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Example: Number-field polyhedral complex

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

Construct a polyhedral complex over an embedded number field.

Systems

Oscar.jl

Generate code (generate.jl) [ edit ]

using Oscar

Qx, x = QQ[:x]
F, a = embedded_number_field(x^2 - 2, -1.0)
IM = incidence_matrix([[1,2,3],[1,3,4]])
vr_F = F.([0 0; 1 0; 1 1; 0 1])
obj = polyhedral_complex(IM, vr_F)

save("data.mrdi", obj)

Data outputs

Profiles: OSCAR v1.0

Not available for OSCAR v1.0.

In OSCAR v1.0-1.1 the generator does not run successfully; the exact failure mode varies across versions.

Profiles: OSCAR v1.1

Not available for OSCAR v1.1.

In OSCAR v1.0-1.1 the generator does not run successfully; the exact failure mode varies across versions.

Profiles: OSCAR v1.2, OSCAR v1.3

Data file: data.mrdi

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.3.1"]},
  "_type": {"name": "PolyhedralComplex", "params": "868e047f-e9bc-4392-a4d5-73ceeb4b7f0a"},
  "data": {
    "_type": {
      "name": "Dict",
      "params": {
        "key_type": "String",
        "_coeff": "EmbeddedNumField",
        "POINTS": {"name": "MatElem", "params": "c9a4ea85-0967-4abc-9b1e-18855c7e7ac1"},
        "INPUT_LINEALITY": {"name": "MatElem", "params": "98ee3a07-4581-4478-a3b9-116e93181e6a"},
        "_type": "String",
        "INPUT_POLYTOPES": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}"
      }
    },
    "data": {
      "_coeff": {
        "num_field": "56f36ea2-5718-4573-a6d6-a9b3dbacee10",
        "embedding": "2cb7e8ba-4365-41bf-8504-a1895941d544"
      },
      "POINTS": [
        [[["0", "1"]], [], []],
        [[["0", "1"]], [["0", "1"]], []],
        [[["0", "1"]], [["0", "1"]], [["0", "1"]]],
        [[["0", "1"]], [], [["0", "1"]]]
      ],
      "INPUT_LINEALITY": [],
      "_type": "fan::PolyhedralComplex<OscarNumber>",
      "INPUT_POLYTOPES": {
        "_ns": {"polymake": ["https://polymake.org", "4.13"]},
        "_type": "common::IncidenceMatrix<NonSymmetric>",
        "data": [[0, 1, 2], [0, 2, 3], {"cols": 4}]
      }
    }
  },
  "_refs": {
    "868e047f-e9bc-4392-a4d5-73ceeb4b7f0a": {
      "_type": "EmbeddedNumField",
      "data": {
        "num_field": "56f36ea2-5718-4573-a6d6-a9b3dbacee10",
        "embedding": "2cb7e8ba-4365-41bf-8504-a1895941d544"
      }
    },
    "c9a4ea85-0967-4abc-9b1e-18855c7e7ac1": {
      "_type": "MatSpace",
      "data": {"base_ring": "868e047f-e9bc-4392-a4d5-73ceeb4b7f0a", "ncols": "3", "nrows": "4"}
    },
    "98ee3a07-4581-4478-a3b9-116e93181e6a": {
      "_type": "MatSpace",
      "data": {"base_ring": "868e047f-e9bc-4392-a4d5-73ceeb4b7f0a", "ncols": "3", "nrows": "0"}
    },
    "56f36ea2-5718-4573-a6d6-a9b3dbacee10": {
      "_type": "AbsSimpleNumField",
      "data": {
        "def_pol": {
          "_type": {"name": "PolyRingElem", "params": "b2b70a11-5c95-46d0-81aa-c61229942ecf"},
          "data": [["0", "-2"], ["2", "1"]]
        },
        "var": "a"
      }
    },
    "2cb7e8ba-4365-41bf-8504-a1895941d544": {
      "_type": "Hecke.AbsSimpleNumFieldEmbedding",
      "data": {
        "num_field": "56f36ea2-5718-4573-a6d6-a9b3dbacee10",
        "data": {
          "_type": {"name": "AcbFieldElem", "params": {"_type": "AcbField", "data": "35"}},
          "data": ["-5a827999f -22 10000001 -3e", "0 0 0 0"]
        }
      }
    },
    "b2b70a11-5c95-46d0-81aa-c61229942ecf": {"_type": "PolyRing", "data": {"base_ring": {"_type": "QQField"}, "symbols": ["x"]}}
  }
}

This serialized output is equivalent for these profiles up to UUID renaming and recorded namespace version strings.

Profiles: OSCAR v1.4, OSCAR v1.5, OSCAR v1.6, OSCAR v1.7

Data file: data.mrdi

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.7.0"]},
  "_type": {
    "name": "PolyhedralComplex",
    "params": {
      "field": "6f902f3c-e34a-4c08-b174-70a336c1e8c8",
      "pm_params": {
        "name": "Dict",
        "params": {
          "key_params": "Symbol",
          "INPUT_POLYTOPES": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
          "INPUT_LINEALITY": {"name": "MatElem", "params": "c7af8b8f-ffce-48ed-9a3a-9d4fc07ccd64"},
          "_polymake_type": "String",
          "POINTS": {"name": "MatElem", "params": "ff2a6398-0f75-403b-947f-d2d00a510cab"}
        }
      }
    }
  },
  "data": {
    "INPUT_POLYTOPES": {
      "_ns": {"polymake": ["https://polymake.org", "4.15"]},
      "data": [[0, 1, 2], [0, 2, 3], {"cols": 4}],
      "_type": "common::IncidenceMatrix<NonSymmetric>"
    },
    "INPUT_LINEALITY": [],
    "_polymake_type": "fan::PolyhedralComplex<OscarNumber>",
    "POINTS": [
      [[["0", "1"]], [], []],
      [[["0", "1"]], [["0", "1"]], []],
      [[["0", "1"]], [["0", "1"]], [["0", "1"]]],
      [[["0", "1"]], [], [["0", "1"]]]
    ]
  },
  "_refs": {
    "6f902f3c-e34a-4c08-b174-70a336c1e8c8": {
      "_type": {"name": "EmbeddedNumField", "params": "df86748c-4085-4fac-a01d-8dae2d23c1d8"},
      "data": []
    },
    "c7af8b8f-ffce-48ed-9a3a-9d4fc07ccd64": {
      "_type": {"name": "MatSpace", "params": "6f902f3c-e34a-4c08-b174-70a336c1e8c8"},
      "data": {"ncols": "3", "nrows": "0"}
    },
    "ff2a6398-0f75-403b-947f-d2d00a510cab": {
      "_type": {"name": "MatSpace", "params": "6f902f3c-e34a-4c08-b174-70a336c1e8c8"},
      "data": {"ncols": "3", "nrows": "4"}
    },
    "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"]}}
  }
}

This serialized output is equivalent for these profiles up to UUID renaming and recorded namespace version strings.