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Example: Element of subgroup of finitely presented group

Profiles: OSCAR v1.0, OSCAR v1.1, OSCAR v1.2, OSCAR v1.3, OSCAR v1.4, OSCAR v1.5, OSCAR v1.6, OSCAR v1.7, OSCAR v1.8

A generator of a subgroup inside a finitely presented group.

Systems

Oscar.jl

Generate code (generate.jl) [ edit ]

using Oscar

F = free_group(2)
x1 = gen(F, 1)
x2 = gen(F, 2)
G = quo(F, [x1^2, x2^2, comm(x1, x2)])[1]
U = sub(G, [gen(G, 1)])[1]
obj = gen(U, 1)

save("data.mrdi", obj)

Data outputs

Profiles: OSCAR v1.0

Data file: data.mrdi

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.0.5"]},
  "_type": {"name": "FPGroupElem", "params": "5004c4f1-5440-4d55-bf76-49efb475aed3"},
  "data": ["1", "1"],
  "_refs": {
    "5004c4f1-5440-4d55-bf76-49efb475aed3": {
      "_type": "FPGroup",
      "data": {
        "X": {
          "GapType": "IsSubgroupFpGroup",
          "wholeGroup": "2c1d5ff1-aacd-4b06-a637-e776982e1878",
          "gens": [["1", "1"]]
        }
      }
    },
    "2c1d5ff1-aacd-4b06-a637-e776982e1878": {
      "_type": "GAP.GapObj",
      "data": {
        "GapType": "IsSubgroupFpGroup",
        "freeGroup": "42a00e07-5da7-4be4-9e4c-21fbd81920ac",
        "relators": [["1", "2"], ["2", "2"], ["1", "-1", "2", "-1", "1", "1", "2", "1"]]
      }
    },
    "42a00e07-5da7-4be4-9e4c-21fbd81920ac": {
      "_type": "GAP.GapObj",
      "data": {"GapType": "IsFreeGroup", "wfilt": "IsLetterWordsFamily", "names": ["f1", "f2"]}
    }
  }
}

Profiles: OSCAR v1.1, OSCAR v1.2, OSCAR v1.3

Data file: data.mrdi

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.3.1"]},
  "_type": {"name": "SubFPGroupElem", "params": "55aeea0f-9188-4768-8ec8-a212f81da389"},
  "data": ["1", "1"],
  "_refs": {
    "55aeea0f-9188-4768-8ec8-a212f81da389": {"_type": "SubFPGroup", "data": {"X": "b994619a-a38c-4cd7-80a1-ac0fafa29cf9"}},
    "b994619a-a38c-4cd7-80a1-ac0fafa29cf9": {
      "_type": "GapObj",
      "data": {
        "GapType": "IsSubgroupFpGroup",
        "wholeGroup": "1ec23d65-6f60-4b78-99df-e89a512b80ab",
        "gens": [["1", "1"]]
      }
    },
    "1ec23d65-6f60-4b78-99df-e89a512b80ab": {
      "_type": "GapObj",
      "data": {
        "GapType": "IsSubgroupFpGroup",
        "freeGroup": "e44dc5e1-955b-4f7c-9582-bb04fe93f713",
        "relators": [["1", "2"], ["2", "2"], ["1", "-1", "2", "-1", "1", "1", "2", "1"]]
      }
    },
    "e44dc5e1-955b-4f7c-9582-bb04fe93f713": {
      "_type": "GapObj",
      "data": {"GapType": "IsFreeGroup", "wfilt": "IsLetterWordsFamily", "names": ["f1", "f2"]}
    }
  }
}

This serialized output is equivalent for these profiles up to UUID renaming and recorded namespace version strings.

Profiles: OSCAR v1.4, OSCAR v1.5, OSCAR v1.6, OSCAR v1.7

Data file: data.mrdi

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.7.0"]},
  "_type": {"name": "SubFPGroupElem", "params": "048f9cfb-7d58-47b0-b3e6-c739ec61616b"},
  "data": ["1", "1"],
  "_refs": {
    "048f9cfb-7d58-47b0-b3e6-c739ec61616b": {"_type": {"name": "SubFPGroup", "params": "fd7eec5c-2ef0-4283-8206-e832182d7cd0"}, "data": []},
    "fd7eec5c-2ef0-4283-8206-e832182d7cd0": {
      "_type": {"name": "GapObj", "params": "10c9f88f-4aeb-4b73-8179-6feed4f94c1a"},
      "data": {"GapType": "IsSubgroupFpGroup", "gens": [["1", "1"]]}
    },
    "10c9f88f-4aeb-4b73-8179-6feed4f94c1a": {
      "_type": {"name": "GapObj", "params": "15109b0e-0740-4dc4-9c35-c7fe419dff59"},
      "data": {
        "GapType": "IsSubgroupFpGroup",
        "relators": [["1", "2"], ["2", "2"], ["1", "-1", "2", "-1", "1", "1", "2", "1"]]
      }
    },
    "15109b0e-0740-4dc4-9c35-c7fe419dff59": {
      "_type": "GapObj",
      "data": {"GapType": "IsFreeGroup", "wfilt": "IsLetterWordsFamily", "names": ["f1", "f2"]}
    }
  }
}

This serialized output is equivalent for these profiles up to UUID renaming and recorded namespace version strings.