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  "Title": "Weierstrass and Jacobi Elliptic Functions",
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  "SystemRequirements": "pari/gp",
  "Description": "A suite of elliptic and related functions including\nWeierstrass and Jacobi forms.  Also includes various tools for\nmanipulating and visualizing complex functions.",
  "Maintainer": "Robin K. S. Hankin <hankin.robin@gmail.com>",
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    "amn",
    "as.primitive",
    "cc",
    "cd",
    "ck",
    "cn",
    "congruence",
    "coqueraux",
    "cs",
    "dc",
    "dd",
    "divisor",
    "dn",
    "ds",
    "e16.28.1",
    "e16.28.2",
    "e16.28.3",
    "e16.28.4",
    "e16.28.5",
    "e16.36.6a",
    "e16.36.6b",
    "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",
    "e18.10.9",
    "e1e2e3",
    "eee.cardano",
    "equianharmonic",
    "eta",
    "eta.series",
    "factorize",
    "farey",
    "fpp",
    "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",
    "H",
    "H1",
    "half.periods",
    "Im<-",
    "integrate.contour",
    "integrate.segments",
    "is.primitive",
    "J",
    "K.fun",
    "lambda",
    "latplot",
    "lattice",
    "lemniscatic",
    "limit",
    "liouville",
    "massage",
    "mn",
    "mob",
    "mobius",
    "myintegrate",
    "nc",
    "nd",
    "near.match",
    "newton_raphson",
    "nn",
    "nome",
    "nome.k",
    "ns",
    "P",
    "P.laurent",
    "P.pari",
    "p1.tau",
    "parameters",
    "Pdash",
    "Pdash.laurent",
    "primes",
    "pseudolemniscatic",
    "Re<-",
    "residue",
    "sc",
    "sd",
    "sigma",
    "sigma.laurent",
    "sigmadash.laurent",
    "sn",
    "sqrti",
    "ss",
    "Theta",
    "theta.00",
    "theta.01",
    "theta.10",
    "theta.11",
    "theta.c",
    "theta.d",
    "theta.n",
    "theta.s",
    "theta1",
    "Theta1",
    "theta1.dash.zero",
    "theta1.dash.zero.q",
    "theta1dash",
    "theta1dashdash",
    "theta1dashdashdash",
    "theta2",
    "theta3",
    "theta4",
    "totient",
    "unimodular",
    "unimodularity",
    "view",
    "zeta",
    "zeta.laurent"
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  "_help": [
    {
      "page": "elliptic-package",
      "title": "Weierstrass and Jacobi Elliptic Functions",
      "topics": [
        "elliptic-package",
        "elliptic"
      ]
    },
    {
      "page": "amn",
      "title": "matrix a on page 637",
      "topics": [
        "18.5.7",
        "18.5.8",
        "amn"
      ]
    },
    {
      "page": "as.primitive",
      "title": "Converts basic periods to a primitive pair",
      "topics": [
        "as.primitive",
        "is.primitive"
      ]
    },
    {
      "page": "ck",
      "title": "Coefficients of the Laurent expansion of the Weierstrass P function",
      "topics": [
        "ck",
        "e18.5.16",
        "e18.5.2",
        "e18.5.3"
      ]
    },
    {
      "page": "congruence",
      "title": "Solves mx+by=1 for x and y",
      "topics": [
        "congruence"
      ]
    },
    {
      "page": "coqueraux",
      "title": "Fast, conceptually simple, iterative scheme for Weierstrass P functions",
      "topics": [
        "coqueraux"
      ]
    },
    {
      "page": "divisor",
      "title": "Number theoretic functions",
      "concept": [
        "Multiplicative functions"
      ],
      "topics": [
        "divisor",
        "factorize",
        "liouville",
        "mobius",
        "primes",
        "totient"
      ]
    },
    {
      "page": "e16.28.1",
      "title": "Numerical verification of equations 16.28.1 to 16.28.5",
      "topics": [
        "e16.28.1",
        "e16.28.2",
        "e16.28.3",
        "e16.28.4",
        "e16.28.5"
      ]
    },
    {
      "page": "e18.10.9",
      "title": "Numerical checks of equations 18.10.9-11, page 650",
      "topics": [
        "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"
      ]
    },
    {
      "page": "e1e2e3",
      "title": "Calculate e1, e2, e3 from the invariants",
      "topics": [
        "e18.3.1",
        "e18.3.7",
        "e18.3.8",
        "e1e2e3",
        "eee.cardano"
      ]
    },
    {
      "page": "equianharmonic",
      "title": "Special cases of the Weierstrass elliptic function",
      "topics": [
        "equianharmonic",
        "lemniscatic",
        "pseudolemniscatic"
      ]
    },
    {
      "page": "eta",
      "title": "Dedekind's eta function",
      "topics": [
        "eta",
        "eta.series"
      ]
    },
    {
      "page": "farey",
      "title": "Farey sequences",
      "topics": [
        "farey"
      ]
