinite(e))return e===1/0&&is_negative_ast(t)||e===-1/0&&is_positive_ast(t)?-1/0:!1===is_nonzero_ast(t)?NaN:1/0;if(0===e)return 0;if(1===e)return t;if(-1===e)return["-",t];if(Array.isArray(t)&&"*"===t[0]&&"number"==typeof t[1])return e*=t[1],t=t[2],1===e?t:-1===e?["-",t]:["*",e,t]}if("number"==typeof t){if(isNaN(t))return NaN;if(!isFinite(t))return t===1/0&&is_negative_ast(e)||t===-1/0&&is_positive_ast(e)?-1/0:!1===is_nonzero_ast(e)?NaN:1/0;if(0===t)return 0;if(1===t)return e;if(-1===t)return["-",e];if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1])return t*=e[1],e=e[2],1===t?e:-1===t?["-",e]:["*",e,t]}if(math$1.define_i&&"i"===e){if("i"===t)return-1;if(Array.isArray(t)&&"*"===t[0]&&"i"===t[1])return["-",t[2]]}else if(math$1.define_i&&"i"===t&&Array.isArray(e)&&"*"===e[0]&&"i"===e[1])return["-",e[2]];return null}function try_evaluate_quotient_of_numbers(e,t,r,n){if("number"==typeof e){if(0===e){let e=is_nonzero_ast(t,r);if(e)return 0;if(!1===e)return NaN}if("number"==typeof t){let r=e/t;if(n===1/0||math$1.round(r,n)===r)return r;if(t<0)return["/",-e,-t]}if(Array.isArray(t)&&"*"===t[0]&&"number"==typeof t[1]){let r=e/t[1];if(n===1/0||math$1.round(r,n)===r)return["/",r,t[2]]}}else if("number"==typeof t){if(Array.isArray(e)&&"*"===e[0]&&"number"==typeof e[1]){let r=e[1]/t;if(n===1/0||math$1.round(r,n)===r)return 1===r?e[2]:["*",r,e[2]];if(t<0)return["/",["*",-e[1],e[2]],-t]}let r=1/t;if(n===1/0||math$1.round(r,n)===r)return["*",r,e];if(t<0)return Array.isArray(e)&&"-"===e[0]?["/",e[1],-t]:["-",["/",e,-t]]}return null}function evaluate_numbers_sub(e,t,r,n,i,a){if(void 0===e)return e;if("number"==typeof e)return a>0&&math$1.abs(e)0&&math$1.abs(t)evaluate_numbers_sub(e,t,r,n,i,a)));if("+"===s){let e=u[0],t=u[1];if(void 0===t)return e;let r=try_evaluate_sum_of_numbers(e,t,n);if(null!==r)return r;if("unit"===e[0]&&"unit"===t[0]){let r=get_unit_of_tree(e),i=get_unit_of_tree(t);if(r&&r===i){let i=try_evaluate_sum_of_numbers(remove_units(e,!1),remove_units(t,!1),n);if(null!==i)return add_unit(i,r)}}return[s].concat(u)}if("-"===s){let e=try_evaluate_negate_number(u[0]);if(null!==e)return e;if("unit"===u[0][0]){let e=get_unit_of_tree(u[0]);if(e){let t=try_evaluate_negate_number(remove_units(u[0],!1));if(null!==t)return add_unit(t,e)}}return[s].concat(u)}if("*"===s){let e=u[0],t=u[1];if(void 0===t)return e;let r=try_evaluate_product_of_numbers(e,t);if(null!==r)return r;if("unit"===e[0]&&"unit"!==t[0]){let r=get_unit_of_tree(e);if(r){let n=try_evaluate_product_of_numbers(remove_units(e,!1),t);if(null!==n)return add_unit(n,r)}}if("unit"!==e[0]&&"unit"===t[0]){let r=get_unit_of_tree(t);if(r){let n=try_evaluate_product_of_numbers(e,remove_units(t,!1));if(null!==n)return add_unit(n,r)}}return[s].concat(u)}if("/"===s){let e=u[0],n=u[1],i=try_evaluate_quotient_of_numbers(e,n,t,r);if(null!==i)return i;if("unit"===e[0]&&"unit"!==n[0]){let i=get_unit_of_tree(e);if(i){let a=try_evaluate_quotient_of_numbers(remove_units(e,!1),n,t,r);if(null!==a)return add_unit(a,i)}}return[s].concat(u)}if("^"===s){let e=u[0],n=u[1];if("number"==typeof n)if(0===n){if(!math$1.pow_strict)return 1;let r=is_nonzero_ast(e,t);if(r&&e!==1/0&&e!==-1/0)return 1;if(!1===r)return NaN}else{if(1===n)return e;if("number"==typeof e){let t=math$1.pow(e,n);if(r===1/0||math$1.round(t,r)===t)return t}}else if(1===e)return 1;return[s].concat(u)}return[s].concat(u)}function evaluate_numbers(e,{assumptions:t,max_digits:r,skip_ordering:n=!1,evaluate_functions:i=!1,set_small_zero:a=0}={}){(void 0===r||!Number.isInteger(r)&&r!==1/0)&&(r=0),!0===a&&(a=1e-14);var o,s=get_tree(e);return contains_blank(s)?s:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),n?o=evaluate_numbers_sub(s=unflattenRight(flatten$5(s)),t,r,n,i,a):(s=move_units_outside_products(s),s=unflattenRight(default_order(flatten$5(s))),o=default_order(evaluate_numbers_sub(s,t,r,n,i,a)),o=default_order(evaluate_numbers_sub(unflattenRight(o),t,r,n,i,a))),flatten$5(o=set_negative_zeros_to_zero(o)))}function set_negative_zeros_to_zero(e){return 0===e?0:Array.isArray(e)?[e[0],...e.slice(1).map(set_negative_zeros_to_zero)]:e}function collect_like_terms_factors(e,t,r){function n(e){return"number"==typeof e||!(!Array.isArray(e)||"-"!==e[0]||"number"!=typeof e[1])}function i(e){return"number"==typeof e&&e<0||!(!Array.isArray(e)||"-"!==e[0]||"number"!=typeof e[1])}function a(e){if("number"==typeof e)return!0;if(Array.isArray(e)&&"-"===e[0]&&"number"==typeof e[1])return!0;var t=evaluate_to_constant(e,{remove_units_first:!1});return!!Number.isFinite(t)}var o=get_tree(e);if(contains_blank(o))return o;void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),o=evaluate_numbers(o,{assumptions:t,max_digits:r,evaluate_functions:!0});var s=[];s.push([["/","x",["^","y","a"]],["*","x",["^","y",["-","a"]]],{evaluate_numbers:!0,max_digits:r}]),s.push([["/","x",["apply","exp","a"]],["*","x",["apply","exp",["-","a"]]],{evaluate_numbers:!0,max_digits:r,variables:{x:!0,a:!0}}]),s.push([["/","x","y"],["*","x",["^","y",["-",1]]],{evaluate_numbers:!0,max_digits:r}]),o=applyAllTransformations(o,s,40),s=[];for(let e in all_units){all_units[e].prefix?(s.push([["+",["unit",e,"x"],["unit",e,"y"]],["unit",e,["+","x","y"]],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["unit",e,"x"],["-",["unit",e,"y"]]],["unit",e,["+","x",["-","y"]]],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}])):(s.push([["+",["unit","x",e],["unit","y",e]],["unit",["+","x","y"],e],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["unit","x",e],["-",["unit","y",e]]],["unit",["+","x",["-","y"]],e],{variables:{x:!0,y:!0},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]))}return s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:e=>is_nonzero_ast(e,t),n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:!0,n:e=>n(e)&&is_positive_ast(e,t),m:e=>n(e)&&is_positive_ast(e,t)},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["^","x","n"],["^","x","m"]],["^","x",["+","n","m"]],{variables:{x:!0,n:e=>n(e)&&is_negative_ast(e,t),m:e=>n(e)&&is_negative_ast(e,t)},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*",["apply","exp","n"],["apply","exp","m"]],["apply","exp",["+","n","m"]],{variables:{n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n","x"],["*","m","x"]],["*",["+","n","m"],"x"],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n1","x"],["*",["/","n2","m2"],"x"]],["*",["+","n1",["/","n2","m2"]],"x"],{variables:{x:!0,n1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n1","x"],["*",["-",["/","n2","m2"]],"x"]],["*",["+","n1",["-",["/","n2","m2"]]],"x"],{variables:{x:!0,n1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*",["/","n1","m1"],"x"],["*",["/","n2","m2"],"x"]],["*",["+",["/","n1","m1"],["/","n2","m2"]],"x"],{variables:{x:!0,n1:n,m1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m1","m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*",["/","n1","m1"],"x"],["*",["-",["/","n2","m2"]],"x"]],["*",["+",["/","n1","m1"],["-",["/","n2","m2"]]],"x"],{variables