1{ 2 "descend": { 3 "fan::HyperplaneArrangement": { 4 "CELL_DECOMPOSITION": "fan::PolyhedralFan", 5 "SUPPORT": "polytope::Cone" 6 }, 7 "fan::PlanarNet": { 8 "POLYTOPE": "polytope::Polytope" 9 }, 10 "fan::PolyhedralComplex": { 11 "COMPACTIFICATION": "graph::Lattice" 12 }, 13 "fan::PolyhedralFan": { 14 "DUAL_GRAPH": "graph::Graph", 15 "GRAPH": "graph::Graph", 16 "GROUP": [ 17 "group::Group", 18 { 19 "MATRIX_ACTION": "group::MatrixActionOnVectors" 20 } 21 ], 22 "HASSE_DIAGRAM": "graph::Lattice", 23 "INTERSECTION_COMPLEX": "topaz::SimplicialComplex" 24 }, 25 "fan::SubdivisionOfPoints": { 26 "POLYHEDRAL_COMPLEX": "fan::PolyhedralComplex", 27 "TIGHT_SPAN": "fan::PolyhedralComplex" 28 }, 29 "fulton::CyclicQuotient": { 30 "VERSAL_COMPONENT": "fulton::VersalComponent" 31 }, 32 "fulton::NormalToricVariety": { 33 "DIVISOR": "fulton::TDivisor", 34 "EFFECTIVE_CONE": "polytope::Cone", 35 "GENERATING_POLYTOPE": "polytope::Polytope", 36 "MORI_CONE": "polytope::Cone", 37 "NEF_CONE": "polytope::Cone", 38 "RATIONAL_DIVISOR_CLASS_GROUP": "fulton::RationalDivisorClassGroup" 39 }, 40 "fulton::TDivisor": { 41 "SECTION_POLYTOPE": "polytope::Polytope" 42 }, 43 "fulton::VersalComponent": { 44 "N_GON_TRIANGULATION": "graph::Graph", 45 "P_RESOLUTION": "fan::PolyhedralFan", 46 "TOTAL_SPACE": "ideal::Ideal" 47 }, 48 "group::Group": { 49 "FACETS_ACTION": "group::PermutationAction", 50 "FACET_NORMALS_ACTION": "group::PermutationAction", 51 "HOMOGENEOUS_COORDINATE_ACTION": "group::PermutationAction", 52 "IMPLICIT_SET_ACTION": "group::ImplicitActionOnSets", 53 "INEQUALITIES_ACTION": "group::PermutationAction", 54 "INPUT_CONES_ACTION": "group::PermutationAction", 55 "INPUT_RAYS_ACTION": "group::PermutationAction", 56 "MAXIMAL_CONES_ACTION": "group::PermutationAction", 57 "PERMUTATION_ACTION": "group::PermutationAction", 58 "RAYS_ACTION": "group::PermutationAction", 59 "REGULAR_REPRESENTATION": "group::MatrixActionOnVectors", 60 "SET_ACTION": "group::PermutationAction", 61 "VECTOR_ACTION": "group::PermutationAction" 62 }, 63 "ideal::Groebner": { 64 "INITIAL_IDEAL": "ideal::Ideal" 65 }, 66 "ideal::Ideal": { 67 "GROEBNER": "ideal::Groebner", 68 "PRIMARY_DECOMPOSITION": "ideal::Ideal", 69 "RADICAL": "ideal::Ideal" 70 }, 71 "matroid::Matroid": { 72 "AUTOMORPHISM_GROUP": "group::Group", 73 "DUAL": "matroid::Matroid", 74 "LATTICE_OF_CYCLIC_FLATS": "graph::Lattice", 75 "LATTICE_OF_FLATS": "graph::Lattice", 76 "POLYTOPE": "polytope::Polytope" 77 }, 78 "polytope::Cone": { 79 "DUAL_GRAPH": "graph::Graph", 80 "GRAPH": "graph::Graph", 81 "GROUP": [ 82 "group::Group", 83 { 84 "BITSET_ACTION": "group::ImplicitActionOnSets", 