module Complex: sig .. end
Complex numbers.
This module provides arithmetic operations on complex numbers.
Complex numbers are represented by their real and imaginary parts
(cartesian representation). Each part is represented by a
double-precision floating-point number (type float).
type t = {
}
The type of complex numbers. re is the real part and im the
imaginary part.
val zero : t
The complex number 0.
val one : t
The complex number 1.
val i : t
The complex number i.
val neg : t -> t
Unary negation.
val conj : t -> t
Conjugate: given the complex x + i.y, returns x - i.y.
val add : t -> t -> t
Addition
val sub : t -> t -> t
Subtraction
val mul : t -> t -> t
Multiplication
val inv : t -> t
Multiplicative inverse (1/z).
val div : t -> t -> t
Division
val 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.
val norm2 : t -> float
Norm squared: given x + i.y, returns x^2 + y^2.
val norm : t -> float
Norm: given x + i.y, returns sqrt(x^2 + y^2).
val 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.
val polar : float -> float -> t
polar norm arg returns the complex having norm norm
and argument arg.
val exp : t -> t
Exponentiation. exp z returns e to the z power.
val log : t -> t
Natural logarithm (in base e).
val pow : t -> t -> t
Power function. pow z1 z2 returns z1 to the z2 power.