# elliptic v1.4-0

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## Weierstrass and Jacobi Elliptic Functions

A suite of elliptic and related functions including Weierstrass and Jacobi forms. Also includes various tools for manipulating and visualizing complex functions.

## Functions in elliptic

 Name Description P.laurent Laurent series for elliptic and related functions eta Dedekind's eta function e16.28.1 Numerical verification of equations 16.28.1 to 16.28.5 e18.10.9 Numerical checks of equations 18.10.9-11, page 650 misc Manipulate real or imaginary components of an object massage Massages numbers near the real line to be real sqrti Generalized square root amn matrix a on page 637 J Various modular functions newton_raphson Newton Raphson iteration to find roots of equations as.primitive Converts basic periods to a primitive pair K.fun quarter period K mob Moebius transformations farey Farey sequences p1.tau Does the right thing when calling g2.fun() and g3.fun() parameters Parameters for Weierstrass's P function e1e2e3 Calculate e1, e2, e3 from the invariants near.match Are two vectors close to one another? elliptic-package elliptic myintegrate Complex integration view Visualization of complex functions pari Wrappers for PARI functions fpp Fundamental period parallelogram sn Jacobi form of the elliptic functions coqueraux Fast, conceptually simple, iterative scheme for Weierstrass P functions theta Jacobi theta functions 1-4 nome Nome in terms of m or k divisor Number theoretic functions theta.neville Neville's form for the theta functions lattice Lattice of complex numbers g.fun Calculates the invariants g2 and g3 latplot Plots a lattice of periods on the complex plane unimodular Unimodular matrices half.periods Calculates half periods in terms of e theta1dash Derivatives of theta functions theta1.dash.zero Derivative of theta1 ck Coefficients of Laurent expansion of Weierstrass P function congruence Solves mx+by=1 for x and y WeierstrassP Weierstrass P and related functions limit Limit the magnitude of elements of a vector equianharmonic Special cases of the Weierstrass elliptic function No Results!