Specification: Elements of Finitely Presented Groups (OSCAR v1.0)

Profiles: OSCAR v1.0 Other versions: Elements of Finitely Presented Groups (OSCAR v1.1-v1.3), Elements of Finitely Presented Groups (OSCAR v1.4-v1.8)

In OSCAR v1.0, FPGroupElem uses a bare _type string, and its ambient group is encoded directly inside the parameter payload.

Encoding Notes

• Use _type: "FPGroupElem".
• Store the word data under data.
• Inline the parent group description in the element parameters rather than referring to _refs.

Canonical Example Payload

The following payload is taken directly from the current rosetta-stone corpus.

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.0.5"]},
  "_type": {"name": "FPGroupElem", "params": "0aa3ecbb-a6c8-4f4e-851e-1ec3f8112d86"},
  "data": ["1", "1"],
  "_refs": {
    "0aa3ecbb-a6c8-4f4e-851e-1ec3f8112d86": {
      "_type": "FPGroup",
      "data": {
        "X": {
          "GapType": "IsSubgroupFpGroup",
          "freeGroup": "b1aea6ab-9c0c-49f5-8393-bb264bbc8b05",
          "relators": [["1", "2"], ["2", "2"], ["1", "-1", "2", "-1", "1", "1", "2", "1"]]
        }
      }
    },
    "b1aea6ab-9c0c-49f5-8393-bb264bbc8b05": {
      "_type": "GAP.GapObj",
      "data": {"GapType": "IsFreeGroup", "wfilt": "IsLetterWordsFamily", "names": ["f1", "f2"]}
    }
  }
}

Documented Profiles in This Corpus

This table records the profile/version pairs currently represented by the rosetta-stone examples for this data type. Add new rows as new systems or encoding revisions are documented.

Rosetta Stone Examples

• Element of finitely presented group
• Element of subgroup of free group
• Element of subgroup of finitely presented group
• Element of free group