Complex Numbers
Info: This resource is for extending the Real Mathematics in Lua to the Complex ones. Notice that the square root of -1 does not have a clear solution, since real numbers multiplied by themselves will always return 0 or a positive number. This is when complex numbers come here; since they are not real numbers some operations will mess up (like Lua math functions), giving results such as NaN (not a number). Some people requested to add Complex Numbers support, this is why this resource was created.
Usage: To use this, just download or use “require()” to install the Complex Math
library. To start using the operations just call the functions with a dot ‘.’ :
local cmplxMath = require(8152231789) -- or the ModuleScript you have in your game
print(cmplxMath.asin(2)) -- calls 'asin' function
--Expected output: 1.5707963267949-1.3169578969248i
Take in mind that almost all ‘cmplxMath’ functions creates CmplxNumber datatype, which is a table (attached to a metatable) that behaves like a number and at the same time as a table. This datatype cannot be used with functions that allow numbers (since it is a table), you can use ‘re’, ‘im’ and ‘ord’ functions to convert this datatype to a number.
Functions:
number cmplxMath.abs (number x)
Returns the length between (0, 0) to x
number cmplxMath.acos (number x)
Returns the arc cosine of x.
number cmplxMath.arg (number x)
Returns the angle between Re axis and x
number cmplxMath.atan (number x)
Returns the arc tangent of x (in radians).
number cmplxMath.atan2 (number y, number x)
Returns the angle between the ray of the point (x, y)* **.
number cmplxMath.asin (number x)
Returns the arc sine of x.
int cmplxMath.ceil (number x)
Returns the smallest integer larger than or equal to x.
number cmplxMath.clamp (number x, number min, number max)
Fixes x between min and max.
bool cmplxMath.cmplx (Variant x)
Verifies if x is a validCmplxNumberdatatype.
CmplxNumber cmplxMath.cmplx (number x, number y)
Convertsx+yito aCmplxNumberdatatype*.
number cmplxMath.conj (number x)
Returns the Re part with opposite Im part.
number cmplxMath.cos (number x)
Returns the cosine of x (in radians).
number cmplxMath.cosh (number x)
Returns the hyperbolic cosine of x.
number cmplxMath.deg (number x)
Converts x to degrees (x in radians).
number cmplxMath.exp (number x)
Returnse ^ x.
int cmplxMath.floor (number x)
Returns the largest integer smaller than or equal to x.
number cmplxMath.fmod (number x, number y)
Returns the remainder ofx / y(truncated division)* **.
number, int cmplxMath.frexp (number x)
Returns m and e such thatx = m*2^e* **.
number cmplxMath.gamma (number x)
Extension of the factorial function.
number cmplxMath.im (number x)
Returns the Im part of x**.
number cmplxMath.ldexp (number x, number e)
Returnsx*2^e(e should be an integer)* **.
number cmplxMath.log (number x, number base = 2.7182818)
Returns the logarithm of x using the given base.
number cmplxMath.log10 (number x)
Returns the base-10 logarithm of x.
number cmplxMath.max (number x, number …)
Returns the maximum value among the numbers passed to the function***.
number cmplxMath.min (number x, number …)
Returns the minimum value among the numbers passed to the function***.
int, number cmplxMath.modf (number x)
Returns the integral part of x and the fractional part of x.
number cmplxMath.noise (number x, number y = 0, number z = 0)
Returns a perlin noise value* **.
number, number cmplxMath.ord (number x)
Returns the Re part and Im part of x**.
number cmplxMath.polar (number x, number y)
Returns the position in the complex plane (x is length, y is angle).
number cmplxMath.pow (number x, number y)
Returnsx ^ y.
number cmplxMath.rad (number x)
Converts x to radians (x in degrees).
number cmplxMath.random (number m = 0.0, number n = 1.0)
Gives a random number between m and n.
void cmplxMath.randomseed (number x)
Sets the seed of the pseudo-random generator*.
number cmplxMath.re (number x)
Returns the Re part of x**.
int cmplxMath.round (number x)
Returns the integer with the smallest difference between it and the given number.
number cmplxMath.sign (number x)
Extracts the sign of x.
number cmplxMath.sin (number x)
Returns the sine of x (in radians).
number cmplxMath.sinh (number x)
Returns the hyperbolic sine of x.
number cmplxMath.sqrt (number x)
Returns the square root of x.
number cmplxMath.tan (number x)
Returns the tangent of x (in radians).
number cmplxMath.tanh (number x)
Returns the hyperbolic tangent of x.
Constants:
number cmplxMath.huge
A value larger than or equal to any other numerical value**.
CmplxNumber cmplxMath.imag
Gives sqrt(-1), instead of NaN.
number cmplxMath.pi
The value of pi**.
* This function only accepts real numbers.
** Returns number datatype.
*** Only accepts pure real or imaginary numbers.
Notes:
- Almost all operations supports complex numbers and returns complex numbers.
Operation |
Lua Built-in Library |
Complex Math Library |
|---|---|---|
math.sqrt(-1) |
-nan(ind) |
i |
math.asin(2) |
-nan(ind) |
1.570796...-1.316957...i |
math.sqrt(-1) ^ 2 |
-nan(ind) |
-1 |
math.log10(-10) |
-nan(ind) |
1+1.3643763538418i |
- This library uses identities and formulas (such as Euler’s Identity).
Operation |
Lua Built-in Library |
Complex Math Library |
|---|---|---|
i ^ i |
-nan(ind) |
0.20787957635076 |
e ^ (i * pi) |
-nan(ind) |
-1 |
cos(i * pi) |
-nan(ind) |
11.591953275522 |
- Some operations have been modificated for this Math library.
Operation |
Lua Built-in Library |
Complex Math Library |
|---|---|---|
inf - inf |
-nan(ind) |
0 |
math.sqrt(inf) |
inf |
-nan(ind)-nan(ind)*i |
- This library is accurate to over 1 part in 100 quintillion.
- Gamma function might have little errors.
Feel free to use it, no credit is needed. Please comment if you have any problem 
(v1.0.2)