elliptic: Elliptic Functions

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

Author
Robin K. S. Hankin
Date of publication
2016-05-26 09:21:13
Maintainer
Robin K. S. Hankin <hankin.robin@gmail.com>
License
GPL-2
Version
1.3-7

View on CRAN

Man pages

amn
matrix a on page 637
as.primitive
Converts basic periods to a primitive pair
ck
Coefficients of Laurent expansion of Weierstrass P function
congruence
Solves mx+by=1 for x and y
coqueraux
Fast, conceptually simple, iterative scheme for Weierstrass P...
divisor
Number theoretic functions
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
e1e2e3
Calculate e1, e2, e3 from the invariants
elliptic-package
Elliptic and modular functions
equianharmonic
Special cases of the Weierstrass elliptic function
eta
Dedekind's eta function
farey
Farey sequences
fpp
Fundamental period parallelogram
g.fun
Calculates the invariants g2 and g3
half.periods
Calculates half periods in terms of e
J
Various modular functions
K.fun
quarter period K
latplot
Plots a lattice of periods on the complex plane
lattice
Lattice of complex numbers
limit
Limit the magnitude of elements of a vector
massage
Massages numbers near the real line to be real
misc
Manipulate real or imaginary components of an object
mob
Moebius transformations
myintegrate
Complex integration
near.match
Are two vectors close to one another?
newton_raphson
Newton Raphson iteration to find roots of equations
nome
Nome in terms of m or k
p1.tau
Does the right thing when calling g2.fun() and g3.fun()
parameters
Parameters for Weierstrass's P function
pari
Wrappers for PARI functions
P.laurent
Laurent series for elliptic and related functions
sn
Jacobi form of the elliptic functions
sqrti
Generalized square root
theta
Jacobi theta functions 1-4
theta1dash
Derivatives of theta functions
theta1.dash.zero
Derivative of theta1
theta.neville
Neville's form for the theta functions
unimodular
Unimodular matrices
view
Visualization of complex functions
WeierstrassP
Weierstrass P and related functions

Files in this package

elliptic
elliptic/inst
elliptic/inst/CITATION
elliptic/inst/doc
elliptic/inst/doc/residuetheorem.R
elliptic/inst/doc/ellipticpaper.R
elliptic/inst/doc/ellipticpaper.Rnw
elliptic/inst/doc/residuetheorem.Rnw
elliptic/inst/doc/residuetheorem.pdf
elliptic/inst/doc/ellipticpaper.pdf
elliptic/tests
elliptic/tests/aaa.R
elliptic/NAMESPACE
elliptic/demo
elliptic/demo/00Index
elliptic/demo/elliptic.R
elliptic/R
elliptic/R/elliptic.R
elliptic/vignettes
elliptic/vignettes/semicircular_path.svg
elliptic/vignettes/elliptic.bib
elliptic/vignettes/semicircular_path.pdf
elliptic/vignettes/ellipticpaper.Rnw
elliptic/vignettes/residuetheorem.Rnw
elliptic/MD5
elliptic/build
elliptic/build/vignette.rds
elliptic/DESCRIPTION
elliptic/man
elliptic/man/as.primitive.Rd
elliptic/man/J.Rd
elliptic/man/half.periods.Rd
elliptic/man/theta1dash.Rd
elliptic/man/unimodular.Rd
elliptic/man/e1e2e3.Rd
elliptic/man/coqueraux.Rd
elliptic/man/P.laurent.Rd
elliptic/man/myintegrate.Rd
elliptic/man/p1.tau.Rd
elliptic/man/lattice.Rd
elliptic/man/mob.Rd
elliptic/man/ck.Rd
elliptic/man/theta.Rd
elliptic/man/divisor.Rd
elliptic/man/K.fun.Rd
elliptic/man/farey.Rd
elliptic/man/pari.Rd
elliptic/man/parameters.Rd
elliptic/man/limit.Rd
elliptic/man/equianharmonic.Rd
elliptic/man/sn.Rd
elliptic/man/e16.28.1.Rd
elliptic/man/newton_raphson.Rd
elliptic/man/e18.10.9.Rd
elliptic/man/amn.Rd
elliptic/man/elliptic-package.Rd
elliptic/man/near.match.Rd
elliptic/man/massage.Rd
elliptic/man/WeierstrassP.Rd
elliptic/man/eta.Rd
elliptic/man/theta1.dash.zero.Rd
elliptic/man/latplot.Rd
elliptic/man/congruence.Rd
elliptic/man/nome.Rd
elliptic/man/misc.Rd
elliptic/man/g.fun.Rd
elliptic/man/sqrti.Rd
elliptic/man/fpp.Rd
elliptic/man/theta.neville.Rd
elliptic/man/view.Rd