FloatEllipticFunctionsΒΆ

special2.spad line 1340

This package implements arbitrary precision numerical elliptic functions. The method is based on descending Landen transform.

ellipticE: (Complex Float, Complex Float) -> Complex Float
ellipticE(z, m) is the incomplete elliptic integral of the second kind.
ellipticE: (Float, Float) -> Float
ellipticE(z, m) is the incomplete elliptic integral of the second kind.
ellipticE: Complex Float -> Complex Float
ellipticE(m) is the complete elliptic integral of the second kind.
ellipticE: Float -> Float
ellipticE(m) is the complete elliptic integral of the second kind.
ellipticF: (Complex Float, Complex Float) -> Complex Float
ellipticF(z, m) is the incomplete elliptic integral of the first kind.
ellipticF: (Float, Float) -> Float
ellipticF(z, m) is the incomplete elliptic integral of the first kind.
ellipticK: Complex Float -> Complex Float
ellipticK(m) is the complete elliptic integral of the first kind.
ellipticK: Float -> Float
ellipticK(m) is the complete elliptic integral of the first kind.
jacobiCn: (Complex Float, Complex Float) -> Complex Float
jacobiCn(z, m) is the Jacobi cn function
jacobiCn: (Float, Float) -> Float
jacobiCn(z, m) is the Jacobi cn function
jacobiDn: (Complex Float, Complex Float) -> Complex Float
jacobiDn(z, m) is the Jacobi dn function
jacobiDn: (Float, Float) -> Float
jacobiDn(z, m) is the Jacobi dn function
jacobiSn: (Complex Float, Complex Float) -> Complex Float
jacobiSn(z, m) is the Jacobi sn function
jacobiSn: (Float, Float) -> Float
jacobiSn(z, m) is the Jacobi sn function
jacobiZeta: (Float, Float) -> Float
jacobiZeta(z, m) is the Jacobi zeta function
kprod: List Complex Float -> Complex Float
Undocumented.
kprod: List Float -> Float
Undocumented.
landen1: (Complex Float, List Complex Float) -> List Complex Float
Undocumented.
landen1: (Float, List Float) -> List Float
Undocumented.
landen2: (Complex Float, List Complex Float, Float) -> List Complex Float
Undocumented.
landen2: (Float, List Float, Float) -> List Float
Undocumented.
landen: (Complex Float, Float) -> List Complex Float
Undocumented.
landen: (Float, Float) -> List Float
Undocumented.
modularInvariantJ: Complex Float -> Complex Float
modularInvariantJ(tau) computes modular invariant j, that is 1728*g2^3/(g2^3 - 27*g3^2) where g2, g3 are invariants corresponding to half periods w1, w2 such that tau = w1/w2.
rabs: Complex Float -> Float
Undocumented.
rabs: Float -> Float
Undocumented.
sn2: (Complex Float, List Complex Float) -> Complex Float
Undocumented.
sn2: (Float, List Float) -> Float
Undocumented.
weierstrassHalfPeriods: (Complex Float, Complex Float) -> List Complex Float
weierstrassHalfPeriods(g2, g3) computes half periods of Weierstrass elliptic functions from invariants g2, g3.
weierstrassInvariants: (Complex Float, Complex Float) -> List Complex Float
weierstrassInvariants(w1, w2) computes invariants g2, g3 of Weierstrass elliptic functions from half periods w1, w2.
weierstrassP: (Complex Float, Complex Float, Complex Float) -> Complex Float
weierstrassP(g2, g3, x) is the Weierstrass P function
weierstrassP: (Float, Float, Float) -> Float
weierstrassP(g2, g3, x) is the Weierstrass P function
weierstrassPPrime: (Complex Float, Complex Float, Complex Float) -> Complex Float
weierstrassPPrime(g2, g3, x) is the derivative of the Weierstrass P function
weierstrassPPrime: (Float, Float, Float) -> Float
weierstrassPPrime(g2, g3, x) is the derivative of the Weierstrass P function