type (#'a:level) t = { re : 'a float; im : 'a float; }
The type of complex numbers. re is the real part and im the
imaginary part.
val zero : 'a t
The complex number 0.
val one : 'a t
The complex number 1.
val i : 'a t
The complex number i.
val neg : 'a t -> 'a t
Unary negation.
val conj : 'a t -> 'a t
Conjugate: given the complex x + i.y, returns x - i.y.
val add : 'a t -> 'a t -> 'a t
Addition
val sub : 'a t -> 'a t -> 'a t
Subtraction
val mul : 'a t -> 'a t -> 'a t
Multiplication
val inv : 'a t -> 'a t
Multiplicative inverse (1/z).
val div : 'a t -> 'a t -> 'a t
Division
val sqrt : 'a t -> 'a 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 : 'a t -> 'a float
Norm squared: given x + i.y, returns x^2 + y^2.
val norm : 'a t -> 'a float
Norm: given x + i.y, returns sqrt(x^2 + y^2).
val arg : 'a t -> 'a 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 : 'a float -> 'a float -> 'a t
polar norm arg returns the complex having norm norm
and argument arg.
val exp : 'a t -> 'a t
Exponentiation. exp z returns e to the z power.
val log : 'a t -> 'a t
Natural logarithm (in base e).
val pow : 'a t -> 'a t -> 'a t
Power function. pow z1 z2 returns z1 to the z2 power.
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).