Abstract
Complex numbers parameterised over the representation of their real parts.
Divided into a module type for modules that implement complex numbers, and a parametric module that can construct such modules.
Synopsis
module type complex = {
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| module mk_complex | : | (T: real) -> (complex with real = T.t with complex = (T.t, T.t)) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Description
- ↑module type complex
The type of modules that implement a notion of complex numbers. Semantically, a complex number can be seen as a pair of two numbers (but this need not be the representation).
- ↑type real
The type of the components of the complex number.
- ↑type complex
The type of complex numbers.
- ↑type t = complex
Helper type for easy compatiblity with other modules.
- ↑val mk: real -> real -> complex
Construct a complex number from real and imaginary components.
- ↑val mk_re: real -> complex
Construct a complex number from just the real component. The imaginary part will be zero.
- ↑val mk_im: real -> complex
Construct a complex number from just the imaginary component. The real part will be zero.
- ↑val i64: i64 -> complex
Construct a complex number from i64. The imaginary part will be zero.
- ↑val conj: complex -> complex
Conjugate a complex number.
- ↑val neg: complex -> complex
Negate a complex number.
- ↑val re: complex -> real
The real part of a complex number.
- ↑val im: complex -> real
The imaginary part of a complex number.
- ↑val mag: complex -> real
The magnitude (or modulus, or absolute value) of a complex number.
- ↑val arg: complex -> real
The argument (or phase) of a complex number.
- ↑val +: complex -> complex -> complex
- ↑val -: complex -> complex -> complex
- ↑val *: complex -> complex -> complex
- ↑val /: complex -> complex -> complex
- ↑val **: complex -> complex -> complex
- ↑val <: complex -> complex -> bool
- ↑val >: complex -> complex -> bool
- ↑val >=: complex -> complex -> bool
- ↑val <=: complex -> complex -> bool
- ↑val sqrt: complex -> complex
- ↑val exp: complex -> complex
- ↑val log: complex -> complex
- ↑val abs: complex -> complex
- ↑val fma: complex -> complex -> complex -> complex
- ↑val sum [n]: [n]complex -> complex
- ↑module mk_complex
Given a module describing a number type, construct a module implementing complex numbers.