.TH "Complex" 3o source: 2019-01-25 OCamldoc "OCaml library"
.SH NAME
Complex \- Complex numbers.
.SH Module
Module   Complex
.SH Documentation
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Module
.BI "Complex"
 : 
.B sig  end

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Complex numbers\&.
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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 
.B float
)\&.

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.I type t 
= {
 re : 
.B float
;
 im : 
.B float
;
 }

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The type of complex numbers\&.  
.B re
is the real part and 
.B im
the
imaginary part\&.

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.I val zero 
: 
.B t
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The complex number 
.B 0
\&.

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.I val one 
: 
.B t
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The complex number 
.B 1
\&.

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.I val i 
: 
.B t
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The complex number 
.B i
\&.

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.I val neg 
: 
.B t -> t
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Unary negation\&.

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.I val conj 
: 
.B t -> t
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Conjugate: given the complex 
.B x + i\&.y
, returns 
.B x \- i\&.y
\&.

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.I val add 
: 
.B t -> t -> t
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Addition

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.I val sub 
: 
.B t -> t -> t
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Subtraction

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.I val mul 
: 
.B t -> t -> t
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Multiplication

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.I val inv 
: 
.B t -> t
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Multiplicative inverse (
.B 1/z
)\&.

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.I val div 
: 
.B t -> t -> t
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Division

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.I val sqrt 
: 
.B t -> t
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Square root\&.  The result 
.B x + i\&.y
is such that 
.B x > 0
or
.B x = 0
and 
.B y >= 0
\&.
This function has a discontinuity along the negative real axis\&.

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.I val norm2 
: 
.B t -> float
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Norm squared: given 
.B x + i\&.y
, returns 
.B x^2 + y^2
\&.

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.I val norm 
: 
.B t -> float
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Norm: given 
.B x + i\&.y
, returns 
.B sqrt(x^2 + y^2)
\&.

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.I val arg 
: 
.B t -> float
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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
.B \-pi
to 
.B pi
\&.  This function has a discontinuity along the
negative real axis\&.

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.I val polar 
: 
.B float -> float -> t
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.B polar norm arg
returns the complex having norm 
.B norm
and argument 
.B arg
\&.

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.I val exp 
: 
.B t -> t
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Exponentiation\&.  
.B exp z
returns 
.B e
to the 
.B z
power\&.

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.I val log 
: 
.B t -> t
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Natural logarithm (in base 
.B e
)\&.

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.I val pow 
: 
.B t -> t -> t
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Power function\&.  
.B pow z1 z2
returns 
.B z1
to the 
.B z2
power\&.

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