elliptic

Various modular functions

quarter period K

Laurent series for elliptic and related functions

Weierstrass P and related functions

matrix a on page 637

Converts basic periods to a primitive pair

Coefficients of Laurent expansion of Weierstrass P function

Solves mx+by=1 for x and y

Fast, conceptually simple, iterative scheme for Weierstrass P functions

Number theoretic functions

Numerical verification of equations 16.28.1 to 16.28.5

Numerical checks of equations 18.10.9-11, page 650

Calculate e1, e2, e3 from the invariants

Weierstrass and Jacobi Elliptic Functions

Special cases of the Weierstrass elliptic function

Dedekind's eta function

Farey sequences

Fundamental period parallelogram

Calculates the invariants g2 and g3

Calculates half periods in terms of e

Plots a lattice of periods on the complex plane

Lattice of complex numbers

Limit the magnitude of elements of a vector

Massages numbers near the real line to be real

Manipulate real or imaginary components of an object

Moebius transformations

Complex integration

Are two vectors close to one another?

Newton Raphson iteration to find roots of equations

Nome in terms of m or k

Does the right thing when calling g2.fun() and g3.fun()

Parameters for Weierstrass's P function

Wrappers for PARI functions

Jacobi form of the elliptic functions

Generalized square root

Jacobi theta functions 1-4

Neville's form for the theta functions

Derivative of theta1

Derivatives of theta functions

Unimodular matrices

Visualization of complex functions