Package: elliptic 1.5-0
elliptic: Weierstrass and Jacobi Elliptic Functions
A suite of elliptic and related functions including Weierstrass and Jacobi forms. Also includes various tools for manipulating and visualizing complex functions.
Authors:
elliptic_1.5-0.tar.gz
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elliptic.pdf |elliptic.html✨
elliptic/json (API)
NEWS
| # Install 'elliptic' in R: |
| install.packages('elliptic', repos = c('https://robinhankin.r-universe.dev', 'https://cloud.r-project.org')) |
Bug tracker:https://github.com/robinhankin/elliptic/issues
Last updated 3 months agofrom:d556341ee6. Checks:OK: 7. Indexed: yes.
| Target | Result | Date |
|---|---|---|
| Doc / Vignettes | OK | Nov 03 2024 |
| R-4.5-win | OK | Nov 03 2024 |
| R-4.5-linux | OK | Nov 03 2024 |
| R-4.4-win | OK | Nov 03 2024 |
| R-4.4-mac | OK | Nov 03 2024 |
| R-4.3-win | OK | Nov 03 2024 |
| R-4.3-mac | OK | Nov 03 2024 |
Exports:%mob%amnas.primitivecccdckcncongruencecoquerauxcsdcdddivisordndse16.28.1e16.28.2e16.28.3e16.28.4e16.28.5e16.36.6ae16.36.6be16.36.7ae16.36.7be16.37.1e16.37.2e16.37.3e16.37.4e16.38.1e16.38.2e16.38.3e16.38.4e18.10.9e1e2e3eee.cardanoequianharmonicetaeta.seriesfactorizefareyfppg.fung2.fung2.fun.directg2.fun.divisorg2.fun.fixedg2.fun.lambertg2.fun.vectorizedg3.fung3.fun.directg3.fun.divisorg3.fun.fixedg3.fun.lambertg3.fun.vectorizedHH1half.periodsIm<-integrate.contourintegrate.segmentsis.primitiveJK.funlambdalatplotlatticelemniscaticlimitliouvillemassagemnmobmobiusmyintegratencndnear.matchnewton_raphsonnnnomenome.knsPP.laurentP.parip1.tauparametersPdashPdash.laurentprimespseudolemniscaticRe<-residuescsdsigmasigma.laurentsigmadash.laurentsnsqrtissThetatheta.00theta.01theta.10theta.11theta.ctheta.dtheta.ntheta.stheta1Theta1theta1.dash.zerotheta1.dash.zero.qtheta1dashtheta1dashdashtheta1dashdashdashtheta2theta3theta4totientunimodularunimodularityviewzetazeta.laurent
Dependencies:MASS
Readme and manuals
Help Manual
| Help page | Topics |
|---|---|
| Weierstrass and Jacobi Elliptic Functions | elliptic-package elliptic |
| matrix a on page 637 | 18.5.7 18.5.8 amn |
| Converts basic periods to a primitive pair | as.primitive is.primitive |
| Coefficients of Laurent expansion of Weierstrass P function | ck e18.5.16 e18.5.2 e18.5.3 |
| Solves mx+by=1 for x and y | congruence |
| Fast, conceptually simple, iterative scheme for Weierstrass P functions | coqueraux |
| Number theoretic functions | divisor factorize liouville mobius primes totient |
| Numerical verification of equations 16.28.1 to 16.28.5 | e16.28.1 e16.28.2 e16.28.3 e16.28.4 e16.28.5 |
| Numerical checks of equations 18.10.9-11, page 650 | e18.10.10 e18.10.10a e18.10.10b e18.10.11 e18.10.11a e18.10.11b e18.10.12 e18.10.12a e18.10.12b e18.10.9 e18.10.9a e18.10.9b |
| Calculate e1, e2, e3 from the invariants | e18.3.1 e18.3.7 e18.3.8 e1e2e3 eee.cardano |
| Special cases of the Weierstrass elliptic function | equianharmonic lemniscatic pseudolemniscatic |
| Dedekind's eta function | eta eta.series |
| Farey sequences | farey |
| Fundamental period parallelogram | fpp mn |
| Calculates the invariants g2 and g3 | e18.1.1 g.fun g2.fun g2.fun.direct g2.fun.divisor g2.fun.fixed g2.fun.lambert g2.fun.vectorized g3.fun g3.fun.direct g3.fun.divisor g3.fun.fixed g3.fun.lambert g3.fun.vectorized |
| Calculates half periods in terms of e | half.periods |
| Various modular functions | J lambda |
| quarter period K | e16.1.1 K.fun |
| Plots a lattice of periods on the complex plane | latplot |
| Lattice of complex numbers | lattice |
| Limit the magnitude of elements of a vector | limit |
| Massages numbers near the real line to be real | massage |
| Manipulate real or imaginary components of an object | Im<- Re<- |
| Moebius transformations | %mob% mob |
| Complex integration | integrate.contour integrate.segments myintegrate residue |
| Are two vectors close to one another? | near.match |
| Newton Raphson iteration to find roots of equations | Newton_Raphson Newton_raphson newton_Raphson newton_raphson |
| Nome in terms of m or k | nome nome.k |
| Laurent series for elliptic and related functions | e18.5.1 e18.5.4 e18.5.5 e18.5.6 e18f.5.3 P.laurent Pdash.laurent sigma.laurent sigmadash.laurent zeta.laurent |
| Does the Right Thing (tm) when calling g2.fun() and g3.fun() | p1.tau |
| Parameters for Weierstrass's P function | e18.3.3 e18.3.37 e18.3.38 e18.3.39 e18.3.5 e18.7.4 e18.7.5 e18.7.7 parameters |
| Wrappers for PARI functions | GP Gp gp P.pari PARI pari |
| Jacobi form of the elliptic functions | cc cd cn cs dc dd dn ds e16.36.3 nc nd nn ns sc sd sn ss |
| Generalized square root | sqrti |
| Jacobi theta functions 1-4 | e16.27.1 e16.27.2 e16.27.3 e16.27.4 e16.31.1 e16.31.2 e16.31.3 e16.31.4 H H1 Theta theta theta.00 theta.01 theta.10 theta.11 Theta1 theta1 theta2 theta3 theta4 |
| Neville's form for the theta functions | e16.36.6 e16.36.6a e16.36.6b e16.36.7 e16.36.7a e16.36.7b e16.37.1 e16.37.2 e16.37.3 e16.37.4 e16.38.1 e16.38.2 e16.38.3 e16.38.4 theta.c theta.d theta.n theta.neville theta.s |
| Derivative of theta1 | e16.28.6 theta1.dash.zero theta1.dash.zero.q |
| Derivatives of theta functions | theta1dash theta1dashdash theta1dashdashdash |
| Unimodular matrices | unimodular unimodularity |
| Visualization of complex functions | view |
| Weierstrass P and related functions | e18.10.1 e18.10.2 e18.10.3 e18.10.4 e18.10.5 e18.10.6 e18.10.7 P Pdash sigma WeierstrassP zeta |
