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.
