Specification: Elements of Finitely Presented Groups (OSCAR v1.1-v1.3)

Profiles: OSCAR v1.1, OSCAR v1.2, OSCAR v1.3 Other versions: Elements of Finitely Presented Groups (OSCAR v1.0), Elements of Finitely Presented Groups (OSCAR v1.4-v1.8)

In OSCAR v1.1 through v1.3, FPGroupElem keeps the bare type name "FPGroupElem", but its parent group is referenced through _refs.

Encoding Notes

• Use _type: "FPGroupElem".
• Store the word data under data.
• Refer to the parent group through a reference id stored in the parameters.

Canonical Example Payload

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

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.3.1"]},
  "_type": {"name": "FPGroupElem", "params": "1dc46124-d0ad-4f2d-8801-0ee9a94757bc"},
  "data": ["1", "1"],
  "_refs": {
    "1dc46124-d0ad-4f2d-8801-0ee9a94757bc": {"_type": "FPGroup", "data": {"X": "f6e033ff-9ee7-4432-bbf9-fb4feefc44d2"}},
    "f6e033ff-9ee7-4432-bbf9-fb4feefc44d2": {
      "_type": "GapObj",
      "data": {
        "GapType": "IsSubgroupFpGroup",
        "freeGroup": "12cd4025-2b7d-4768-9178-8b44c4e47276",
        "relators": [["1", "2"], ["2", "2"], ["1", "-1", "2", "-1", "1", "1", "2", "1"]]
      }
    },
    "12cd4025-2b7d-4768-9178-8b44c4e47276": {
      "_type": "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 free group