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5.6  Module Complex

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 (#'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.



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