{
  "descend": {
    "fan::HyperplaneArrangement": {
      "CHAMBER_DECOMPOSITION": "fan::PolyhedralFan",
      "SUPPORT": "polytope::Cone"
    },
    "fan::PlanarNet": {
      "POLYTOPE": "polytope::Polytope"
    },
    "fan::PolyhedralComplex": {
      "COMPACTIFICATION": "graph::Lattice"
    },
    "fan::PolyhedralFan": {
      "DUAL_GRAPH": "graph::Graph",
      "GRAPH": "graph::Graph",
      "GROUP": [
        "group::Group",
        {
          "MATRIX_ACTION": "group::MatrixActionOnVectors"
        }
      ],
      "HASSE_DIAGRAM": "graph::Lattice",
      "INTERSECTION_COMPLEX": "topaz::SimplicialComplex"
    },
    "fan::SubdivisionOfPoints": {
      "POLYHEDRAL_COMPLEX": "fan::PolyhedralComplex",
      "TIGHT_SPAN": "fan::PolyhedralComplex"
    },
    "fulton::CyclicQuotient": {
      "VERSAL_COMPONENT": "fulton::VersalComponent"
    },
    "fulton::NormalToricVariety": {
      "DIVISOR": "fulton::TDivisor",
      "EFFECTIVE_CONE": "polytope::Cone",
      "GENERATING_POLYTOPE": "polytope::Polytope",
      "MORI_CONE": "polytope::Cone",
      "NEF_CONE": "polytope::Cone",
      "RATIONAL_DIVISOR_CLASS_GROUP": "fulton::RationalDivisorClassGroup"
    },
    "fulton::TDivisor": {
      "SECTION_POLYTOPE": "polytope::Polytope"
    },
    "fulton::VersalComponent": {
      "N_GON_TRIANGULATION": "graph::Graph",
      "P_RESOLUTION": "fan::PolyhedralFan",
      "TOTAL_SPACE": "ideal::Ideal"
    },
    "group::Group": {
      "FACETS_ACTION": "group::PermutationAction",
      "FACET_NORMALS_ACTION": "group::PermutationAction",
      "HOMOGENEOUS_COORDINATE_ACTION": "group::PermutationAction",
      "IMPLICIT_SET_ACTION": "group::ImplicitActionOnSets",
      "INEQUALITIES_ACTION": "group::PermutationAction",
      "INPUT_CONES_ACTION": "group::PermutationAction",
      "INPUT_RAYS_ACTION": "group::PermutationAction",
      "MAXIMAL_CONES_ACTION": "group::PermutationAction",
      "PERMUTATION_ACTION": "group::PermutationAction",
      "RAYS_ACTION": "group::PermutationAction",
      "REGULAR_REPRESENTATION": "group::MatrixActionOnVectors",
      "SET_ACTION": "group::PermutationAction",
      "VECTOR_ACTION": "group::PermutationAction"
    },
    "ideal::Groebner": {
      "INITIAL_IDEAL": "ideal::Ideal"
    },
    "ideal::Ideal": {
      "GROEBNER": "ideal::Groebner",
      "PRIMARY_DECOMPOSITION": "ideal::Ideal",
      "RADICAL": "ideal::Ideal"
    },
    "matroid::Matroid": {
      "AUTOMORPHISM_GROUP": "group::Group",
      "DUAL": "matroid::Matroid",
      "LATTICE_OF_CYCLIC_FLATS": "graph::Lattice",
      "LATTICE_OF_FLATS": "graph::Lattice",
      "POLYTOPE": "polytope::Polytope"
    },
    "polytope::Cone": {
      "DUAL_GRAPH": "graph::Graph",
      "GRAPH": "graph::Graph",
      "GROUP": [
        "group::Group",
        {
          "BITSET_ACTION": "group::ImplicitActionOnSets",
          "MATRIX_ACTION": "group::MatrixActionOnVectors"
        }
      ],
      "HASSE_DIAGRAM": "graph::Lattice",
