Copyright	(c) Stéphane Laurent 2023
License	BSD3
Maintainer	laurent_step@outlook.fr
Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.Weierstrass

Description

Provides some Weierstrass functions and related functions.

Synopsis

halfPeriods :: Complex Double -> Complex Double -> (Complex Double, Complex Double)
ellipticInvariants :: Complex Double -> Complex Double -> (Complex Double, Complex Double)
weierstrassP :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassP' :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassPdash :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassPdash' :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassPinv :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassPinv' :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassSigma :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassSigma' :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassZeta :: Complex Double -> Complex Double -> Complex Double -> Complex Double
weierstrassZeta' :: Complex Double -> Complex Double -> Complex Double -> Complex Double

Documentation

halfPeriods Source #

Arguments

:: Complex Double	g2
-> Complex Double	g3
-> (Complex Double, Complex Double)	omega1, omega2

Half-periods from elliptic invariants.

ellipticInvariants Source #

Arguments

:: Complex Double	omega1
-> Complex Double	omega2
-> (Complex Double, Complex Double)	g2, g3

Elliptic invariants from half-periods.

weierstrassP Source #

Arguments

:: Complex Double	z
-> Complex Double	half-period omega1
-> Complex Double	half-period omega2
-> Complex Double

Weierstrass p-function given the half-periods

weierstrassP' Source #

Arguments

:: Complex Double	z
-> Complex Double	elliptic invariant g2
-> Complex Double	elliptic invariant g3
-> Complex Double

Weierstrass p-function given the elliptic invariants

weierstrassPdash Source #

Arguments

:: Complex Double	z
-> Complex Double	half-period omega1
-> Complex Double	half-period omega2
-> Complex Double

Derivative of Weierstrass p-function given the half-periods

weierstrassPdash' Source #

Arguments

:: Complex Double	z
-> Complex Double	elliptic invariant g2
-> Complex Double	elliptic invariant g3
-> Complex Double

Derivative of Weierstrass p-function given the elliptic invariants

weierstrassPinv Source #

Arguments

:: Complex Double	w
-> Complex Double	half-period omega1
-> Complex Double	half-period omega2
-> Complex Double

Inverse of Weierstrass p-function given the half-periods

weierstrassPinv' Source #

Arguments

:: Complex Double	z
-> Complex Double	elliptic invariant g2
-> Complex Double	elliptic invariant g3
-> Complex Double

Inverse of Weierstrass p-function given the elliptic invariants

weierstrassSigma Source #

Arguments

:: Complex Double	z
-> Complex Double	half-period omega1
-> Complex Double	half-period omega2
-> Complex Double

Weierstrass sigma function given the half-periods

weierstrassSigma' Source #

Arguments

:: Complex Double	z
-> Complex Double	elliptic invariant g2
-> Complex Double	elliptic invariant g3
-> Complex Double

Weierstrass sigma function given the elliptic invariants

weierstrassZeta Source #

Arguments

:: Complex Double	z
-> Complex Double	half-period omega1
-> Complex Double	half-period omega2
-> Complex Double

Weierstrass zeta function given the half-periods

weierstrassZeta' Source #

Arguments

:: Complex Double	z
-> Complex Double	elliptic invariant g2
-> Complex Double	elliptic invariant g3
-> Complex Double

Weierstrass zeta function given the elliptic invariants