Weierstrass and Jacobi Elliptic Functions
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Documentation for package ‘elliptic’ version 1.4-0
- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Code demos. Use demo() to run them.
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A C D E F G H I J K L M N P R S T U V W Z misc
| elliptic-package | Weierstrass and Jacobi Elliptic Functions |
-- A --
| amn | matrix a on page 637 |
| as.primitive | Converts basic periods to a primitive pair |
-- C --
| cc | Jacobi form of the elliptic functions |
| cd | Jacobi form of the elliptic functions |
| ck | Coefficients of Laurent expansion of Weierstrass P function |
| cn | Jacobi form of the elliptic functions |
| congruence | Solves mx+by=1 for x and y |
| coqueraux | Fast, conceptually simple, iterative scheme for Weierstrass P functions |
| cs | Jacobi form of the elliptic functions |
-- D --
| dc | Jacobi form of the elliptic functions |
| dd | Jacobi form of the elliptic functions |
| divisor | Number theoretic functions |
| dn | Jacobi form of the elliptic functions |
| ds | Jacobi form of the elliptic functions |
-- E --
| e16.1.1 | quarter period K |
| e16.27.1 | Jacobi theta functions 1-4 |
| e16.27.2 | Jacobi theta functions 1-4 |
| e16.27.3 | Jacobi theta functions 1-4 |
| e16.27.4 | Jacobi theta functions 1-4 |
| e16.28.1 | Numerical verification of equations 16.28.1 to 16.28.5 |
| e16.28.2 | Numerical verification of equations 16.28.1 to 16.28.5 |
| e16.28.3 | Numerical verification of equations 16.28.1 to 16.28.5 |
| e16.28.4 | Numerical verification of equations 16.28.1 to 16.28.5 |
| e16.28.5 | Numerical verification of equations 16.28.1 to 16.28.5 |
| e16.28.6 | Derivative of theta1 |
| e16.31.1 | Jacobi theta functions 1-4 |
| e16.31.2 | Jacobi theta functions 1-4 |
| e16.31.3 | Jacobi theta functions 1-4 |
| e16.31.4 | Jacobi theta functions 1-4 |
| e16.36.3 | Jacobi form of the elliptic functions |
| e16.36.6 | Neville's form for the theta functions |
| e16.36.6a | Neville's form for the theta functions |
| e16.36.6b | Neville's form for the theta functions |
| e16.36.7 | Neville's form for the theta functions |
| e16.36.7a | Neville's form for the theta functions |
| e16.36.7b | Neville's form for the theta functions |
| e16.37.1 | Neville's form for the theta functions |
| e16.37.2 | Neville's form for the theta functions |
| e16.37.3 | Neville's form for the theta functions |
| e16.37.4 | Neville's form for the theta functions |
| e16.38.1 | Neville's form for the theta functions |
| e16.38.2 | Neville's form for the theta functions |
| e16.38.3 | Neville's form for the theta functions |
| e16.38.4 | Neville's form for the theta functions |
| e18.1.1 | Calculates the invariants g2 and g3 |
| e18.10.1 | Weierstrass P and related functions |
| e18.10.10 | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.10a | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.10b | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.11 | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.11a | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.11b | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.12 | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.12a | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.12b | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.2 | Weierstrass P and related functions |
| e18.10.3 | Weierstrass P and related functions |
| e18.10.4 | Weierstrass P and related functions |
| e18.10.5 | Weierstrass P and related functions |
| e18.10.6 | Weierstrass P and related functions |
| e18.10.7 | Weierstrass P and related functions |
| e18.10.9 | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.9a | Numerical checks of equations 18.10.9-11, page 650 |
| e18.10.9b | Numerical checks of equations 18.10.9-11, page 650 |
| e18.3.1 | Calculate e1, e2, e3 from the invariants |
| e18.3.3 | Parameters for Weierstrass's P function |
| e18.3.37 | Parameters for Weierstrass's P function |
| e18.3.38 | Parameters for Weierstrass's P function |
| e18.3.39 | Parameters for Weierstrass's P function |
| e18.3.5 | Parameters for Weierstrass's P function |
| e18.3.7 | Calculate e1, e2, e3 from the invariants |
| e18.3.8 | Calculate e1, e2, e3 from the invariants |
| e18.5.1 | Laurent series for elliptic and related functions |
| e18.5.16 | Coefficients of Laurent expansion of Weierstrass P function |
| e18.5.2 | Coefficients of Laurent expansion of Weierstrass P function |
| e18.5.3 | Coefficients of Laurent expansion of Weierstrass P function |
| e18.5.4 | Laurent series for elliptic and related functions |
| e18.5.5 | Laurent series for elliptic and related functions |
| e18.5.6 | Laurent series for elliptic and related functions |
| e18.7.4 | Parameters for Weierstrass's P function |
| e18.7.5 | Parameters for Weierstrass's P function |
| e18.7.7 | Parameters for Weierstrass's P function |
| e18f.5.3 | Laurent series for elliptic and related functions |
| e1e2e3 | Calculate e1, e2, e3 from the invariants |
| eee.cardano | Calculate e1, e2, e3 from the invariants |
| elliptic | Weierstrass and Jacobi Elliptic Functions |