:{x:!0,n1:n,m1:n,n2:n,m2:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m1","m2","n1","n2"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["+",["*","n","x"],["-",["*","m","x"]]],["*",["+","n",["-","m"]],"x"],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_implicit_identities:["m","n"],allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["^",["*","x","y"],"a"],["*",["^","x","a"],["^","y","a"]],{allow_permutations:!0}]),s.push([["^",["^","x","n"],"m"],["^","x",["*","n","m"]],{variables:{x:!0,n:n,m:n},evaluate_numbers:!0,max_digits:r,allow_permutations:!0}]),s.push([["-",["+","a","b"]],["+",["-","a"],["-","b"]]]),s.push([["*","x","y"],["*","x","y"],{variables:{x:a,y:a},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),o=applyAllTransformations(o,s,40),(s=[]).push([["*","x",["^","y",["-","a"]]],["/","x",["^","y","a"]],{allow_extended_match:!0,allow_permutations:!0,evaluate_numbers:!0,max_digits:r,max_group:1}]),s.push([["*","x",["apply","exp",["-","a"]]],["/","x",["apply","exp","a"]],{allow_extended_match:!0,allow_permutations:!0,evaluate_numbers:!0,max_digits:r,max_group:1,variables:{x:!0,a:!0}}]),s.push([["*","x",["^","y","n"]],["/","x",["^","y",["-","n"]]],{variables:{x:!0,y:!0,n:i},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["*","x",["apply","exp","n"]],["/","x",["apply","exp",["-","n"]]],{variables:{x:!0,n:i},evaluate_numbers:!0,max_digits:r,allow_extended_match:!0,allow_permutations:!0,max_group:1}]),o=applyAllTransformations(o,s,40),(s=[]).push([["^","y","n"],["/",1,["^","y",["-","n"]]],{variables:{y:!0,n:i},evaluate_numbers:!0,max_digits:r}]),s.push([["apply","exp","n"],["/",1,["apply","exp",["-","n"]]],{variables:{n:i},evaluate_numbers:!0,max_digits:r}]),o=applyAllTransformations(o,s,40),(s=[]).push([["*","x",["/","y","z"]],["/",["*","x","y"],"z"],{allow_extended_match:!0,allow_permutations:!0,max_group:1}]),s.push([["/",["/","x","y"],"z"],["/","x",["*","y","z"]],{allow_extended_match:!0,allow_permutations:!0}]),s.push([["/","x",["/","y","z"]],["/",["*","x","z"],"y"],{allow_extended_match:!0,allow_permutations:!0}]),o=evaluate_numbers(o=applyAllTransformations(o,s,40),{assumptions:t,max_digits:r})}function simplify_ratios(e,t){function r(e){var t=1;return e=e.map((function(e){if("number"==typeof e)return e<0?(t*=-1,-e):e;if(!Array.isArray(e))return e;if("-"===e[0])return t*=-1,e[1];if("+"!==e[0])return e;var r=!1;if(("number"==typeof e[1]&&e[1]<0||Array.isArray(e[1])&&"-"===e[1][0]||Array.isArray(e[1])&&"*"===e[1][0]&&Number(e[1][1])<0)&&(r=!0),r){t*=-1;var n=e.slice(1).map((e=>["-",e]));return evaluate_numbers(["+"].concat(n))}return e})),{factors:e,sign_change:t}}var n=get_tree(e);return contains_blank(n)?n:(void 0===t&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(t=e.context.get_assumptions([e.variables()])),function e(t,n){if(!Array.isArray(t))return n?["-",t]:t;var i=t[0];if("-"===i)return e(t[1],n=!0);var a=t.slice(1).map((t=>e(t)));if("/"!==i)return n?["-",[i,...a]]:[i,...a];var o,s=a[0],u=a[1];s=default_order(s,{ignore_negatives:!0});var c,l=r(o=Array.isArray(s)&&"*"===s[0]?s.slice(1):[s]);o=l.factors,n&&(l.sign_change*=-1),u=default_order(u,{ignore_negatives:!0});var f=r(c=Array.isArray(u)&&"*"===u[0]?u.slice(1):[u]);return c=f.factors,l.sign_change*f.sign_change<0&&(o[0]=["-",o[0]]),["/",s=1===o.length?o[0]:["*"].concat(o),u=1===c.length?c[0]:["*"].concat(c)]}(n))}function contains_blank(e){return"＿"===e||!!Array.isArray(e)&&e.some(contains_blank)}let all_units=get_all_units();function remove_units(e,t=!0){var r=get_tree(e);if(!Array.isArray(r))return r;let n=r[0],i=r.slice(1);if("unit"===n){let e=all_units[get_unit_of_tree(r)];if(!e)return r;let n=remove_units(e.prefix?i[1]:i[0],t);return t?e.scale(n):n}return[n,...i.map((e=>remove_units(e,t)))]}function remove_scaling_units(e){var t=get_tree(e);if(!Array.isArray(t))return t;let r=t[0],n=t.slice(1);if("unit"===r){let e=all_units[get_unit_of_tree(t)];if(!e||!e.only_scales)return t;let r=remove_scaling_units(e.prefix?n[1]:n[0]);return e.scale(r)}return[r,...n.map((e=>remove_scaling_units(e)))]}function add_unit(e,t){var r=get_tree(e);let n=all_units[t];return n?n.prefix?["unit",t,r]:["unit",r,t]:r}function move_units_outside_products(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("*"===t){let e=[],t=[];for(let n of r){let r=get_unit_value_of_tree(n);r?(e.push(r[0]),t.push(r[1])):t.push(n)}let n=["*",...t];for(let t of e)n=add_unit(n,t);return n}return[t,...r.map(move_units_outside_products)]}var simplify$1=Object.freeze({__proto__:null,clean:clean,simplify:simplify,simplify_logical:simplify_logical,evaluate_numbers:evaluate_numbers,collect_like_terms_factors:collect_like_terms_factors,collapse_unary_minus:collapse_unary_minus,simplify_ratios:simplify_ratios,default_order:default_order,perform_vector_matrix_additions_scalar_multiplications:perform_vector_matrix_additions_scalar_multiplications,remove_units:remove_units,add_unit:add_unit,remove_scaling_units:remove_scaling_units});function solve_linear(e,t,r){if("string"==typeof t){void 0===r&&void 0!==e.context&&void 0!==e.context.get_assumptions&&(r=e.context.get_assumptions([e.variables()]));var n=simplify(get_tree(e),r);if(Array.isArray(n)){var i=n[0],a=n.slice(1);if("="===i||"ne"===i||"<"===i||"le"===i||">"===i||"ge"===i){var o=simplify(["+",a[0],["-",a[1]]],r),s=e=>!variables(e).includes(t);if(variables(o=simplify(applyAllTransformations(o,[[["+",["*","_a",t],["*","_b",t]],["*",["+","_a","_b"],t],{variables:{_a:s,_b:s},allow_permutations:!0,allow_extended_match:!0,allow_implicit_identities:["_a","_b"],evaluate_numbers:!0}]],20))).includes(t)){var u=match$2(o,["+",["*","_a",t],"_b"],{variables:{_a:s,_b:s},allow_permutations:!0,allow_implicit_identities:["_a","_b"]});if(u){var c=simplify(u._a),l=simplify(u._b);if(is_nonzero_ast(c,r)){if("="===i||"ne"===i||is_positive_ast(c,r)){let e=simplify(["/",["-",l],c]);return[i,t,e]}if(is_negative_ast(c,r)){var f=simplify(["/",["-",l],c]);return[i="<"===i?">":"le"===i?"ge":">"===i?"<":"le",t,f]}}}}}}}}var 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n=this.factor(e);this.simple_factor_or_function_or_parens(e)||"_"===e[0]&&"string"==typeof e[1]||(n="\\left("+n+"\\right)");for(let e=0;e1?s=s.trimRight()+"^{"+a+"}"+this.stringConvert(o):s+=this.stringConvert(o),s="\\frac{ "+s+" }{ ";let u=1;Array.isArray(i)&&(u=i.length-1);for(let t=1;t<=u;t++){let r=i[t],n=1,a="";Array.isArray(r)?(a=r[1],n=r[2]):a=r,s=s+e+this.stringConvert(a),n>1&&(s=s+"^{"+n+"}"),s+=" "}return s+="}",s}if("apply"===t){if("abs"===r[0])return"\\left|"+this.statement(r[1])+"\\right|";if("floor"===r[0])return"\\left\\lfloor "+this.statement(r[1])+" \\right\\rfloor";if("ceil"===r[0])return"\\left\\lceil "+this.statement(r[1])+" \\right\\rceil";if("factorial"===r[0]){let e=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||"_"===r[1][0]&&"string"==typeof r[1][1]?e+"!":"\\left("+e+"\\right)!"