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
= {
re :
float
;
im :
float
;
}
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 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.