Specification: Permutation Group Elements (OSCAR v1.0-v1.1)

Profiles: OSCAR v1.0, OSCAR v1.1 Other versions: Permutation Group Elements (OSCAR v1.2-v1.3), Permutation Group Elements (OSCAR v1.4-v1.5), Permutation Group Elements (OSCAR v1.6-v1.8)

In OSCAR v1.0 and v1.1, PermGroupElem uses the bare type name and refers to a parent permutation group whose attributes, if any, remain inside data.

Encoding Notes

• Use _type: "PermGroupElem".
• Store the permutation word under data.
• Refer to the parent group according to the matching PermGroup encoding.

Canonical Example Payload

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

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.1.2"]},
  "_type": {"name": "PermGroupElem", "params": "11ae54c9-4d34-42c5-8370-35cb53a5d7e8"},
  "data": ["2", "1"],
  "_refs": {
    "11ae54c9-4d34-42c5-8370-35cb53a5d7e8": {
      "_type": "PermGroup",
      "data": {"degree": "5", "gens": [["2", "1"], ["1", "2", "4", "3"], ["3", "4", "1", "2"]]}
    }
  }
}

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 subgroup of symmetric group
• Element of symmetric group