Factoring Trinomials and Difference of Squares #41

aliang8 · 2017-06-02T02:09:23Z

PERFECT_SQUARE_TRINOMIAL and FACTOR_TRINOMIAL logic is somewhat redundant, not sure if we should remove it and just have one rule. Code should be refactored if possible.

kevinbarabash · 2017-06-13T02:00:52Z

lib/rules.js

+// assume monic polynomial
+// TODO: add min and max to evaluate
+
+export const FACTOR_SYMBOL = defineRuleString('#a^#b_0 + ...', '#a^#eval(min(#b_0, ...)) (#a^#eval(#b_0 - min(#b_0, ...)) + ...)', {b: query.isNumber})


Neato! Could you provide an example what this does?

Ahhh, this doesn't exactly work yet. This rule only applies to addition (x^2 + x^3 + x^4 -> x^2(x^0 + x^1 + x^2). Not exactly sure if we want two separate rules for addition and subtraction or if there is a way to do both in a rule string. I also need the min and max functions to be exposed in math-evaluator.

I think this should work with subtraction as is. Have you tried writing a test case with subtraction?

Yeah, I need min and max to support nary parameters.

kevinbarabash · 2017-06-13T02:05:11Z

lib/rules.js

+    (node) => {
+        const isFactorable = canApplyRule(FACTOR_SUM_PRODUCT_RULE, node)
+        if (isFactorable) {
+            const result = applyRule(FACTOR_SUM_PRODUCT_RULE, node)


kevinbarabash · 2017-06-13T02:06:40Z

lib/rules.js

@@ -353,6 +353,267 @@ export const GROUP_TERMS_BY_ROOT = defineRule(
 // e.g nthRoot(9, 2) -> 3
 export const NTH_ROOT_VALUE = defineRuleString('nthRoot(#a, #b)', '#eval(nthRoot(#a, #b))', {a: query.isNumber, b: query.isNumber})

+// FACTOR


Can you put these in their own file? I'd like eventually rename this file to be simple-rules.js and have it contain only rules which can be full expressed with patterns.

kevinbarabash · 2017-06-13T02:09:47Z

lib/rules.js

+                let isFactorable = false
+                const {constants, coefficientMap} = getCoefficientsAndConstants(node)
+                const variables = Object.keys(coefficientMap).map(key => parse(key))
+                const coefficients = Object.keys(coefficientMap).map(key => {return coefficientMap[key]})


const coeffs = Object.keys(coeffMap).map(key => coeffMap[key][0])

This keeps it to a single line and you don't have to do coeffs[1][0] later you can just do coeffs[1].

kevinbarabash · 2017-06-13T02:14:52Z

lib/rules.js

+            const isTrinomial =
+                  isPolynomialTerm(firstTerm)
+                  && isPolynomialTerm(secondTerm)
+                  && (query.isNumber(thirdTerm) || isPolynomialTerm(thirdTerm))


We should probably handle things like 1 + 2x + x^2 as well... maybe we should have a transform to order terms in a polynomial in descending order. This can be a TODO.

Yup I was thinking to go with the second approach.

kevinbarabash · 2017-06-13T02:22:27Z

lib/rules.js

+    (node) => {
+        const {constants, coefficientMap} = getCoefficientsAndConstants(node)
+        const variables = Object.keys(coefficientMap).map(key => parse(key))
+        const coefficients = Object.keys(coefficientMap).map(key => {return coefficientMap[key]})


return isn't necessary.

kevinbarabash · 2017-06-13T02:26:44Z

lib/rules.js

+        for (var i in firstFactors){
+            for (var j in thirdFactors) {
+                const l1 = firstFactors[i]
+                const l2 = thirdFactors[j]


I have no idea what's going on here. Can you add a comment explaining this algorithm?

kevinbarabash · 2017-06-13T02:27:56Z

lib/rules.js

+                   build.apply(
+                       'mul',
+                       [build.number(factor[0]), ...firstPoly.map(
+                           term =>


term -> factor

kevinbarabash · 2017-06-13T02:29:00Z

lib/rules.js

+        }
+
+        const result = build.applyNode
+        ('mul',


All of the these implicit muls can be build using build.implicitMul.

kevinbarabash · 2017-06-13T02:29:39Z

lib/rules.js

+        }
+        if (combo == []) {
+            throw new Error('cannot factor polynomial')
+        }


If feels weird that canApplyRule might be successful, but applyRule might still fail.

Good point, I have to fix this.

Not entirely sure how to without replicating the code for rewriteFn.

I would extract a common function. Obviously it's not ideal to run the same code twice, but I'd rather maintain the invariant that if canApplyRule returns true that applyRule will succeed.

kevinbarabash · 2017-06-18T21:54:18Z

lib/factor-rules.js

+
+const getExponent = (node) => {
+    if (query.isNumber(node)) {
+        return 0


This seems like a weird value to return for a number. I would expect the exponent to be 1. Maybe there should be an if statement before calling getExponent to check if the node is a number.

