Specification: Subdivisions of Points

Profiles: OSCAR v1.2, OSCAR v1.3, OSCAR v1.4, OSCAR v1.5, OSCAR v1.6, OSCAR v1.7, OSCAR v1.8

SubdivisionOfPoints is currently documented in the OSCAR v1.7 profile through the rosetta-stone corpus. This page records the present encoding shape and should be read as a profile-specific type description.

Encoding Notes

• Set _type to "SubdivisionOfPoints" when this type appears at the root of a serialized object.
• Interpret the payload under data according to the active namespace and profile version.
• Follow the linked examples for the currently documented payload shape and referenced ambient objects.

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": "SubdivisionOfPoints",
    "params": {
      "field": "c8abb118-3e41-4220-ab32-e76c501ffa80",
      "pm_params": {
        "name": "Dict",
        "params": {
          "key_params": "Symbol",
          "_polymake_type": "String",
          "MAXIMAL_CELLS": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
          "POINTS": {"name": "MatElem", "params": "5b2222f9-03b8-4da6-967d-c7ac8f02c34f"}
        }
      }
    }
  },
  "data": {
    "_polymake_type": "fan::SubdivisionOfPoints<OscarNumber>",
    "MAXIMAL_CELLS": {
      "_ns": {"polymake": ["https://polymake.org", "4.15"]},
      "data": [[3, 4, 5], [0, 1, 3], [1, 3, 4], [1, 2, 4], [2, 4, 5], [0, 2, 5], [0, 3, 5], {"cols": 6}],
      "_type": "common::IncidenceMatrix<NonSymmetric>"
    },
    "POINTS": [
      [[["0", "1"]], [["0", "4"]], [], []],
      [[["0", "1"]], [], [["0", "4"]], []],
      [[["0", "1"]], [], [], [["0", "4"]]],
      [[["0", "1"]], [["0", "2"]], [["0", "1"]], [["0", "1"]]],
      [[["0", "1"]], [["0", "1"]], [["0", "2"]], [["0", "1"]]],
      [[["0", "1"]], [["0", "1"]], [["0", "1"]], [["0", "2"]]]
    ]
  },
  "_refs": {
    "c8abb118-3e41-4220-ab32-e76c501ffa80": {
      "_type": {"name": "EmbeddedNumField", "params": "df86748c-4085-4fac-a01d-8dae2d23c1d8"},
      "data": []
    },
    "5b2222f9-03b8-4da6-967d-c7ac8f02c34f": {
      "_type": {"name": "MatSpace", "params": "c8abb118-3e41-4220-ab32-e76c501ffa80"},
      "data": {"ncols": "4", "nrows": "6"}
    },
    "df86748c-4085-4fac-a01d-8dae2d23c1d8": {
      "_type": {"name": "Hecke.AbsSimpleNumFieldEmbedding", "params": "503279d5-fda8-4fbd-96d2-d6a5080024ba"},
      "data": ["-5a827999f -22 10000001 -3e", "0 0 0 0"]
    },
    "503279d5-fda8-4fbd-96d2-d6a5080024ba": {
      "_type": {"name": "AbsSimpleNumField", "params": "a78c482c-7f1a-4290-9be9-a4c6c8f3a0fa"},
      "data": {"def_pol": [["0", "-2"], ["2", "1"]], "var": "a"}
    },
    "a78c482c-7f1a-4290-9be9-a4c6c8f3a0fa": {"_type": {"name": "PolyRing", "params": {"_type": "QQField"}}, "data": {"symbols": ["x"]}}
  }
}

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

• Number-field subdivision
• Subdivision of points