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elliptic (version 1.2-6)

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

1.2-6

License

GPL-2

Maintainer

Robin K S Hankin

Last Published

January 27th, 2011

Functions in elliptic (1.2-6)

Jacobi theta functions 1-4

Are two vectors close to one another?

Number theoretic functions

Fast, conceptually simple, iterative scheme for Weierstrass P functions

Manipulate real or imaginary components of an object

Dedekind's eta function

Moebius transformations

Generalized square root

Fundamental period parallelogram

matrix a on page 637

Numerical checks of equations 18.10.9-11, page 650

quarter period K

Calculate e1, e2, e3 from the invariants

theta1.dash.zero

Derivative of theta1

Limit the magnitude of elements of a vector

Derivatives of theta functions

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

Parameters for Weierstrass's P function

Farey sequences

Neville's form for the theta functions

Lattice of complex numbers

elliptic-package

Elliptic and modular functions

Nome in terms of m or k

Solves mx+by=1 for x and y

Massages numbers near the real line to be real

Special cases of the Weierstrass elliptic function

Visualization of complex functions

Weierstrass P and related functions

Coefficients of Laurent expansion of Weierstrass P function

Newton Raphson iteration to find roots of equations

Complex integration

Converts basic periods to a primitive pair

Calculates the invariants g2 and g3

Laurent series for elliptic and related functions

Plots a lattice of periods on the complex plane

Unimodular matrices

Numerical verification of equations 16.28.1 to 16.28.5

Calculates half periods in terms of e

Jacobi form of the elliptic functions

Wrappers for PARI functions

Various modular functions