module Complex: Complex;
type t = {
|
re : float; |
|
im : float; |
}
The type of complex numbers. re is the real part and im the
imaginary part.
let zero: t;
The complex number 0.
let one: t;
The complex number 1.
let i: t;
The complex number i.
let neg: t => t;
Unary negation.
let conj: t => t;
Conjugate: given the complex x + i.y, returns x - i.y.
let add: (t, t) => t;
Addition
let sub: (t, t) => t;
Subtraction
let mul: (t, t) => t;
Multiplication
let inv: t => t;
Multiplicative inverse (1/z).
let div: (t, t) => t;
Division
let sqrt: t => t;
Square root. The result x + i.y is such that x > 0 or
x = 0 and y >= 0.
This function has a discontinuity along the negative real axis.
let norm2: t => float;
Norm squared: given x + i.y, returns x^2 + y^2.
let norm: t => float;
Norm: given x + i.y, returns sqrt(x^2 + y^2).
let arg: t => float;
Argument. The argument of a complex number is the angle
in the complex plane between the positive real axis and a line
passing through zero and the number. This angle ranges from
-pi to pi. This function has a discontinuity along the
negative real axis.
let polar: (float, float) => t;
polar norm arg returns the complex having norm norm
and argument arg.
let exp: t => t;
Exponentiation. exp z returns e to the z power.
let log: t => t;
Natural logarithm (in base e).
let pow: (t, t) => t;
Power function. pow z1 z2 returns z1 to the z2 power.