85 "MATRIX_ACTION": "group::MatrixActionOnVectors" 86 } 87 ], 88 "HASSE_DIAGRAM": "graph::Lattice", 89 "TRIANGULATION": "topaz::GeometricSimplicialComplex" 90 }, 91 "polytope::LinearProgram": { 92 "DIRECTED_BOUNDED_GRAPH": "graph::Graph", 93 "DIRECTED_GRAPH": "graph::Graph" 94 }, 95 "polytope::PointConfiguration": { 96 "CONVEX_HULL": "polytope::Polytope", 97 "GRAPH": "graph::Graph", 98 "GROUP": [ 99 "group::Group", 100 { 101 "POINTS_ACTION": [ 102 "group::PermutationAction", 103 { 104 "SYMMETRIZED_COCIRCUIT_EQUATIONS": "polytope::SymmetrizedCocircuitEquations" 105 } 106 ] 107 } 108 ], 109 "POLYTOPAL_SUBDIVISION": "fan::SubdivisionOfPoints", 110 "SPLIT_COMPATIBILITY_GRAPH": "graph::Graph", 111 "TRIANGULATION": "topaz::GeometricSimplicialComplex" 112 }, 113 "polytope::Polytope": { 114 "BOUNDED_COMPLEX": "fan::PolyhedralComplex", 115 "GROUP": [ 116 "group::Group", 117 { 118 "COORDINATE_ACTION": [ 119 "group::PermutationAction", 120 { 121 "NOP_GRAPH": "graph::Graph" 122 } 123 ], 124 "VERTICES_ACTION": [ 125 "group::PermutationAction", 126 { 127 "SYMMETRIZED_COCIRCUIT_EQUATIONS": "polytope::SymmetrizedCocircuitEquations" 128 } 129 ] 130 } 131 ], 132 "LP": "polytope::LinearProgram", 133 "MILP": "polytope::MixedIntegerLinearProgram", 134 "POLYTOPAL_SUBDIVISION": "fan::SubdivisionOfPoints", 135 "QUOTIENT_SPACE": "polytope::QuotientSpace", 136 "SCHLEGEL_DIAGRAM": "polytope::SchlegelDiagram", 137 "SLACK_IDEAL": "polytope::SlackIdeal", 138 "SPLIT_COMPATIBILITY_GRAPH": "graph::Graph", 139 "TILING_LATTICE": "polytope::AffineLattice" 140 }, 141 "polytope::PropagatedPolytope": { 142 "SUM_PRODUCT_GRAPH": "graph::Graph" 143 }, 144 "polytope::QuotientSpace": { 145 "IDENTIFICATION_ACTION": "group::PermutationAction", 146 "SIMPLICIAL_COMPLEX": "topaz::SimplicialComplex", 147 "SYMMETRY_GROUP": "group::Group" 148 }, 149 "polytope::SlackIdeal": { 150 "NON_SATURATED": "ideal::Ideal" 151 }, 152 "polytope::VectorConfiguration": { 153 "GROUP": [ 154 "group::Group", 155 { 156 "MATRIX_ACTION": "group::MatrixActionOnVectors" 157 } 158 ] 159 }, 160 "polytope::VoronoiPolyhedron": { 161 "CRUST_GRAPH": "graph::Graph", 162 "DELAUNAY_DIAGRAM": "fan::PolyhedralComplex", 163 "DELAUNAY_GRAPH": "graph::Graph", 164 "ITERATED_DELAUNAY_GRAPH": "graph::Graph", 165 "ITERATED_VORONOI_GRAPH": "graph::GeometricGraph", 166 "NN_CRUST_GRAPH": "graph::Graph", 167 "NN_GRAPH": "graph::Graph", 168 "VORONOI_DIAGRAM": "fan::PolyhedralComplex", 169 "VORONOI_GRAPH": "graph::GeometricGraph" 170 }, 171 "topaz::HyperbolicSurface": { 172 "SECONDARY_FAN": "fan::PolyhedralFan" 173 }, 174 "topaz::SimplicialComplex": { 