      "TRIANGULATION": "topaz::GeometricSimplicialComplex"
    },
    "polytope::LinearProgram": {
      "DIRECTED_BOUNDED_GRAPH": "graph::Graph",
      "DIRECTED_GRAPH": "graph::Graph"
    },
    "polytope::PointConfiguration": {
      "CONVEX_HULL": "polytope::Polytope",
      "GRAPH": "graph::Graph",
      "GROUP": [
        "group::Group",
        {
          "POINTS_ACTION": [
            "group::PermutationAction",
            {
              "SYMMETRIZED_COCIRCUIT_EQUATIONS": "polytope::SymmetrizedCocircuitEquations"
            }
          ]
        }
      ],
      "POLYTOPAL_SUBDIVISION": "fan::SubdivisionOfPoints",
      "SPLIT_COMPATIBILITY_GRAPH": "graph::Graph",
      "TRIANGULATION": "topaz::GeometricSimplicialComplex"
    },
    "polytope::Polytope": {
      "BOUNDED_COMPLEX": "fan::PolyhedralComplex",
      "GROUP": [
        "group::Group",
        {
          "VERTICES_ACTION": [
            "group::PermutationAction",
            {
              "SYMMETRIZED_COCIRCUIT_EQUATIONS": "polytope::SymmetrizedCocircuitEquations"
            }
          ]
        }
      ],
      "LP": "polytope::LinearProgram",
      "MILP": "polytope::MixedIntegerLinearProgram",
      "POLYTOPAL_SUBDIVISION": "fan::SubdivisionOfPoints",
      "QUOTIENT_SPACE": "polytope::QuotientSpace",
      "SCHLEGEL_DIAGRAM": "polytope::SchlegelDiagram",
      "SLACK_IDEAL": "polytope::SlackIdeal",
      "SPLIT_COMPATIBILITY_GRAPH": "graph::Graph",
      "TILING_LATTICE": "polytope::AffineLattice"
    },
    "polytope::PropagatedPolytope": {
      "SUM_PRODUCT_GRAPH": "graph::Graph"
    },
    "polytope::QuotientSpace": {
      "IDENTIFICATION_ACTION": "group::PermutationAction",
      "SIMPLICIAL_COMPLEX": "topaz::SimplicialComplex",
      "SYMMETRY_GROUP": "group::Group"
    },
    "polytope::SlackIdeal": {
      "NON_SATURATED": "ideal::Ideal"
    },
    "polytope::VectorConfiguration": {
      "GROUP": [
        "group::Group",
        {
          "MATRIX_ACTION": "group::MatrixActionOnVectors"
        }
      ]
    },
    "polytope::VoronoiPolyhedron": {
      "CRUST_GRAPH": "graph::Graph",
      "DELAUNAY_DIAGRAM": "fan::PolyhedralComplex",
      "DELAUNAY_GRAPH": "graph::Graph",
      "ITERATED_DELAUNAY_GRAPH": "graph::Graph",
      "ITERATED_VORONOI_GRAPH": "graph::GeometricGraph",
      "NN_CRUST_GRAPH": "graph::Graph",
      "NN_GRAPH": "graph::Graph",
      "VORONOI_DIAGRAM": "fan::PolyhedralComplex",
      "VORONOI_GRAPH": "graph::GeometricGraph"
    },
    "topaz::HyperbolicSurface": {
      "SECONDARY_FAN": "fan::PolyhedralFan"
    },
    "topaz::SimplicialComplex": {
      "BOUNDARY": "topaz::SimplicialComplex",
      "DUAL_GRAPH": "graph::Graph",
      "GRAPH": "graph::Graph",
      "GROUP": "group::Group",
      "HASSE_DIAGRAM": "graph::Lattice",
      "KNOT": "topaz::SimplicialComplex",
      "MIXED_GRAPH": "graph::Graph",
      "MORSE_MATCHING": "topaz::MorseMatching",
      "ODD_SUBCOMPLEX": "topaz::SimplicialComplex"
    },
    "tropical::Cycle": {