}if("sqrt"===r[0])return"\\sqrt{"+this.statement(r[1])+"}";let e,t=r[0];if("^"===t[0]&&(t=t[1]),"_"===t[0]&&(t=t[1]),"int"===t){let e,t=this.factor(r[0]),n=r[1];if(Array.isArray(n)&&"*"===n[0]){let t=[],r=["*"];for(let e=1;e0&&(e[e.length-1].match(/[a-zA-Z]/)&&(e+="\\,"),e+=t.map((e=>"d"+this.factor(e[1]))).join("\\,"))}return e||(e=this.term(r[1])),t+" "+e}e="log10"===r[0]?"\\log_{10}":"re"===r[0]?"\\Re":"im"===r[0]?"\\Im":this.factor(r[0]);let n=this.statement(r[1]);return"tuple"!==r[1][0]&&(n="\\left("+n+"\\right)"),e+n}if("angle"===t){let e=r.every((e=>{if("string"==typeof e&&1===e.length)return!0;if(!Array.isArray(e))return!1;let t=e[0];return"_"===t||"^"===t||"prime"===t}));return operators$1[t](r.map(function(e,t){return this.statement(e)}.bind(this)),e)}return"+"===t&&2===e.length?"+ "+this.factor(e[1]):"\\left("+this.statement(e)+"\\right)"}factorWithParenthesesIfNegatedOrExplicitPlus(e){var t=this.factor(e);return t.match(/^-/)||t.match(/^\+/)?"\\left("+t+"\\right)":t}termWithPlusIfNotNegated(e){var t=this.term(e);return t.match(/^-/)?t.match(/^-[^ ]/)?"- "+t.slice(1):t:"+ "+t}}const textToAst$2=new textToAst$4,astToLatex=new astToLatex$1;var derivatives={sin:textToAst$2.convert("cos x"),cos:textToAst$2.convert("-(sin x)"),tan:textToAst$2.convert("(sec x)^2"),cot:textToAst$2.convert("-((csc x)^2)"),sec:textToAst$2.convert("(sec x)*(tan x)"),csc:textToAst$2.convert("-(csc x)*(cot x)"),sqrt:textToAst$2.convert("1/(2*sqrt(x))"),log:textToAst$2.convert("1/x"),ln:textToAst$2.convert("1/x"),exp:textToAst$2.convert("exp(x)"),arcsin:textToAst$2.convert("1/sqrt(1 - x^2)"),arccos:textToAst$2.convert("-1/sqrt(1 - x^2)"),arctan:textToAst$2.convert("1/(1 + x^2)"),arccsc:textToAst$2.convert("-1/(sqrt(-1/x^2 + 1)*x^2)"),arcsec:textToAst$2.convert("1/(sqrt(-1/x^2 + 1)*x^2)"),arccot:textToAst$2.convert("-1/(1 + x^2)"),abs:textToAst$2.convert("abs(x)/x")};function derivative(e,t,r=[]){var n=get_tree(e),i="\\frac{d}{d"+t+"} ";if("number"==typeof n)return r.push("The derivative of a constant is zero, that is, \\("+i+astToLatex.convert(n)+" = 0\\)."),0;if(variables(n).indexOf(t)<0)return r.push("The derivative of a constant is zero, that is, \\("+i+astToLatex.convert(n)+" = 0\\)."),0;if("string"==typeof n)return t===n?(r.push("We know the derivative of the identity function is one, that is, \\("+i+astToLatex.convert(n)+" = 1\\)."),1):(r.push("As far as \\("+astToLatex.convert(t)+"\\) is concerned, \\("+astToLatex.convert(n)+"\\) is constant, so "+i+astToLatex.convert(n)+" = 0\\)."),0);if(!Array.isArray(n))return null;var a=n[0],o=n.slice(1);if("+"===a||"-"===a||"~"===a){r.push("Using the sum rule, \\("+i+astToLatex.convert(n)+" = "+o.map((function(e,t){return i+astToLatex.convert(e)})).join(" + ")+"\\).");let e=[a].concat(o.map((function(e,n){return derivative(e,t,r)})));return e=simplify(e),r.push("So using the sum rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("*"===a){let e=[],a=[];for(let r=0;r0){if(0===e.length){return r.push("Since the derivative of a constant is zero, \\("+i+astToLatex.convert(n)+" = 0.\\)"),0}let o=["*"].concat(e);if(1===e.length&&(o=e[0]),o===t){r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+a.map((function(e,t){return astToLatex.convert(e)})).join(" \\cdot ")+"\\).");let e=["*"].concat(a);return e=simplify(e),e}r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+a.map((function(e,t){return astToLatex.convert(e)})).join(" \\cdot ")+" \\cdot "+i+"\\left("+astToLatex.convert(o)+"\\right)\\).");let s=derivative(o,t,r),u=["*"].concat(a.concat([s]));return u=simplify(u),r.push("And so \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}r.push("Using the product rule, \\("+i+astToLatex.convert(n)+" = "+o.map((function(e,t){return o.map((function(r,n){return t===n?i+"\\left("+astToLatex.convert(e)+"\\right)":astToLatex.convert(r)})).join(" \\cdot ")})).join(" + ")+"\\).");let s=o.slice(),u=["+"].concat(o.map((function(e,n){return["*"].concat(s.map((function(e,i){if(n===i){let n=derivative(e,t,r);return 1===n?null:n}return e})).filter((function(e){return null!=e})))})));return u=simplify(u),r.push("So using the product rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if("/"===a){let e=o[0],a=o[1];if(variables(a).indexOf(t)<0){r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(["/",1,a])+" \\cdot "+i+"\\left("+astToLatex.convert(e)+"\\right)\\).");let o=derivative(e,t,r),s=textToAst$2.convert("(1/g)*d"),u=substitute$1(s,{d:o,g:a});return u=simplify(u),r.push("So \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if(variables(e).indexOf(t)<0){1!==e&&r.push("By the constant multiple rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+" \\cdot "+i+"\\left("+astToLatex.convert(["/",1,a])+"\\right)\\)."),r.push("Since \\(\\frac{d}{du} \\frac{1}{u}\\) is \\(\\frac{-1}{u^2}\\), the chain rule gives \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\cdot \\frac{-1}{ "+astToLatex.convert(a)+"^2} \\cdot "+i+astToLatex.convert(a)+"\\).");let o=derivative(a,t,r),s=textToAst$2.convert("f * (-a/(g^2))"),u=substitute$1(s,{f:e,a:o,g:a});return u=simplify(u),r.push("So since \\(\\frac{d}{du} \\frac{1}{u}\\) is \\(\\frac{-1}{u^2}\\), the chain rule gives \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}r.push("Using the quotient rule, \\("+i+astToLatex.convert(n)+" = \\frac{"+i+"\\left("+astToLatex.convert(e)+"\\right) \\cdot "+astToLatex.convert(a)+" - "+astToLatex.convert(e)+"\\cdot "+i+"\\left("+astToLatex.convert(a)+"\\right)}{ \\left( "+astToLatex.convert(a)+" \\right)^2} \\).");let s=derivative(e,t,r),u=derivative(a,t,r),c=textToAst$2.convert("(a * g - f * b)/(g^2)"),l=substitute$1(c,{a:s,b:u,f:e,g:a});return l=simplify(l),r.push("So using the quotient rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(l)+"\\)."),l}if("^"===a){let e=o[0],a=o[1];if(variables(a).indexOf(t)<0){if("string"==typeof e&&"x"===e){if("number"==typeof a){let t=textToAst$2.convert("n * (f^m)"),o=substitute$1(t,{n:a,m:a-1,f:e});return o=simplify(o),r.push("By the power rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"}\\)."),o}let t=textToAst$2.convert("n * (f^(n-1))"),o=substitute$1(t,{n:a,f:e});return o=simplify(o),r.push("By the power rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"}\\)."),o}1!