Weierstrass and Jacobi Elliptic 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 function...
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
tools:::Rd_package_title("elliptic")
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
Various modular functions
quarter period K
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
Laurent series for elliptic and related functions
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
Neville's form for the theta functions
Jacobi theta functions 1-4
Derivative of theta1
Derivatives of theta functions
Unimodular matrices
Visualization of complex functions
Weierstrass P and related functions
A suite of elliptic and related functions including Weierstrass and Jacobi forms. Also includes various tools for manipulating and visualizing complex functions.
Useful links