      "WEIGHT_CONE": "polytope::Cone"
    },
    "tropical::Hypersurface": {
      "DOME": "polytope::Polytope",
      "DUAL_SUBDIVISION": "fan::SubdivisionOfPoints",
      "PATCHWORK": "tropical::Patchwork"
    },
    "tropical::LinesInCubic": {
      "CUBIC": "tropical::Cycle",
      "LIST_FAMILY_FIXED_EDGE": "tropical::Cycle",
      "LIST_FAMILY_FIXED_VERTEX": "tropical::Cycle",
      "LIST_FAMILY_MOVING_EDGE": "tropical::Cycle",
      "LIST_FAMILY_MOVING_VERTEX": "tropical::Cycle",
      "LIST_ISOLATED_EDGE": "tropical::Cycle",
      "LIST_ISOLATED_NO_EDGE": "tropical::Cycle"
    },
    "tropical::Morphism": {
      "DOMAIN": "tropical::Cycle"
    },
    "tropical::Polytope": {
      "DOME": "polytope::Polytope",
      "ENVELOPE": "polytope::Polytope",
      "POLYTOPE_COVECTOR_DECOMPOSITION": "tropical::CovectorLattice",
      "TORUS_COVECTOR_DECOMPOSITION": "tropical::CovectorLattice"
    },
    "tropical::RationalCurve": {
      "GRAPH": "graph::Graph"
    },
    "tropical::TropicalRationalFunction": {
      "DOMAIN": "tropical::Cycle"
    }
  },
  "super": {
    "fan::HyperplaneArrangement": [
      "polytope::VectorConfiguration"
    ],
    "fan::PlanarNet": [
      "fan::PolyhedralComplex",
      "fan::PolyhedralFan"
    ],
    "fan::PolyhedralComplex": [
      "fan::PolyhedralFan"
    ],
    "fan::SubdivisionOfPoints": [
      "fan::SubdivisionOfVectors"
    ],
    "fulton::CyclicQuotient": [
      "fan::PolyhedralFan",
      "fulton::NormalToricVariety"
    ],
    "fulton::NormalToricVariety": [
      "fan::PolyhedralFan"
    ],
    "graph::GeometricGraph": [
      "graph::Graph"
    ],
    "graph::Lattice": [
      "graph::Graph"
    ],
    "group::ImplicitActionOnSets": [
      "group::Action",
      "group::PermutationAction"
    ],
    "group::MatrixActionOnVectors": [
      "group::Action"
    ],
    "group::PermutationAction": [
      "group::Action"
    ],
    "group::PermutationActionOnSets": [
      "group::Action",
      "group::PermutationAction"
    ],
    "matroid::ValuatedMatroid": [
      "matroid::Matroid"
    ],
    "polytope::PointConfiguration": [
      "polytope::VectorConfiguration"
    ],
    "polytope::Polytope": [
      "polytope::Cone"
    ],
    "polytope::PropagatedPolytope": [
      "polytope::Cone",
      "polytope::Polytope"
    ],
    "polytope::SlackIdeal": [
      "ideal::Ideal"
    ],
    "polytope::VoronoiPolyhedron": [
      "polytope::Cone",
      "polytope::Polytope"
    ],
    "topaz::GeometricSimplicialComplex": [
      "topaz::SimplicialComplex"
    ],
    "tropical::CovectorLattice": [
      "graph::Graph",
      "graph::Lattice"
    ],
    "tropical::Cycle": [
      "fan::PolyhedralComplex",
      "fan::PolyhedralFan"
    ],
    "tropical::Hypersurface": [
      "fan::PolyhedralComplex",
      "fan::PolyhedralFan",
      "tropical::Cycle"
    ],
    "tropical::MatroidRingCycle": [
      "fan::PolyhedralComplex",
      "fan::PolyhedralFan",
      "tropical::Cycle"
    ]
  }
}
