Specification: Finite Field Elements

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

FqFieldElem represents elements of finite fields in the current OSCAR profile.

Encoding Notes

• Set _type to the concrete finite-field element type used by the active profile.
• Encode the payload together with whatever ambient references are required to recover the parent field.
• Treat the linked examples as the current authoritative shape for this prototype.

Canonical Example Payload

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

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.7.0"]},
  "_type": {"name": "FqFieldElem", "params": "df441132-2db5-4e70-8e25-9f07e8a409a7"},
  "data": [["1", "1"]],
  "_refs": {
    "df441132-2db5-4e70-8e25-9f07e8a409a7": {
      "_type": {
        "_instance": "FqField",
        "name": "FiniteField",
        "params": "f6e86bd7-f1a4-4362-9321-2d30caec1b5c"
      },
      "data": [["0", "2"], ["1", "4"], ["2", "1"]]
    },
    "f6e86bd7-f1a4-4362-9321-2d30caec1b5c": {
      "_type": {"name": "PolyRing", "params": "5576c715-03ed-445e-a54a-6915905399d6"},
      "data": {"symbols": ["x"]}
    },
    "5576c715-03ed-445e-a54a-6915905399d6": {"_type": {"name": "FiniteField", "_instance": "FqField"}, "data": "5"}
  }
}

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

• Generator of GF(5^2)
• One in GF(5)