    },
    {
      "page": "fpp",
      "title": "Fundamental period parallelogram",
      "topics": [
        "fpp",
        "mn"
      ]
    },
    {
      "page": "g.fun",
      "title": "Calculates the invariants g2 and g3",
      "topics": [
        "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"
      ]
    },
    {
      "page": "half.periods",
      "title": "Calculates half periods in terms of e",
      "topics": [
        "half.periods"
      ]
    },
    {
      "page": "J",
      "title": "Various modular functions",
      "concept": [
        "Klein's modular function",
        "Klein's modular function J",
        "Klein's invariant function",
        "Dedekind's valenz function",
        "Dedekind's valenz function J",
        "lambda function",
        "Dedekind"
      ],
      "topics": [
        "J",
        "lambda"
      ]
    },
    {
      "page": "K.fun",
      "title": "quarter period K",
      "topics": [
        "e16.1.1",
        "K.fun"
      ]
    },
    {
      "page": "latplot",
      "title": "Plots a lattice of periods on the complex plane",
      "topics": [
        "latplot"
      ]
    },
    {
      "page": "lattice",
      "title": "Lattice of complex numbers",
      "topics": [
        "lattice"
      ]
    },
    {
      "page": "limit",
      "title": "Limit the magnitude of elements of a vector",
      "topics": [
        "limit"
      ]
    },
    {
      "page": "massage",
      "title": "Massages numbers near the real line to be real",
      "topics": [
        "massage"
      ]
    },
    {
      "page": "misc",
      "title": "Manipulate real or imaginary components of an object",
      "topics": [
        "Im<-",
        "Re<-"
      ]
    },
    {
      "page": "mob",
      "title": "Moebius transformations",
      "topics": [
        "%mob%",
        "mob"
      ]
    },
    {
      "page": "myintegrate",
      "title": "Complex integration",
      "concept": [
        "Complex integration",
        "Path integration",
        "Contour integration",
        "Cauchy's theorem",
        "Cauchy's integral theorem",
        "Cauchy's formula",
        "Residue theorem"
      ],
      "topics": [
        "integrate.contour",
        "integrate.segments",
        "myintegrate",
        "residue"
      ]
    },
    {
      "page": "near.match",
      "title": "Are two vectors close to one another?",
      "topics": [
        "near.match"
      ]
    },
    {
      "page": "newton_raphson",
      "title": "Newton Raphson iteration to find roots of equations",
      "topics": [
        "Newton_Raphson",
        "Newton_raphson",
        "newton_Raphson",
        "newton_raphson"
      ]
    },
    {
      "page": "nome",
      "title": "Nome in terms of m or k",
      "topics": [
        "nome",
        "nome.k"
      ]
    },
    {
      "page": "P.laurent",
      "title": "Laurent series for elliptic and related functions",
      "topics": [
        "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"
      ]
    },
    {
      "page": "p1.tau",
      "title": "Does the Right Thing (tm) when calling g2.fun() and g3.fun()",
      "topics": [
        "p1.tau"
      ]
    },
    {
      "page": "parameters",
      "title": "Parameters for Weierstrass's P function",
      "topics": [
        "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"
      ]
    },
    {
      "page": "pari",
      "title": "Wrappers for PARI functions",
      "topics": [
        "GP",
        "Gp",
        "gp",
        "P.pari",
        "PARI",
        "pari"
      ]
    },
    {
      "page": "sn",
      "title": "Jacobi form of the elliptic functions",
      "concept": [
        "Jacobi elliptic functions",
        "Jacobi's elliptic functions",
        "Jacobian elliptic functions"
      ],
      "topics": [
        "cc",
        "cd",
        "cn",
        "cs",
        "dc",
        "dd",
        "dn",
        "ds",
        "e16.36.3",
        "nc",
        "nd",
        "nn",
        "ns",
        "sc",
        "sd",
        "sn",
        "ss"
      ]
    },
    {
      "page": "sqrti",
      "title": "Generalized square root",
      "topics": [
        "sqrti"
      ]
    },
    {
      "page": "theta",
      "title": "Jacobi theta functions 1-4",
      "topics": [
        "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"
      ]
    },
    {
      "page": "theta.neville",
      "title": "Neville's form for the theta functions",
      "concept": [
        "Neville's theta functions"
      ],
      "topics": [
        "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",
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