NAME

       Complex - Complex numbers.

Module

       Module   Complex

Documentation

       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 .  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.