==a&&r.push("By the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+" \\cdot \\left("+astToLatex.convert(e)+"\\right)^{"+astToLatex.convert(["-",a,1])+"} \\cdot "+i+astToLatex.convert(e)+"\\).");let o=derivative(e,t,r);if(1===a)return o;if("number"==typeof a){let t=textToAst$2.convert("n * (f^m) * a"),s=substitute$1(t,{n:a,m:a-1,f:e,a:o});return s=simplify(s),r.push("So by the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}let s=textToAst$2.convert("n * (f^(n-1)) * a"),u=substitute$1(s,{n:a,f:e,a:o});return u=simplify(u),r.push("So by the power rule and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}if("e"===e&&math$1.define_e){if("string"==typeof a&&a===t){let e=textToAst$2.convert("e^(f)"),o=substitute$1(e,{f:a});return o=simplify(o),r.push("The derivative of \\(e^"+astToLatex.convert(t)+"\\) is itself, that is, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(n)+"\\)."),o}r.push("Using the rule for \\(e^x\\) and the chain rule, we know \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(n)+" \\cdot "+i+astToLatex.convert(a)+"\\).");let e=textToAst$2.convert("e^(f)*d"),o=derivative(a,t,r),s=substitute$1(e,{f:a,d:o});return s=simplify(s),r.push("So using the rule for \\(e^x\\) and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}if("number"==typeof e){if("string"==typeof a&&a===t){let o=textToAst$2.convert("a^(f) * log(a)"),s=substitute$1(o,{a:e,f:a});return s=simplify(s),r.push("The derivative of \\(a^"+astToLatex.convert(t)+"\\) is \\(a^{"+astToLatex.convert(t)+"} \\, \\log a\\), that is, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+"\\)."),s}let o=textToAst$2.convert("a^(f) * log(a)"),s=substitute$1(o,{a:e,f:a});r.push("Using the rule for \\(a^x\\) and the chain rule, we know \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(s)+" \\cdot "+i+astToLatex.convert(a)+"\\).");let u=textToAst$2.convert("a^(b)*log(a)*d"),c=derivative(a,t,r),l=substitute$1(u,{a:e,b:a,d:c});return l=simplify(l),r.push("So using the rule for \\(a^x\\) and the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(l)+"\\)."),l}let s=e,u=a;r.push("Recall the general rule for exponents, namely that \\(\\frac{d}{dx} u(x)^{v(x)} = u(x)^{v(x)} \\cdot \\left( v'(x) \\cdot \\log u(x) + \\frac{v(x) \\cdot u'(x)}{u(x)} \\right)\\). In this case, \\(u(x) = "+astToLatex.convert(s)+"\\) and \\(v(x) = "+astToLatex.convert(u)+"\\).");let c=derivative(s,t,r),l=derivative(u,t,r),f=textToAst$2.convert("(f^g)*(b * log(f) + (g * a)/f)"),p=substitute$1(f,{a:c,b:l,f:s,g:u});return p=simplify(p),r.push("So by the general rule for exponents, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(p)+"\\)."),p}if("apply"===a&&!(o[0]in derivatives)){let e=o[1];r.push("By the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(substitute$1(["apply",o[0]+"'","x"],{x:e}))+" \\cdot "+i+astToLatex.convert(e)+"\\).");let a=["*",substitute$1(["apply",o[0]+"'","x"],{x:e}),derivative(e,t,r)];return a=simplify(a),r.push("So by the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(a)+"\\)."),a}if("apply"===a&&o[0]in derivatives||a in derivatives){let e=!1;"apply"===a&&(a=o[0],o=o.slice(1),e=!0);let s=o[0];if("number"==typeof s){let e=0;return r.push("The derivative of a constant is zero so \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("string"==typeof s&&s===t){let e=["*",substitute$1(derivatives[a],{x:s})];return e=simplify(e),r.push("It is the case that \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}if("string"==typeof s&&s!==t){let e=0;return r.push("Since the derivative of a constant is zero, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(e)+"\\)."),e}{let o=[a,"u"];e&&(o=["apply"].concat(o)),r.push("Recall \\(\\frac{d}{du}"+astToLatex.convert(o)+" = "+astToLatex.convert(derivative(o,"u",[]))+"\\)."),r.push("By the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(substitute$1(derivatives[a],{x:s}))+" \\cdot "+i+astToLatex.convert(s)+"\\).");let u=["*",substitute$1(derivatives[a],{x:s}),derivative(s,t,r)];return u=simplify(u),r.push("So by the chain rule, \\("+i+astToLatex.convert(n)+" = "+astToLatex.convert(u)+"\\)."),u}}return 0}function lowercaseFirstLetter(e){return e.charAt(0).toLowerCase()+e.slice(1)}function simplify_story(e){for(let t=e.length-1;t>=1;t--)e[t]===e[t-1]&&e.splice(t,1);for(let t=0;t":function(e){return e.join(" > ")},lts:function(e){return e.join(" < ")},gts:function(e){return e.join(" > ")},le:function(e){return e.join(" ≤ ")},ge:function(e){return e.join(" ≥ ")},ne:function(e){return e.join(" ≠ ")},forall:function(e){return"∀ "+e[0]},exists:function(e){return"∃ "+e[0]},in:function(e){return e[0]+" ∈ "+e[1]},notin:function(e){return e[0]+" ∉ "+e[1]},ni:function(e){return e[0]+" ∋ "+e[1]},notni:function(e){return e[0]+" ∌ "+e[1]},subset:function(e){return e[0]+" ⊂ "+e[1]},subseteq:function(e){return e[0]+" ⊆ "+e[1]},notsubset:function(e){return e[0]+" ⊄ "+e[1]},notsubseteq:function(e){return e[0]+" ⊈ "+e[1]},superset:function(e){return e[0]+" ⊃ "+e[1]},superseteq:function(e){return e[0]+" ⊇ "+e[1]},notsuperset:function(e){return e[0]+" ⊅ "+e[1]},notsuperseteq:function(e){return e[0]+" ⊉ "+e[1]},union:function(e){return e.join(" ∪ ")},intersect:function(e){return e.join(" ∩ ")},perp:function(e){return e.join(" ⟂ ")},parallel:function(e){return e.join(" ∥ ")},derivative_leibniz:function(e){return"d"+e[0]+"/d"+e[1]},partial_derivative_leibniz:function(e){return"∂"+e[0]+"/∂"+e[1]},"|":function(e){return e[0]+" | "+e[1]},":":function(e){return e[0]+" : "+e[1]},binom:function(e){return"binom( "+e[0]+", "+e[1]+" )"},vec:function(e){return"vec("+e[0]+")"},linesegment:function(e){return"linesegment( "+e.join(", ")+" )"},angle:function(e,t){return t?"∠"+e.join(""):"∠( "+e.join(", ")+" )"},unit:function(e){return e[0]+" "+e[1]}},nonunicode_operators={"+":function(e){return e.join(" ")},"-":function(e){return"-"+e[0]},"*":function(e){return e.join(" ")},"/":function(e){return e[0]+"/"+e[1]},_:function(e){return e[0]+"_"+e[1]},"^":function(e){return e[0]+"^"+e[1]},prime:function(e){return e[0]+"'"},tuple:function(e){return"( "+e.join(", ")+" )"},array:function(e){return"[ "+e.join(", ")+" ]"},list:function(e){return e.join(", ")},set:function(e){return"{ "+e.join(", ")+" }"},vector:function(e){return"( "+e.join(", ")+" )"},altvector:function(e){return"( "+e.join(", ")+" )"},interval:function(e){return"( "+e.join(", ")+" )"},matrix:function(e){return"( "+e.join(", ")+" )"},and:function(e){return e.join(" and ")},or:function(e){return e.join(" or ")},not:function(e){return"not "+e[0]},"=":function(e){return e.join(" = ")},"<":function(e){return e.join(" < ")},">":function(e){return e.join(" > ")},lts:function(e){return e.join(" < ")},gts:function(e){return e.join(" > ")},le:function(e){return e.join(" <= ")},ge:function(e){return e.join(" >= ")},ne:function(e){return e.join(" ne ")},forall:function(e){return"forall "+e[0]},exists:function(e){return"exists "+e[0]},in:function(e){return e[0]+" elementof "+e[1]},notin:function(e){return e[0]+" notelementof "+e[1]},ni:function(e){return e[0]+" containselement "+e[1]},notni:function(e){return e[0]+" notcontainselement "+e[1]},subset:function(e){return e[0]+" subset "+e[1]},subseteq:function(e){return e[0]+" subseteq "+e[1]},notsubset:function(e){return e[0]+" notsubset "+e[1]},notsubseteq:function(e){return e[0]+" notsubseteq "+e[1]},superset:function(e){return e[0]+" superset "+e[1]},superseteq:function(e){return e[0]+" superseteq "+e[1]},notsuperset:function(e){return e[0]+" notsuperset "+e[1]},notsuperseteq:function(e){return e[0]+" notsuperseteq "+e[1]},union:function(e){return e.join(" union ")},intersect:function(e){return e.join(" intersect ")},perp:function(e){return e.join(" perp ")},parallel:function(e){return e.join(" parallel ")},derivative_leibniz:function(e){return"d"+e[0]+"/d"+e[1]},partial_derivative_leibniz:function(e){return"∂"+e[0]+"/∂"+e[1]},"|":function(e){return e[0]+" | "+e[1]},":":function(e){return e[0]+" : "+e[1]},binom:function(e){return"binom( "+e[0]+", "+e[1]+" )"},vec:function(e){return"vec("+e[0]+")"},linesegment:function(e){return"linesegment( "+e.join(", ")+" )"},angle:function(e,t){return t?"angle "+e.join(""):"angle( "+e.join(", ")+" )"},unit:function(e){return e[0]+" "+e[1]}},output_unicodeDefault=!0;class astToText$2{constructor({output_unicode:e=output_unicodeDefault,padToDigits:t=null,padToDecimals:r=null,showBlanks:n=!0}={}){this.output_unicode=e,this.operators=unicode_operators,e||(this.operators=nonunicode_operators),this.padToDigits=t,this.padToDecimals=r,this.showBlanks=n}convert(e){return this.statement(e)}statement(e){if(!Array.isArray(e))return this.single_statement(e);let t=e[0],r=e.slice(1);if("ldots"===t)return"...";if(!