# elliptic: Elliptic Functions Version 1.3-7

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 License GPL-2 Version 1.3-7 Package repository View on CRAN Installation Install the latest version of this package by entering the following in R: ``install.packages("elliptic")``

### Popular man pages

 ck: Coefficients of Laurent expansion of Weierstrass P function e1e2e3: Calculate e1, e2, e3 from the invariants eta: Dedekind's eta function fpp: Fundamental period parallelogram half.periods: Calculates half periods in terms of e J: Various modular functions limit: Limit the magnitude of elements of a vector

## 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

## Functions

18.5.7 Man page
18.5.8 Man page
GP Man page
Gp Man page
H Man page
H1 Man page
Im<- Man page
J Man page
K.fun Man page
Newton_Raphson Man page
Newton_raphson Man page
P Man page
P.laurent Man page
P.pari Man page
PARI Man page
Pdash Man page
Pdash.laurent Man page
Re<- Man page
Theta Man page
Theta1 Man page
WeierstrassP Man page
\%mob\% Man page
amn Man page
as.primitive Man page
cc Man page
cd Man page
ck Man page
cn Man page
congruence Man page
coqueraux Man page
cs Man page
dc Man page
dd Man page
divisor Man page
dn Man page
ds Man page
e16.1.1 Man page
e16.27.1 Man page
e16.27.2 Man page
e16.27.3 Man page
e16.27.4 Man page
e16.28.1 Man page
e16.28.2 Man page
e16.28.3 Man page
e16.28.4 Man page
e16.28.5 Man page
e16.28.6 Man page
e16.31.1 Man page
e16.31.2 Man page
e16.31.3 Man page
e16.31.4 Man page
e16.36.3 Man page
e16.36.6 Man page
e16.36.6a Man page
e16.36.6b Man page
e16.36.7 Man page
e16.36.7a Man page
e16.36.7b Man page
e16.37.1 Man page
e16.37.2 Man page
e16.37.3 Man page
e16.37.4 Man page
e16.38.1 Man page
e16.38.2 Man page
e16.38.3 Man page
e16.38.4 Man page
e18.1.1 Man page
e18.10.1 Man page
e18.10.10 Man page
e18.10.10a Man page
e18.10.10b Man page
e18.10.11 Man page
e18.10.11a Man page
e18.10.11b Man page
e18.10.12 Man page
e18.10.12a Man page
e18.10.12b Man page
e18.10.2 Man page
e18.10.3 Man page
e18.10.4 Man page
e18.10.5 Man page
e18.10.6 Man page
e18.10.7 Man page
e18.10.9 Man page
e18.10.9a Man page
e18.10.9b Man page
e18.3.1 Man page
e18.3.3 Man page
e18.3.37 Man page
e18.3.38 Man page
e18.3.39 Man page
e18.3.5 Man page
e18.3.7 Man page
e18.3.8 Man page
e18.5.1 Man page
e18.5.16 Man page
e18.5.2 Man page
e18.5.3 Man page
e18.5.4 Man page
e18.5.5 Man page
e18.5.6 Man page
e18.7.4 Man page
e18.7.5 Man page
e18.7.7 Man page
e18f.5.3 Man page
e1e2e3 Man page
eee.cardano Man page
elliptic Man page
elliptic-package Man page
equianharmonic Man page
eta Man page
eta.series Man page
factorize Man page
farey Man page
fpp Man page
g.fun Man page
g2.fun Man page
g2.fun.direct Man page
g2.fun.divisor Man page
g2.fun.fixed Man page
g2.fun.lambert Man page
g2.fun.vectorized Man page
g3.fun Man page
g3.fun.direct Man page
g3.fun.divisor Man page
g3.fun.fixed Man page
g3.fun.lambert Man page
g3.fun.vectorized Man page
gp Man page
half.periods Man page
integrate.contour Man page
integrate.segments Man page
is.primitive Man page
lambda Man page
latplot Man page
lattice Man page
lemniscatic Man page
limit Man page
liouville Man page
massage Man page
mn Man page
mob Man page
mobius Man page
myintegrate Man page
nc Man page
nd Man page
near.match Man page
newton_Raphson Man page
newton_raphson Man page
nn Man page
nome Man page
nome.k Man page
ns Man page
p1.tau Man page
parameters Man page
pari Man page
primes Man page
pseudolemniscatic Man page
residue Man page
sc Man page
sd Man page
sigma Man page
sigma.laurent Man page
sn Man page
sqrti Man page
ss Man page
theta Man page
theta.00 Man page
theta.01 Man page
theta.10 Man page
theta.11 Man page
theta.c Man page
theta.d Man page
theta.n Man page
theta.neville Man page
theta.s Man page
theta1 Man page
theta1.dash.zero Man page
theta1.dash.zero.q Man page
theta1dash Man page
theta1dashdash Man page
theta1dashdashdash Man page
theta2 Man page
theta3 Man page
theta4 Man page
totient Man page
unimodular Man page
unimodularity Man page
view Man page
zeta Man page
zeta.laurent Man page

## Files

inst
inst/CITATION
inst/doc
inst/doc/residuetheorem.R
inst/doc/ellipticpaper.R
inst/doc/ellipticpaper.Rnw
inst/doc/residuetheorem.Rnw
inst/doc/residuetheorem.pdf
inst/doc/ellipticpaper.pdf
tests
tests/aaa.R
NAMESPACE
demo
demo/00Index
demo/elliptic.R
R
R/elliptic.R
vignettes
vignettes/semicircular_path.svg
vignettes/elliptic.bib
vignettes/semicircular_path.pdf
vignettes/ellipticpaper.Rnw
vignettes/residuetheorem.Rnw
MD5
build
build/vignette.rds
DESCRIPTION
man
man/as.primitive.Rd
man/J.Rd
man/half.periods.Rd
man/theta1dash.Rd
man/unimodular.Rd
man/e1e2e3.Rd
man/coqueraux.Rd
man/P.laurent.Rd
man/myintegrate.Rd
man/p1.tau.Rd
man/lattice.Rd
man/mob.Rd
man/ck.Rd
man/theta.Rd
man/divisor.Rd
man/K.fun.Rd
man/farey.Rd
man/pari.Rd
man/parameters.Rd
man/limit.Rd
man/equianharmonic.Rd
man/sn.Rd
man/e16.28.1.Rd
man/newton_raphson.Rd
man/e18.10.9.Rd
man/amn.Rd
man/elliptic-package.Rd
man/near.match.Rd
man/massage.Rd
man/WeierstrassP.Rd
man/eta.Rd
man/theta1.dash.zero.Rd
man/latplot.Rd
man/congruence.Rd
man/nome.Rd
man/misc.Rd
man/g.fun.Rd
man/sqrti.Rd
man/fpp.Rd
man/theta.neville.Rd
man/view.Rd
elliptic documentation built on May 19, 2017, 7:06 p.m.