.. index:: single: lua
|rezonator| uses Lua internally to calculate custom formulas. Here are some citations from the original documentation to get a brief intro into the language. Provided information should be sufficient to write formulas for :ref:`schema parameters <params_window>`, :doc:`custom elements <elem_formula>` or to carry out calculations in :doc:`calc_formula`.
Lua is a free-form language. It ignores spaces (including newlines) and comments between lexical elements (tokens), except as delimiters between names and keywords.
Variables are places that store values.
Lua is a case-sensitive language: and is a reserved word, but And and AND are two different, valid names.
The following keywords are reserved and cannot be used as names:
and, break, do, else, elseif, end,
false, for, function, goto, if, in,
local, nil, not, or, repeat, return,
then, true, until, while.
A numeric value can be written with an optional fractional part and an optional decimal exponent, marked by a letter e or E. Examples of valid values are 3, 3.1416, 314.16e-2, 0.31416E1, 34e1
Lua allows multiple assignments:
x, y = 10, 20 x, y, z = y, z, x
Lua supports the following arithmetic operators:
+ --- addition
- --- subtraction
* --- multiplication
/ --- float division
// --- floor division
% --- modulo (remainder of a division that rounds the quotient towards minus infinity)
^ --- exponentiation (it works for non-integer exponents too)
- --- unary minus
Lua supports the following relational operators:
== --- equality
~= --- inequality
< --- less than
> --- greater than
<= --- less or equal
>= --- greater or equal
A comment starts with a double hyphen (--) and runs until the end of the line.
Lua provides a set of mathematical functions in the math library. One has to call them using the library name, e.g., math.sin(math.pi / 4). For convenience, |rezonator| supports its own set of standard mathematical functions that can be used without any additional prefix, e.g., sin(pi()/4).
sin --- returns the sine of the angle in radians.
sinh --- returns the hyperbolic sine of the argument.
asin --- returns the arcsine of the argument as an angle in radians.
cos --- returns the cosine of the angle in radians.
cosh --- returns the hyperbolic cosine of the argument.
acos --- returns the arccosine of the argument as an angle in radians.
tan --- returns the tangent of the angle in radians.
tanh --- returns the hyperbolic tangent of the argument.
atan --- returns the arctangent of the argument as an angle in radians.
cot --- returns the cotangent of the angle in radians.
coth --- returns the hyperbolic cotangent of the argument.
acot --- returns the arccotangent of the argument as an angle in radians.
sec --- returns the secant of the angle in radians.
sech --- returns the hyperbolic secant of the argument.
csc --- returns the cosecant of the angle in radians.
csch --- returns the hyperbolic cosecant of the argument.
abs --- returns the absolute value of the argument.
floor --- returns the largest integer that is not greater than the argument. For example, floor(41.2) = 41.
ceil --- returns the smallest integer that is not less than the argument. For example, ceil(41.2) = 42.
exp --- returns the value of e to the power of the argument, where e is the base of natural logarithms.
ln --- returns the natural logarithm of the argument. Natural logarithm uses base e.
lg --- returns the logarithm of the argument in base 10.
sqrt --- returns the square root of the argument.
deg2rad --- converts the angle from degrees to radians.
rad2deg --- converts the angle from radians to degrees.
pi --- returns value π.