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  "Title": "The Free Group",
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  "Maintainer": "Robin K. S. Hankin <hankin.robin@gmail.com>",
  "Description": "The free group in R; juxtaposition is represented by a\nplus.  Includes inversion, multiplication by a scalar,\ngroup-theoretic power operation, and Tietze forms.  To cite the\npackage in publications please use Hankin (2022)\n<doi:10.48550/ARXIV.2212.05883>.",
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  "VignetteBuilder": "knitr",
  "License": "GPL-2",
  "URL": "https://github.com/RobinHankin/freegroup,\nhttps://robinhankin.github.io/freegroup/",
  "BugReports": "https://github.com/RobinHankin/freegroup/issues",
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  "Date/Publication": "2026-03-17 08:46:59 UTC",
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    "alpha",
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    "as.free",
    "autosub",
    "autosub_lowlevel",
    "backwards",
    "bigness",
    "char_to_free",
    "char_to_matrix",
    "consolidate",
    "cyclically_reduce",
    "cyclically_reduce_tietze",
    "discard",
    "donames",
    "flip",
    "free",
    "free_equal",
    "free_power",
    "free_repeat",
    "getlet",
    "id",
    "inverse",
    "is_proper",
    "is_reduced",
    "is.abelian",
    "is.conjugate",
    "is.conjugate_single",
    "is.cyclically_reduced",
    "is.free",
    "is.id",
    "is.power",
    "is.primitive",
    "juxtapose",
    "keep",
    "list_to_free",
    "number",
    "permsymb",
    "permsymb_single_f",
    "permsymb_single_X",
    "permsymb_vec",
    "reduce",
    "remove_zero_powers",
    "rfree",
    "rfreee",
    "rfreeee",
    "shift",
    "size",
    "subs",
    "subsu",
    "tietze",
    "total",
    "vec_to_matrix"
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      "title": "Class \"dot\"",
      "object": "dot",
      "class": [
        "dot"
      ],
      "fields": [],
      "table": false,
      "tojson": false
    }
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    {
      "page": "freegroup-package",
      "title": "The Free Group",
      "topics": [
        "freegroup-package",
        "freegroup"
      ]
    },
    {
      "page": "abelianize",
      "title": "Abelianization of free group elements",
      "topics": [
        "abelianize",
        "abelianized",
        "is.abelian"
      ]
    },
    {
      "page": "abs",
      "title": "Absolute value of a 'free' object",
      "topics": [
        "abs",
        "abs.free"
      ]
    },
    {
      "page": "alpha",
      "title": "Alphabetical free group elements",
      "topics": [
        "abc",
        "alpha",
        "alphabet"
      ]
    },
    {
      "page": "backwards",
      "title": "Write free objects backwards",
      "topics": [
        "backwards"
      ]
    },
    {
      "page": "c",
      "title": "Concatenation of free objects",
      "topics": [
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        "c.free",
        "rep.free"
      ]
    },
    {
      "page": "char_to_free",
      "title": "Convert character vectors to free objects",
      "topics": [
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        "char_to_matrix"
      ]
    },
    {
      "page": "cumsum",
      "title": "Cumulative sum",
      "topics": [
        "cumsum",
        "cumsum.free"
      ]
    },
    {
      "page": "cycred",
      "title": "Cyclic reductions of a word",
      "topics": [
        "%~%",
        "allconj",
        "as.cyclically_reduced",
        "conjugate",
        "cyclic",
        "cyclically",
        "cyclically_reduce",
        "cyclically_reduced",
        "cyclically_reduce_tietze",
        "cyclic_reduction",
        "cycred",
        "is.conjugate",
        "is.conjugate.free",
        "is.conjugate_single",
        "is.cyclically.reduced",
        "is.cyclically_reduced"
      ]
    },
    {
      "page": "donames",
      "title": "Names attributes of free group elements",
      "topics": [
        "donames",
        "names"
      ]
    },
    {
      "page": "dot",
      "title": "Class \"dot\"",
      "topics": [
        ".",
        "commutator",
        "dot",
        "dot-class",
        "dot_error",
        "extract",
        "jacobi",
        "[,dot,ANY,ANY-method",
        "[,dot,ANY,missing-method",
        "[,dot,free,ANY,ANY-method",
        "[,dot,free,ANY-method",
        "[,dot,matrix,matrix-method",
        "[,dot,missing,ANY-method",
        "[,dot,missing,missing-method",
        "[,dot-method",
        "[.dot"
      ]
    },
    {
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      "title": "Extract or replace parts of a free group object",
      "topics": [
        "Extract.free",
        "[.free",
        "[<-.free"
      ]
    },
    {
      "page": "free",
      "title": "Objects of class 'free'",
      "topics": [
        "as.free",
        "free",
        "free-class",
        "is.free",
        "list_to_free"
      ]
    },
    {
      "page": "getlet",
      "title": "Get letters of a freegroup object",
      "topics": [
        "getlet"
      ]
    },
    {
      "page": "identity",
      "title": "The identity element",
      "topics": [
        "id",
        "identity",
        "is.id",
        "is.id.free",
        "is.identity",
        "neutral"
      ]
    },
    {
      "page": "keep",
      "title": "Keep or drop symbols",
      "topics": [
        "discard",
        "drop",
        "drop.free",
        "keep",
        "retain"
      ]
    },
    {
      "page": "outer",
      "title": "Outer automorphisms of the free group",
      "topics": [
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        "automorphisms",
        "autosub",
        "autosub_lowlevel",
        "nielsen",
        "outer",
        "permsymb",
        "permsymb_single_f",
        "permsymb_single_X",
        "permsymb_vec"
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    },
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      "topics": [
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        "free_power",
        "free_repeat",
        "inverse",
        "inverse.free",
        "inverse.matrix",
        "juxtapose",
        "ops",
        "Ops.free"
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    },
    {
      "page": "primitive",
      "title": "Primitive elements of the free algebra",
      "topics": [
        "is.power",
        "is.primitive",
        "primitive"
      ]
    },
    {
      "page": "print",
      "title": "Print free objects",
      "topics": [
        "as.character_free",
        "print.free",
        "print.freegroup"
      ]
    },
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        "is_proper",
        "is_reduced",
        "reduce",
        "remove_zero_powers"
      ]
    },
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      "title": "Random free objects",
      "topics": [
        "rfree",
        "rfreee",
        "rfreeee"
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        "total"
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        "subs",
        "subsu"
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        "sum.free"
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        "tietze",
        "tietze.free",
        "tietze.matrix",
        "vec_to_matrix"
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