Oh, the getExponent function is to get the degree of x for a given polynomial term. So for instance, 6x^2 + 3x + 1, getExponent on 1 would return 0 because it is 1x^0. Maybe the function name itself is a bit misleading?

kevinbarabash · 2017-06-18T21:55:38Z

lib/factor-rules.js

+    } else if (query.isPow(node)) {
+        return query.getValue(node.args[1])
+    } else if (query.isMul(node)){
+        return getExponent(node.args[1])


Shouldn't this be return Math.max(...node.args.map(getExponent))?

It's okay to limit ourselves to single variables for now, but we should have a TODO somewhere.

kevinbarabash · 2017-06-18T21:56:38Z

lib/factor-rules.js

+}
+
+// e.g. 2 + 3x^2 + 3x - 4x^3 -> -4x^3 + 3x^2 + 3x + 2
+export const REARRANGE_TERMS = defineRule(


This doesn't take into account polynomials with multiple variables. Maybe add a TODO.

kevinbarabash · 2017-06-18T22:00:43Z

lib/factor-rules.js

+
+  3. Cross multiply the factors and check if
+  the result matches one of the eight conditions
+  (the second factor shld also multiply to equal the thirdCoef)


shld --> should

kevinbarabash · 2017-06-18T22:04:13Z

lib/factor-rules.js

+
+  Check: 1 * 2 + 6 * 1 ?= 7 so on and so forth
+  Once we reach 2 * 2 + 3 * 1 ?= 7, we have found a match.
+  (Note: 3 * 1 = 3 satisfying the second condition)


I'm confused about this note.... don't we want to check if the multiple the first candidate coefficients results in the first coefficient of the trinomial and multiplying the both of the second candidate numbers results in the constant of the trinomial. In this case 2 * 3 = 6 and 2 * 1 = 2 so it works out.

You already know that 2 * 3 = 6 and 2 * 1 = 2. It comes from the fact that those are the factors of 6 and 2 respectively (pairs that we got from firstFactors and thirdFactors). The note here is just to make sure we don't have an erroneous combo / solution (this happened a few times in my test cases).

I need to spend some more time with this to really understand what's going on. I have some of pieces but not everything. This is eventually going to get re-reviewed when it gets moved over to mathsteps so I'm okay with merging this.

Awesome, let me know when you merge this, so I can update my other PRs.

kevinbarabash · 2017-06-18T22:06:23Z

lib/factor-rules.js

+    }
+)
+
+const getFactors = (num) => {


This should maybe be called getFactorPairs or add a comment describing what it does. I was confused b/c I thought calling getFactors(12) would return [1, 2, 3, 4, 6, 12] but in fact it returns [[1, 12], [2, 6], [3, 4]].

kevinbarabash · 2017-06-18T22:10:15Z

lib/factor-rules.js

+        ? query.isMul(variables[2])
+        ? variables[2].args
+        : [variables[2]]
+        : null


Can you rewrite this ternary as an if-else?

kevinbarabash · 2017-06-18T22:10:20Z

lib/factor-rules.js

+        query.getValue(coeffs[2])
+    : constants[0]
+    ? query.getValue(constants[0])
+    : null


kevinbarabash · 2017-06-18T22:12:09Z

lib/factor-rules.js

+  At this point, we find that the correct combination is
+  : [2,3] and [1,2] -> (2x + 3)(1x + 2)
+*/
+const factor_trinomial_helper = (node) => {


Does this handle cases where the lead coefficient is negative?

We assume that lead coefficient is positive because it should have been factored out previously by another rule.

kevinbarabash · 2017-06-18T22:20:12Z

lib/factor-rules.js

+              ? query.isMul(variables[2])
+              ? variables[2].args
+          : [variables[2]]
+        : null


The indentation is a little off here. It should probably be:

const thirdPoly = variables[2] ? query.isMul(variables[2]) ? variables[2].args : [variables[2]] : null

even that is hard to parse... since the default is null maybe do:

let thirdPoly = null; if (variables[2]) { if (query.isMul(variables[2]) { thirdPoly = variables[2].args } else { thirdPoly = [variables[2]] } }

kevinbarabash · 2017-06-18T22:20:47Z

lib/factor-rules.js

+      ? query.isMul(variables[2])
+          ? variables[2].args
+      : [variables[2]]
+          : null


Please rewrite as if-else statements.

aliang8 added 30 commits April 30, 2017 13:48

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kevinbarabash reviewed Jun 18, 2017

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lib/factor-rules.js Outdated

query.getValue(coeffs[2])

: constants[0]

? query.getValue(constants[0])

: null

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aliang8 added 3 commits June 18, 2017 20:48

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Factoring Trinomials and Difference of Squares #41

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Factoring Trinomials and Difference of Squares #41

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aliang8 commented Jun 2, 2017

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aliang8 Jun 19, 2017 • edited Loading

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