.TH "Stdlib.Complex" 3o 2023-09-18 OCamldoc "OCaml library"
.SH NAME
Stdlib.Complex \- no description
.SH Module
Module   Stdlib.Complex
.SH Documentation
.sp
Module
.BI "Complex"
 : 
.B (module Stdlib__Complex)

.sp

.sp

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

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

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

.sp

.I val polar 
: 
.B float -> float -> t
.sp

.ft B
polar norm arg
.ft R
returns the complex having norm 
.ft B
norm
.ft R
and argument 
.ft B
arg
.ft R
\&.

.sp

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

.sp

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

.sp

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

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