(t in this.operators)&&"apply"!==t)throw new Error("Badly formed ast: operator "+t+" not recognized.");return"and"===t||"or"===t?this.operators[t](r.map(function(e,t){let r=this.single_statement(e);return r.match(/ /)&&!r.match(/^\(.*\)$/)?"("+r+")":r}.bind(this))):this.single_statement(e)}single_statement(e){if(!Array.isArray(e))return this.expression(e);let t=e[0],r=e.slice(1);if("not"===t)return this.operators[t](r.map(function(e,t){let r=this.single_statement(e);return r.match(/ /)&&!r.match(/^\(.*\)$/)?"("+r+")":r}.bind(this)));if("exists"===t||"forall"===t)return this.operators[t]([this.single_statement(r[0])]);if("="===t||"ne"===t||"<"===t||">"===t||"le"===t||"ge"===t||"in"===t||"notin"===t||"ni"===t||"notni"===t||"subset"===t||"notsubset"===t||"subseteq"===t||"notsubseteq"===t||"superset"===t||"notsuperset"===t||"superseteq"===t||"notsuperseteq"===t)return this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this)));if("lts"===t||"gts"===t){let e=r[0],n=r[1];if("tuple"!==e[0]||"tuple"!==n[0])throw new Error("Badly formed ast");let i=this.expression(e[1]);for(let r=1;r ":"lts"===t?this.output_unicode?i+=" ≤ ":i+=" <= ":this.output_unicode?i+=" ≥ ":i+=" >= ",i+=this.expression(e[r+1]);return i}return this.expression(e)}expression(e){if(!Array.isArray(e))return this.term(e);let t=e[0],r=e.slice(1);return"+"===t?1===r.length?"+"+this.term(r[0]):this.operators[t](r.map(function(e,t){return t>0?this.termWithPlusIfNotNegated(e):this.term(e)}.bind(this))):["union","intersect","perp","parallel"].includes(t)?this.operators[t](r.map(function(e,t){return this.term(e)}.bind(this))):this.term(e)}term(e){if(!Array.isArray(e))return this.factor(e);let t=e[0],r=e.slice(1);if("-"===t)return this.operators[t](r.map(function(e,t){return this.term(e)}.bind(this)));if("*"===t)return this.operators[t](r.map(function(e,t){let n;return t>0?(n=this.factorWithParenthesesIfNegatedOrExplicitPlus(e),n.match(/^[0-9]/)?"* "+n:"angle"===e[0]&&r.length>1?"( "+n+" )":n):(n=this.factor(e),"angle"===e[0]&&r.length>1?"( "+n+" )":n)}.bind(this)));if("/"===t){let e=this.factor(r[0]),n=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[0])||(e="("+e+")"),this.simple_factor_or_function_or_parens(r[1])||(n="("+n+")"),this.operators[t]([e,n])}return"unit"===t?this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this))):this.factor(e)}symbolConvert(e){let t={alpha:"α",beta:"β",Gamma:"Γ",gamma:"γ",Delta:"Δ",delta:"δ",epsilon:"ε",zeta:"ζ",eta:"η",Theta:"ϴ",theta:"θ",iota:"ι",kappa:"κ",Lambda:"Λ",lambda:"λ",mu:"μ",nu:"ν",Xi:"Ξ",xi:"ξ",Pi:"Π",pi:"π",rho:"ρ",Sigma:"Σ",sigma:"σ",tau:"τ",Upsilon:"Υ",upsilon:"υ",Phi:"Φ",phi:"ϕ",Psi:"Ψ",psi:"ψ",Omega:"Ω",omega:"ω",perp:"⟂",int:"∫"};return this.output_unicode&&e in t?t[e]:this.showBlanks||"＿"!==e?e:""}simple_factor_or_function_or_parens(e){let t=this.factor(e);return!!(t.length<=1||"string"==typeof e&&e.match(/^\w+$/)||Array.isArray(e)&&"apply"===e[0]||t.match(/^\(.*\)$/)||t.match(/^⟨.*⟩$/))||"number"==typeof e&&(e>=0&&!e.toString().includes("e"))}factor(e){if("string"==typeof e)return this.symbolConvert(e);if("number"==typeof e){if(e===1/0)return this.output_unicode?"∞":"infinity";if(e===-1/0)return this.output_unicode?"-∞":"-infinity";if(Number.isNaN(e))return"NaN";{let t=e.toString(),r=t.indexOf("e");if(-1===r)return null!==this.padToDigits?t=padNumberStringToDigits(t,this.padToDigits):null!==this.padToDecimals&&(t=padNumberStringToDecimals(t,this.padToDecimals)),t;let n=t.substring(0,r),i=t.substring(r+1);if(null!==this.padToDigits)n=padNumberStringToDigits(n,this.padToDigits);else if(null!==this.padToDecimals){let r=Number(i);if(r>0)return t=e.toLocaleString("fullwide",{useGrouping:!1}),padNumberStringToDecimals(t,this.padToDecimals);n=padNumberStringToDecimals(n,this.padToDecimals+r)}return"+"===i[0]?n+" * 10^"+i.substring(1):n+" * 10^("+i+")"}}if(!Array.isArray(e))return"";let t=e[0],r=e.slice(1);if("^"===t){if(Number.isInteger(r[0])&&Number.isInteger(r[1])){let e;return e=r[0]<0?"("+r[0].toString()+")":r[0].toString(),r[1]<0?e+"^("+r[1].toString()+")":e+"^"+r[1].toString()}let e=this.factor(r[0]),t=r[0];for(;"prime"===t[0];)t=t[1];this.simple_factor_or_function_or_parens(t)||"_"===t[0]&&"string"==typeof t[1]||(e="("+e.toString()+")");let n=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||(n="("+n.toString()+")"),e+"^"+n}if("_"===t)return this.operators[t](r.map(function(e,t){let r=this.factor(e);return this.simple_factor_or_function_or_parens(e)?r:"("+r+")"}.bind(this)));if("prime"===t){let e=r[0],t=1;for(;"prime"===e[0];)t+=1,e=e[1];let n=this.factor(e);this.simple_factor_or_function_or_parens(e)||"_"===e[0]&&"string"==typeof e[1]||(n="("+n+")");for(let e=0;e1&&(s=s+"^"+a),s=s+this.symbolConvert(o)+"/";let u=1;Array.isArray(i)&&(u=i.length-1);for(let t=1;t<=u;t++){let r=i[t],n=1,a="";Array.isArray(r)?(a=r[1],n=r[2]):a=r,s=s+e+this.symbolConvert(a),n>1&&(s=s+"^"+n)}return s}if("apply"===t){if("abs"===r[0])return"|"+this.statement(r[1])+"|";if("factorial"===r[0]){let e=this.factor(r[1]);return this.simple_factor_or_function_or_parens(r[1])||"_"===r[1][0]&&"string"==typeof r[1][1]?e+"!":"("+e+")!"}let e=r[0];if("^"===e[0]&&(e=e[1]),"_"===e[0]&&(e=e[1]),"int"===e){let e,t=this.factor(r[0]),n=r[1];if(Array.isArray(n)&&"*"===n[0]){let t=[],r=["*"];for(let e=1;e0&&(e+=" "+t.map((e=>"d"+this.factor(e[1]))).join(" "))}return e||(e=this.term(r[1])),t+" "+e}let t=this.factor(r[0]),n=this.statement(r[1]);return"tuple"!==r[1][0]&&(n="("+n+")"),t+n}if("angle"===t){let e=r.every((e=>{if("string"==typeof e&&1===e.length)return!0;if(!Array.isArray(e))return!1;let t=e[0];return"_"===t||"^"===t||"prime"===t}));return this.operators[t](r.map(function(e,t){return this.statement(e)}.bind(this)),e)}return"+"===t&&2===e.length?"+ "+this.factor(e[1]):"("+this.statement(e)+")"}factorWithParenthesesIfNegatedOrExplicitPlus(e){var t=this.factor(e);return t.match(/^-/)||t.match(/^\+/)?"("+t+")":t}termWithPlusIfNotNegated(e){let t=this.term(e);return t.match(/^-/)?t.match(/^-[^ ]/)?"