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elliptic (version 1.3-0)

elliptic functions

Description

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

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Version

Install

install.packages('elliptic')

Monthly Downloads

25,111

Version

1.3-0

License

GPL-2

Maintainer

Robin K S Hankin

Last Published

January 21st, 2013

Functions in elliptic (1.3-0)

Farey sequences

Coefficients of Laurent expansion of Weierstrass P function

Weierstrass P and related functions

Massages numbers near the real line to be real

Jacobi theta functions 1-4

Visualization of complex functions

Derivatives of theta functions

Parameters for Weierstrass's P function

Special cases of the Weierstrass elliptic function

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

Complex integration

Are two vectors close to one another?

Numerical verification of equations 16.28.1 to 16.28.5

quarter period K

Fast, conceptually simple, iterative scheme for Weierstrass P functions

matrix a on page 637

Limit the magnitude of elements of a vector

Lattice of complex numbers

Calculates half periods in terms of e

Laurent series for elliptic and related functions

Nome in terms of m or k

Numerical checks of equations 18.10.9-11, page 650

Plots a lattice of periods on the complex plane

Wrappers for PARI functions

Solves mx+by=1 for x and y

Various modular functions

Newton Raphson iteration to find roots of equations

Neville's form for the theta functions

Manipulate real or imaginary components of an object

Converts basic periods to a primitive pair

Jacobi form of the elliptic functions

elliptic-package

Elliptic and modular functions

Moebius transformations

theta1.dash.zero

Derivative of theta1

Calculates the invariants g2 and g3

Number theoretic functions

Generalized square root

Dedekind's eta function

Unimodular matrices

Calculate e1, e2, e3 from the invariants

Fundamental period parallelogram