| equianharmonic | Special cases of the Weierstrass elliptic function |
| eta | Dedekind's eta function |
| eta.series | Dedekind's eta function |
-- F --
| factorize | Number theoretic functions |
| farey | Farey sequences |
| fpp | Fundamental period parallelogram |
-- G --
| g.fun | Calculates the invariants g2 and g3 |
| g2.fun | Calculates the invariants g2 and g3 |
| g2.fun.direct | Calculates the invariants g2 and g3 |
| g2.fun.divisor | Calculates the invariants g2 and g3 |
| g2.fun.fixed | Calculates the invariants g2 and g3 |
| g2.fun.lambert | Calculates the invariants g2 and g3 |
| g2.fun.vectorized | Calculates the invariants g2 and g3 |
| g3.fun | Calculates the invariants g2 and g3 |
| g3.fun.direct | Calculates the invariants g2 and g3 |
| g3.fun.divisor | Calculates the invariants g2 and g3 |
| g3.fun.fixed | Calculates the invariants g2 and g3 |
| g3.fun.lambert | Calculates the invariants g2 and g3 |
| g3.fun.vectorized | Calculates the invariants g2 and g3 |
| GP | Wrappers for PARI functions |
| Gp | Wrappers for PARI functions |
| gp | Wrappers for PARI functions |
-- H --
| H | Jacobi theta functions 1-4 |
| H1 | Jacobi theta functions 1-4 |
| half.periods | Calculates half periods in terms of e |
-- I --
| Im<- | Manipulate real or imaginary components of an object |
| integrate.contour | Complex integration |
| integrate.segments | Complex integration |
| is.primitive | Converts basic periods to a primitive pair |
-- J --
| J | Various modular functions |
-- K --
| K.fun | quarter period K |
-- L --
| lambda | Various modular functions |
| latplot | Plots a lattice of periods on the complex plane |
| lattice | Lattice of complex numbers |
| lemniscatic | Special cases of the Weierstrass elliptic function |
| limit | Limit the magnitude of elements of a vector |
| liouville | Number theoretic functions |
-- M --
| massage | Massages numbers near the real line to be real |
| mn | Fundamental period parallelogram |
| mob | Moebius transformations |
| mobius | Number theoretic functions |
| myintegrate | Complex integration |
-- N --
| nc | Jacobi form of the elliptic functions |
| nd | Jacobi form of the elliptic functions |
| near.match | Are two vectors close to one another? |
| Newton_Raphson | Newton Raphson iteration to find roots of equations |
| Newton_raphson | Newton Raphson iteration to find roots of equations |
| newton_Raphson | Newton Raphson iteration to find roots of equations |
| newton_raphson | Newton Raphson iteration to find roots of equations |
| nn | Jacobi form of the elliptic functions |
| nome | Nome in terms of m or k |
| nome.k | Nome in terms of m or k |
| ns | Jacobi form of the elliptic functions |
-- P --
| P | Weierstrass P and related functions |
| P.laurent | Laurent series for elliptic and related functions |
| P.pari | Wrappers for PARI functions |
| 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 |
| pari | Wrappers for PARI functions |
| Pdash | Weierstrass P and related functions |
| Pdash.laurent | Laurent series for elliptic and related functions |
| primes | Number theoretic functions |
| pseudolemniscatic | Special cases of the Weierstrass elliptic function |
-- R --
| Re<- | Manipulate real or imaginary components of an object |
| residue | Complex integration |
-- S --
| sc | Jacobi form of the elliptic functions |
| sd | Jacobi form of the elliptic functions |
| sigma | Weierstrass P and related functions |
| sigma.laurent | Laurent series for elliptic and related functions |
| sigmadash.laurent | Laurent series for elliptic and related functions |
| sn | Jacobi form of the elliptic functions |
| sqrti | Generalized square root |
| ss | Jacobi form of the elliptic functions |
-- T --
| Theta | Jacobi theta functions 1-4 |
| theta | Jacobi theta functions 1-4 |
| theta.00 | Jacobi theta functions 1-4 |
| theta.01 | Jacobi theta functions 1-4 |
| theta.10 | Jacobi theta functions 1-4 |
| theta.11 | Jacobi theta functions 1-4 |
| theta.c | Neville's form for the theta functions |
| theta.d | Neville's form for the theta functions |
| theta.n | Neville's form for the theta functions |
| theta.neville | Neville's form for the theta functions |
| theta.s | Neville's form for the theta functions |
| Theta1 | Jacobi theta functions 1-4 |
| theta1 | Jacobi theta functions 1-4 |
| theta1.dash.zero | Derivative of theta1 |
| theta1.dash.zero.q | Derivative of theta1 |
| theta1dash | Derivatives of theta functions |
| theta1dashdash | Derivatives of theta functions |
| theta1dashdashdash | Derivatives of theta functions |
| theta2 | Jacobi theta functions 1-4 |
| theta3 | Jacobi theta functions 1-4 |
| theta4 | Jacobi theta functions 1-4 |
| totient | Number theoretic functions |
-- U --
| unimodular | Unimodular matrices |
| unimodularity | Unimodular matrices |
-- V --
| view | Visualization of complex functions |
-- W --
| WeierstrassP | Weierstrass P and related functions |
-- Z --
| zeta | Weierstrass P and related functions |
| zeta.laurent | Laurent series for elliptic and related functions |
-- misc --
| %mob% | Moebius transformations |
| 18.5.7 | matrix a on page 637 |
| 18.5.8 | matrix a on page 637 |