- "+t.slice(1):t:"+ "+t}}var astToText$1=new astToText$2;function subscripts_to_strings(e,t=!1){var r=get_tree(e);if(!Array.isArray(r))return r;let n=r[0],i=r.slice(1);return"_"===n&&(t||i.every((e=>["number","string"].includes(typeof e))))?astToText$1.convert(r):[n].concat(i.map((e=>subscripts_to_strings(e,t))))}function strings_to_subscripts(e){var t=get_tree(e);if("string"==typeof t){let e=t.match(/^([0-9a-zA-Z]+)_([a-zA-Z]+|[0-9]+)$/);if(e){let t=Number(e[1]);isNaN(t)&&(t=e[1]);let r=Number(e[2]);return isNaN(r)&&(r=e[2]),["_",t,r]}return t}if(!Array.isArray(t))return t;let r=t[0],n=t.slice(1);return[r].concat(n.map(strings_to_subscripts))}var normalization=Object.freeze({__proto__:null,normalize_function_names:normalize_function_names,normalize_applied_functions:normalize_applied_functions,log_subscript_to_two_arg_log:log_subscript_to_two_arg_log,substitute_abs:substitute_abs,default_order:default_order,constants_to_floats:constants_to_floats,normalize_angle_linesegment_arg_order:normalize_angle_linesegment_arg_order,tuples_to_vectors:tuples_to_vectors,to_intervals:to_intervals,altvectors_to_vectors:altvectors_to_vectors,subscripts_to_strings:subscripts_to_strings,strings_to_subscripts:strings_to_subscripts}),astToText=new astToText$2;function generate_random_integer(e,t,r){return e=math$1.ceil(e),t=math$1.floor(t),math$1.floor(r()*(t-e+1))+e}const equals$5=function({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,relative_tolerance:a=1e-12,absolute_tolerance:o=0,tolerance_for_zero:s=1e-15,allowed_error_in_numbers:u=0,include_error_in_number_exponents:c=!1,allowed_error_is_absolute:l=!1,rng:f}){if(Array.isArray(e.tree)&&Array.isArray(t.tree)){let p=e.tree[0],m=e.tree.slice(1),d=t.tree[0],h=t.tree.slice(1);if("tuple"===p||"vector"===p||"altvector"===p||"list"===p||"array"===p||"matrix"===p||"interval"===p){if(d!==p)return!1;if(h.length!==m.length)return!1;for(let e=0;e","<","ge","le"].includes(p)){if(2!==h.length)return!1;if(">"===p?(p="<",m=[m[1],m[0]]):"ge"===p&&(p="le",m=[m[1],m[0]]),">"===d?(d="<",h=[h[1],h[0]]):"ge"===d&&(d="le",h=[h[1],h[0]]),p!==d)return!1;let e=["+",m[0],["-",m[1]]],t=["+",h[0],["-",h[1]]],y="="!==p;return component_equals({expr:n.fromAst(e),other:i.fromAst(t),randomBindings:r,expr_context:n,other_context:i,allow_proportional:!0,require_positive_proportion:y,relative_tolerance:a,absolute_tolerance:o,tolerance_for_zero:s,allowed_error_in_numbers:u,include_error_in_number_exponents:c,allowed_error_is_absolute:l,rng:f})}}return component_equals({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,relative_tolerance:a,absolute_tolerance:o,tolerance_for_zero:s,allowed_error_in_numbers:u,include_error_in_number_exponents:c,allowed_error_is_absolute:l,rng:f})},component_equals=function({expr:e,other:t,randomBindings:r,expr_context:n,other_context:i,allow_proportional:a=!1,require_positive_proportion:o=!1,relative_tolerance:s,absolute_tolerance:u,tolerance_for_zero:c,allowed_error_in_numbers:l,include_error_in_number_exponents:f,allowed_error_is_absolute:p,rng:m}){var d=1e-20*Number.MAX_VALUE,h=0,y=10;e=e.normalize_function_names(),t=t.normalize_function_names(),e=e.log_subscript_to_two_arg_log(),t=t.log_subscript_to_two_arg_log(),e=e.subscripts_to_strings(),t=t.subscripts_to_strings(),e=e.normalize_applied_functions(),t=t.normalize_applied_functions();let g=rename_functions_with_exponents(e.tree),v=rename_functions_with_exponents(t.tree);e=n.fromAst(rename_vecs(g)),t=i.fromAst(rename_vecs(v));var x=[...new Set([...e.variables(),...t.variables()])];math$1.define_pi&&(x=x.filter((function(e){return"pi"!==e}))),math$1.define_i&&(x=x.filter((function(e){return"i"!==e}))),math$1.define_e&&(x=x.filter((function(e){return"e"!==e})));var b=[];for(let e=0;e1===e.length||e.includes("_")||e.includes("^"))),w=_.filter((e=>x.includes(e)));if(_=_.filter((e=>!x.includes(e))),w.length>0){let r=e.tree,a=t.tree,o="x1";for(;[..._,...x].includes(o);)o+="x1";let s="x2";for(;[..._,...x].includes(s);)s+="x2";for(let e of w){let t=e+e;for(;[..._,...x].includes(t);)t+=e;let n=[[["apply",e,o],["apply",t,o],{variables:{[o]:!0}}]];r=applyAllTransformations(r,n),a=applyAllTransformations(a,n),_.push(t)}e=n.fromAst(r),t=i.fromAst(a)}try{var N=e.f(),$=t.f()}catch(r){return e.equalsViaSyntax(t,{allow_blanks:!0})}let A,M,S;if(l>0){let t=replace_numbers_with_parameters({expr:e,variables:x,include_exponents:f});A=n.fromAst(t.expr_with_params),M=t.parameters;let r=Object.keys(M);if(r.length>0){let e=A.derivative(r[0]);if(p||(e=e.multiply(M[r[0]])),r.length>1)for(let t of r.slice(1)){let r=A.derivative(t);p||(r=r.multiply(M[t])),e=e.add(r)}let t=e.multiply(l);try{S=t.f()}catch(e){}}}var E=1,T=[10,1,100,.1,1e3,.01],O=0;let C=0,k=!0,D=0;for(let e=0;e<1e3;e++){try{var I=B(T[O],m)}catch(e){continue}if(!1===I.always_zero&&(k=!1),!I.equal&&!I.out_of_bounds&&!I.always_zero&&!1!==I.sufficient_finite_values&&(D++,D>100))return!1;if(I.equal){if(I.always_zero){if(!k)continue;if(C+=1,C>5&&(O+=1,C=0),O>=T.length)return!0;continue}return!0}}return!1;function B(e,t){var n,i=r(t,x,e);for(let e=0;eh)||!(0===m||m>h))return{out_of_bounds:!0,always_zero:!1};var g=Math.min(p,m),v=Math.max(p,m),w=1;let A=0;if(S){try{A=math$1.abs(S(n))}catch(e){return{equal_at_start:!1,always_zero:!1}}if(!Number.isFinite(A))return{equal_at_start:!1,always_zero:!1}}if(A+=g*s,A=Math.min(A,.1*g),A+=0!==A||0!==l&&0!==f?u:c,!(0===v||math$1.abs(math$1.subtract(l,f))0))return{equal_at_start:!1,always_zero:!1}}var T=0===v,O=0;for(let e=0;e<100;e++){var C,k=r(t,x,E/100,i);for(let e=0;e=y)return{equal:!0,always_zero:T}}}return{sufficient_finite_values:!1,always_zero:T}}};function replace_numbers_with_parameters({expr:e,variables:t,include_exponents:r=!1}){let n={},i=0;function a(){i++;let e="par"+i;for(;t.includes(e);)i++,e="par"+i;return e}return{expr_with_params:function e(t){if("number"==typeof t){if(0===t)return t;{let e=a();return n[e]=t,e}}if("string"==typeof t){if("pi"===t){if(math$1.define_pi){let e=a();return n[e]=math$1.PI,e}}else if("e"===t&&math$1.define_e){let e=a();return n[e]=math$1.e,e}return t}if(!Array.isArray(t))return t;let i=t[0],o=t.slice(1);return"^"!==i||r?[i,...o.map(e)]:[i,e(o[0]),o[1]]}((e=e.evaluate_numbers({max_digits:1/0})).tree),parameters:n}}function rename_functions_with_exponents(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);if("apply"===t){let e=r[0];return Array.isArray(e)&&"^"===e[0]&&e.slice(1).every((e=>["number","string"].includes(typeof e)))&&(e=astToText.convert(e)),["apply",e,r[1]]}return[t,...r.map(rename_functions_with_exponents)]}function rename_vecs(e){if(!Array.isArray(e))return e;let t=e[0],r=e.slice(1);return"vec"===t&&1===r.length?"__vec_"+astToText.convert(r[0]):[t,...r.map(rename_vecs)]}function randomComplexBindings(e,t,r,n){var i={};return void 0===n?t.forEach((function(t){i[t]=math$1.complex(2*e()*r-r,2*e()*r-r)})):t.forEach((function(t){i[t]=math$1.complex(n[t].re+2*e()*r-r,n[t].im+2*e()*r-r)})),i}const equals$4=function(e,t,{relative_tolerance:r=1e-12,absolute_tolerance:n=0,tolerance_for_zero:i=1e-15,allowed_error_in_numbers:a=0,include_error_in_number_exponents:o=!1,allowed_error_is_absolute:s=!1,allow_blanks:u=!1}={}){if(!u&&(e.variables().includes("＿")||t.variables().includes("＿")))return!1;let c=seedrandom$1("complex_seed");return e=e.remove_scaling_units(),t=t.remove_scaling_units(),!