Specification: Permutation Group Elements (OSCAR v1.6-v1.8)

Profiles: OSCAR v1.6, OSCAR v1.7, OSCAR v1.8 Other versions: Permutation Group Elements (OSCAR v1.0-v1.1), Permutation Group Elements (OSCAR v1.2-v1.3), Permutation Group Elements (OSCAR v1.4-v1.5)

In OSCAR v1.6 through v1.8, PermGroupElem refers to a PermGroup whose attributes live in a top-level attrs block and use the newer nested encodings.

Encoding Notes

• Use _type: "PermGroupElem".
• Store the permutation word under data.
• Refer to the parent group according to the matching OSCAR v1.6-v1.8 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",
      "1.8.0-DEV-1-8dea7e5a4d0cdef038b2fa2cd018d08201b4ac07"
    ]
  },
  "_type": {"name": "PermGroupElem", "params": "e3ab165d-a996-434e-924f-40bd240a1e07"},
  "data": ["2", "1"],
  "_refs": {
    "e3ab165d-a996-434e-924f-40bd240a1e07": {
      "_type": "PermGroup",
      "data": {"degree": "5", "gens": [["2", "1"], ["1", "2", "4", "3"], ["3", "4", "1", "2"]]},
      "attrs": {
        "order": {"_type": {"name": "ZZRingElem", "params": {"_type": "ZZRing"}}, "data": "8"},
        "is_nilpotent": {"_type": "Bool", "data": true},
        "is_perfect": {"_type": "Bool", "data": false},
        "is_solvable": {"_type": "Bool", "data": true}
      }
    }
  }
}

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