(!e.isAnalytic({allow_abs:!0,allow_arg:!0,allow_relation:!0})||!t.isAnalytic({allow_abs:!0,allow_arg:!0,allow_relation:!0}))&&equals$5({expr:e,other:t,randomBindings:randomComplexBindings,expr_context:e.context,other_context:t.context,relative_tolerance:r,absolute_tolerance:n,tolerance_for_zero:i,allowed_error_in_numbers:a,include_error_in_number_exponents:o,allowed_error_is_absolute:s,rng:c})};function randomRealBindings(e,t,r,n){var i={};return void 0===n?t.forEach((function(t){i[t]=2*e()*r-r})):t.forEach((function(t){i[t]=n[t]+2*e()*r-r})),i}const equals$3=function(e,t,{relative_tolerance:r=1e-12,absolute_tolerance:n=0,tolerance_for_zero:i=1e-15,allowed_error_in_numbers:a=0,include_error_in_number_exponents:o=!1,allowed_error_is_absolute:s=!1}={}){if(!e.isAnalytic()||!t.isAnalytic())return!1;let u=seedrandom("real_seed");return equals$5({expr:e,other:t,randomBindings:randomRealBindings,expr_context:e.context,other_content:t.context,relative_tolerance:r,absolute_tolerance:n,tolerance_for_zero:i,allowed_error_in_numbers:a,include_error_in_number_exponents:o,allowed_error_is_absolute:s,rng:u})},equals$2=function(e,t,{allowed_error_in_numbers:r=0,include_error_in_number_exponents:n=!1,allowed_error_is_absolute:i=!1,allow_blanks:a=!1}={}){if(!a&&(e.variables().includes("＿")||t.variables().includes("＿")))return!1;let o=e.normalize_function_names().normalize_applied_functions().normalize_angle_linesegment_arg_order(),s=t.normalize_function_names().normalize_applied_functions().normalize_angle_linesegment_arg_order();return equal(o.tree,s.tree,{allowed_error_in_numbers:r,include_error_in_number_exponents:n,allowed_error_is_absolute:i})},equals$1=function(e,t,{min_elements_match:r=3,match_partial:n=!1}={}){if(!is_discrete_infinite_set(e))return!1;if(is_discrete_infinite_set(t)){var i=[];let r=e.context.get_assumptions(e);if(void 0!==r&&i.push(r),r=t.context.get_assumptions(t),void 0!==r&&i.push(r),i=0===i.length?void 0:1===i.length?i[0]:clean_assumptions(["and"].concat(i)),n){let r=contained_in(e.tree,t.tree,i,n);if(!1===r)return 0;let a=contained_in(t.tree,e.tree,i,n);return!1===a?0:!0===r?!0===a?1:a:!0===a?r:Math.min(r,a)}return contained_in(e.tree,t.tree,i,n)&&contained_in(t.tree,e.tree,i,n)}{let n=t.tree;if("list"!==n[0])return!1;let i=n.length-2;if("ldots"!==n[i+1][0])return!1;if(icontained_in(e,t,r)))}var i=e[1],a=e[2],o=e[3],s=e[4];if(!Array.isArray(o)||"-"!==o[0]||o[1]!==1/0||s!==1/0)return!1;i=simplify(["/",i,a],r,1/0);var u=t.slice(1),c=[];for(let e=0;ee[0])))];let f=0;for(let e of l){let t=c.map((function(t,r){let n=e/t[0];return Number.isInteger(n)?[t[0],n,r]:void 0})).filter((e=>e)),a=[];for(let n of t){let t=n[0],o=n[1],s=n[2],u=c[s][2],l=c[s][3];for(let n=0;nf&&(f=t)}}return!!(n&&f>0)&&f}function sequence_from_discrete_infinite(e,t){var r=e.tree.slice(1);if(r.length>1)return;let n=r[0][1],i=r[0][2],a=evaluate_numbers(r[0][3]),o=r[0][4];if(!Number.isInteger(a)||o!==1/0)return;let s=[];for(let e=0;e0))throw Error(`Have not implemented equality check with ${n} sign errors.`);if(n>1){let e=r;r=function(t,r){return equalSpecifiedSignErrors(t,r,{equalityFunction:e,n_sign_errors:n-1})}}var i,a,o=e.tree,s=[[o]],u=0;e.tree=["-",o];var c=r(e,t);if(e.tree=o,c)return!0;for(;i=s[u++];)if(i=i[0],Array.isArray(i))for(a=1;a"];function isAnalytic(e,{allow_abs:t=!1,allow_arg:r=!1,allow_relation:n=!1}={}){var i=normalize_applied_functions(normalize_function_names(e)),a=operators$3(i=subscripts_to_strings(i));for(let e=0;e+")},"-":function(e){return"-"+e.join("-")+""},"*":function(e){return e.join('\\cdot*')},"/":function(e){return astToGuppy$1.dfrac(e[0],e[1])},"^":function(e){return astToGuppy$1.power(e[0],e[1])},sin:function(e){return astToGuppy$1.trig("sin",e[0])},cos:function(e){return astToGuppy$1.trig("cos",e[0])},tan:function(e){return astToGuppy$1.trig("tan",e[0])},arcsin:function(e){return astToGuppy$1.trig("arcsin",e[0])},arccos:function(e){return astToGuppy$1.trig("arccos",e[0])},arctan:function(e){return astToGuppy$1.trig("arctan",e[0])},arccsc:function(e){return astToGuppy$1.trig("arccsc",e[0])},arcsec:function(e){return astToGuppy$1.trig("arcsec",e[0])},arccot:function(e){return astToGuppy$1.trig("arccot",e[0])},csc:function(e){return astToGuppy$1.trig("csc",e[0])},sec:function(e){return astToGuppy$1.trig("sec",e[0])},cot:function(e){return astToGuppy$1.trig("cot",e[0])},log:function(e){return astToGuppy$1.trig("log",e[0])},exp:function(e){return astToGuppy$1.trig("exp",e[0])},ln:function(e){return astToGuppy$1.trig("ln",e[0])},sqrt:function(e){return astToGuppy$1.sqrt(e[0])},abs:function(e){return astToGuppy$1.abs(e[0])}}}static dfrac(e,t){return'\\dfrac{}{}\\frac{}{}()/()'+e+''+t+""}static trig(e,t){return'\\'+e+'\\left(\\right) '+e+'()'+t+""}static sqrt(e){return'\\sqrt{}sqrt()'+e+""}static power(e,t){return'{}^{}()^()'+e+''+t+""}static abs(e){return'\\left|\\right|abs()'+e+""}static paren(e){return'\\left(\\right)()'+e+""}static isFunctionSymbol(e){return-1!==["sin","cos","tan","csc","sec","cot","arcsin","arccos","arctan","arccsc","arcsec","arccot","log","ln","exp","sqrt","abs","this.factorial"].indexOf(e)}static isGreekLetterSymbol(e){return-1!==["pi","theta","theta","Theta","alpha","nu","beta","xi","Xi","gamma","Gamma","delta","Delta","pi","Pi","epsilon","epsilon","rho","rho","zeta","sigma","Sigma","eta","tau","upsilon","Upsilon","iota","phi","phi","Phi","kappa","chi","lambda","Lambda","psi","Psi","omega","Omega"].indexOf(e)}factorWithParenthesesIfNegated(e){var t=this.factor(e);return t.toString().match(/^-/)?astToGuppy$1.paren(t.toString()):t}factor(e){if("string"==typeof e)return astToGuppy$1.isGreekLetterSymbol(e)?'\\'+e+' $'+e+"":""+e+"";if("number"==typeof e)return""+e+"";if(!Array.isArray(e))return"";var t=e[0],r=e.slice(1);return"apply"===t&&(t=e[1],r=e.slice(2)),"abs"===t?this.operators[t](r.map(function(e,t){return this.expression(e)}.bind(this))):astToGuppy$1.isFunctionSymbol(t)?"this.factorial"!==t||1!==r[0].toString().length&&!r[0].toString().match(/^[0-9]*$/)?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):this.operators[t](r):"^"===t||"~"===t?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):astToGuppy$1.paren(this.expression(e))}term(e){if(!Array.isArray(e))return this.factor(e);var t=e[0],r=e.slice(1);return"*"===t?this.operators[t](r.map(function(e,t){var r=this.factorWithParenthesesIfNegated(e);return r.toString().match(/^[0-9]/)&&t>0?" * "+r:r}.bind(this))):"/"===t?this.operators[t](r.map(function(e,t){return this.factor(e)}.bind(this))):this.factor(e)}expression(e){if(!Array.isArray(e))return this.term(e);var t=e[0],r=e.slice(1);return"+"===t||"-"===t?this.operators[t](r.map(function(e,t){return this.factorWithParenthesesIfNegated(e)}.bind(this))):this.term(e)}convert(e){return(""+this.expression(e)+"").replace(/<\/e>/g,"")}}const glslOperators={"+":function(e){var t=e[0];return e.slice(1).forEach((function(e){t=t+"+"+e})),t},"-":function(e){var t="-"+e[0];return e.slice(1).forEach((function(e){t=t+"-"+e})),t},"~":function(e){var t="vec2(0.0,0.0)";return e.forEach((function(e){t=t+"-"+e})),t},"*":function(e){var t=e[0];return e.slice(1).forEach((function(e){t="cmul("+t+","+e+")"})),t},"/":function(e){var t=e[0];return e.slice(1).forEach((function(e){t="cdiv("+t+","+e+")"})),t},sin:function(e){return"csin("+e[0]+")"},cos:function(e){return"ccos("+e[0]+")"},tan:function(e){return"ctan("+e[0]+")"},sinh:function(e){return"csinh("+e[0]+")"},cosh:function(e){return"ccosh("+e[0]+")"},arcsin:function(e){return"carcsin("+e[0]+")"},arccos:function(e){return"carccos("+e[0]+")"},arctan:function(e){return"carctan("+e[0]+")"},arccsc:function(e){return"carcsin(cdiv(vec2(1.0,0),"+e[0]+"))"},arcsec:function(e){return"carccos(cdiv(vec2(1.0,0),"+e[0]+"))"},arccot:function(e){return"carctan(cdiv(vec2(1.0,0),"+e[0]+"))"},csc:function(e){return"ccsc("+e[0]+")"},sec:function(e){return"csec("+e[0]+")"},cot:function(e){return"ccot("+e[0]+")"},exp:function(e){return"cexp("+e[0]+")"},conj:function(e){return"conjugate("+e[0]+")"},sqrt:function(e){return"cpower("+e[0]+",vec2(0.5,0.0))"},log:function(e){return"clog("+e[0]+")"},ln:function(e){return"clog("+e[0]+")"},"^":function(e){return"cpower("+e[0]+","+e[1]+")"},abs:function(e){return"cabs("+e[0]+")"},apply:function(e){return"vec2(NaN,NaN)"}};class astToGLSL$1{constructor(){}convert(e){if("boolean"==typeof e)throw Error("no support for boolean");if("string"==typeof e)return"e"===e?"vec2(2.71828182845905,0.0)":"pi"===e?"vec2(3.14159265358979,0.0)":"i"===e?"vec2(0.0,1.0)":String(e);if("number"==typeof e)return"vec2("+String(e)+",0.0)";if("real"in e&&"imaginary"in e)return e;if(!Array.isArray(e))throw Error("Invalid ast");var t=e[0],r=e.slice(1);if("apply"===t){if("string"!=typeof r[0])throw Error("Non string functions not implemented for conversion to GLSL");t=r[0],r=r.slice(1);return glslOperators[t](r.map(function(e,t){return this.convert(e)}.bind(this)))}if(t in glslOperators)return glslOperators[t](r.map(function(e,t){return this.convert(e)}.bind(this)));throw Error("Operator "+t+" not implemented for conversion to mathjs")}}var astToGuppy=new astToGuppy$1,astToGLSL=new astToGLSL$1;const tex=function(e,t){return new astToLatex$1(t).convert(e.tree)},toLatex=tex,toString=function(e,t){return new astToText$2(t).convert(e.tree)},toGLSL=function(e){return astToGLSL.convert(e.tree)},toXML=function(e){return astToGuppy.convert(e.tree)};var printing=Object.freeze({__proto__:null,tex:tex,toLatex:toLatex,toString:toString,toXML:toXML,toGLSL:toGLSL});const integrateNumerically=function(e,t,r,n){for(var i=0,a={},o=0;o<100;o++){var s=r+(n-r)*(o+.5)/100;a[t]=s,i+=e.evaluate(a)}return i*(n-r)/100};var integration=Object.freeze({__proto__:null,integrateNumerically:integrateNumerically});function expression_to_polynomial(e){var t=get_tree(e);if("string"==typeof t)return"pi"===t&&math$1.define_pi||"i"===t&&math$1.define_i||"e"===t&&math$1.define_e?t:["polynomial",t,[[1,1]]];if("number"==typeof t)return t;var r=evaluate_to_constant(t,{remove_units_first:!1});if(Number.isFinite(r))return simplify(t);if(!Array.isArray(t))return!1;if(!operators$3(t).every((e=>["+","-","*","^","/","_","prime"].includes(e))))return!1;var n=t[0],i=t.slice(1);if("+"===n){let e=i.map(expression_to_polynomial);return!!e.every((e=>!1!==e))&&e.reduce(((e,t)=>polynomial_add(e,t)))}if("-"===n){let e=expression_to_polynomial(i[0]);return!!e&&polynomial_neg(e)}if("*"===n){let e=i.map(expression_to_polynomial);return!!e.every((e=>!1!==e))&&e.reduce(((e,t)=>polynomial_mul(e,t)))}if("^"===n){let e=i[0],r=expression_to_polynomial(e);if(!1===r)return!1;let n=simplify(i[1]);if("number"!=typeof n||n<0||!Number.isInteger(n)){let r=evaluate_to_constant(n,{remove_units_first:!1});if(Number.isFinite(r)){let t=math$1.fraction(r);if(t.d<=100){e=t.s<0?["^",e,["/",-1,t.d]]:["^",e,["/",1,t.d]];var a=["polynomial",simplify(e),[]];return a[2].push([t.n,1]),a}}return["polynomial",t,[[1,1]]]}return 0===n?1:1===n?r:polynomial_pow(r,n)}if("/"===n){var o=i[1],s=evaluate_to_constant(o,{remove_units_first:!1});return Number.isFinite(s)?polynomial_mul(expression_to_polynomial(i[0]),["/",1,s]):["polynomial",t,[[1,1]]]}return["polynomial",t,[[1,1]]]}function polynomials_in_same_leading_variable(e,t){return e[1]!==t[1]&&(compare_function(e[1],t[1])<0?t=["polynomial",e[1],[[0,t]]]:e=["polynomial",t[1],[[0,e]]]),[e,t]}function polynomial_add(e,t){if("polynomial"!==e[0]){if("polynomial"!==t[0])return simplify(["+",e,t]);e=["polynomial",t[1],[[0,e]]]}else if("polynomial"!==t[0])t=["polynomial",e[1],[[0,t]]];else{let r=polynomials_in_same_leading_variable(e,t);e=r[0],t=r[1]}let r=["polynomial",e[1],[]],n=e[2],i=t[2],a=r[2],o=n.length,s=i.length,u=0,c=0;for(;u0;)1&t&&(r=polynomial_mul(r,e)),e=polynomial_mul(e,e),t>>=1;return r}function polynomial_to_expression(e){if(!Array.isArray(e)||"polynomial"!==e[0])return e;let t=e[1],r=e[2],n=[],i=r.length;for(var a=0;an[s][1])return!1}return i!==a&&o!==a}function mono_gcd(e,t){if(!Array.isArray(e)||!Array.isArray(t)||"monomial"!==e[0]||"monomial"!==t[0])return 1;let r=e[2],n=t[2],i=[],a=r.length,o=n.length,s=0,u=0;for(;s=0;){var n=[];n.push([e[2][t][1],r]),r=["polynomial",e[2][t][0],n],t-=1}return r}function max_div_init(e,t){if(0===e)return 0;let r=e,n=[];for(;Array.isArray(r)&&"polynomial"===r[0];){let e=r[1],t=r[2],i=t[t.length-1][0];r=t[t.length-1][1],n.push([e,i])}let i=["monomial",r,n],a=t.length;for(var o=0;o0?choice_lowest_degree(a):0}function update_hij_table(e,t,r){let n=t.length;t.push(r);let i=0,a=1,o=[];for(;a0?choice_lowest_degree(o):0}function choice_lowest_degree(e){let t=[],r=e.length;for(i=0;i Date: Wed, 29 Mar 2023 22:18:41 +0000 Subject: [PATCH 2/2] Bump webpack from 5.75.0 to 5.77.0 Bumps [webpack](https://github.com/webpack/webpack) from 5.75.0 to 5.77.0. - [Release notes](https://github.com/webpack/webpack/releases) - [Commits](https://github.com/webpack/webpack/compare/v5.75.0...v5.77.0) --- updated-dependencies: - dependency-name: webpack dependency-type: indirect ... Signed-off-by: dependabot[bot] --- package-lock.json | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/package-lock.json b/package-lock.json index 262d56b..7a6514e 100644 --- a/package-lock.json +++ b/package-lock.json @@ -11725,9 +11725,9 @@ } }, "node_modules/webpack": { - "version": "5.75.0", - "resolved": "https://registry.npmjs.org/webpack/-/webpack-5.75.0.tgz", - "integrity": "sha512-piaIaoVJlqMsPtX/+3KTTO6jfvrSYgauFVdt8cr9LTHKmcq/AMd4mhzsiP7ZF/PGRNPGA8336jldh9l2Kt2ogQ==", + "version": "5.77.0", + "resolved": "https://registry.npmjs.org/webpack/-/webpack-5.77.0.tgz", + "integrity": "sha512-sbGNjBr5Ya5ss91yzjeJTLKyfiwo5C628AFjEa6WSXcZa4E+F57om3Cc8xLb1Jh0b243AWuSYRf3dn7HVeFQ9Q==", "dev": true, "peer": true, "dependencies": {