175 "BOUNDARY": "topaz::SimplicialComplex", 176 "DUAL_GRAPH": "graph::Graph", 177 "GRAPH": "graph::Graph", 178 "GROUP": "group::Group", 179 "HASSE_DIAGRAM": "graph::Lattice", 180 "KNOT": "topaz::SimplicialComplex", 181 "MIXED_GRAPH": "graph::Graph", 182 "MORSE_MATCHING": "topaz::MorseMatching", 183 "ODD_SUBCOMPLEX": "topaz::SimplicialComplex" 184 }, 185 "tropical::Cycle": { 186 "WEIGHT_CONE": "polytope::Cone" 187 }, 188 "tropical::Hypersurface": { 189 "DOME": "polytope::Polytope", 190 "DUAL_SUBDIVISION": "fan::SubdivisionOfPoints", 191 "PATCHWORK": "tropical::Patchwork" 192 }, 193 "tropical::LinesInCubic": { 194 "CUBIC": "tropical::Cycle", 195 "LIST_FAMILY_FIXED_EDGE": "tropical::Cycle", 196 "LIST_FAMILY_FIXED_VERTEX": "tropical::Cycle", 197 "LIST_FAMILY_MOVING_EDGE": "tropical::Cycle", 198 "LIST_FAMILY_MOVING_VERTEX": "tropical::Cycle", 199 "LIST_ISOLATED_EDGE": "tropical::Cycle", 200 "LIST_ISOLATED_NO_EDGE": "tropical::Cycle" 201 }, 202 "tropical::Morphism": { 203 "DOMAIN": "tropical::Cycle" 204 }, 205 "tropical::Polytope": { 206 "DOME": "polytope::Polytope", 207 "ENVELOPE": "polytope::Polytope", 208 "POLYTOPE_COVECTOR_DECOMPOSITION": "tropical::CovectorLattice", 209 "TORUS_COVECTOR_DECOMPOSITION": "tropical::CovectorLattice" 210 }, 211 "tropical::RationalCurve": { 212 "GRAPH": "graph::Graph" 213 }, 214 "tropical::RationalFunction": { 215 "DOMAIN": "tropical::Cycle" 216 } 217 }, 218 "super": { 219 "fan::PlanarNet": [ 220 "fan::PolyhedralComplex", 221 "fan::PolyhedralFan" 222 ], 223 "fan::PolyhedralComplex": [ 224 "fan::PolyhedralFan" 225 ], 226 "fan::SubdivisionOfPoints": [ 227 "fan::SubdivisionOfVectors" 228 ], 229 "fulton::BinomialIdeal": [ 230 "ideal::Ideal" 231 ], 232 "fulton::CyclicQuotient": [ 233 "fan::PolyhedralFan", 234 "fulton::NormalToricVariety" 235 ], 236 "fulton::NormalToricVariety": [ 237 "fan::PolyhedralFan" 238 ], 239 "graph::GeometricGraph": [ 240 "graph::Graph" 241 ], 242 "graph::Lattice": [ 243 "graph::Graph" 244 ], 245 "group::ImplicitActionOnSets": [ 246 "group::Action", 247 "group::PermutationAction" 248 ], 249 "group::MatrixActionOnVectors": [ 250 "group::Action" 251 ], 252 "group::PermutationAction": [ 253 "group::Action" 254 ], 255 "group::PermutationActionOnSets": [ 256 "group::Action", 257 "group::PermutationAction" 258 ], 259 "matroid::ValuatedMatroid": [ 260 "matroid::Matroid" 261 ], 262 "polytope::PointConfiguration": [ 263 "polytope::VectorConfiguration" 264 ], 265 "polytope::Polytope": [ 266 "polytope::Cone" 267 ], 268 "polytope::PropagatedPolytope": [ 269 "polytope::Cone", 270 "polytope::Polytope" 271 ], 272 "polytope::SlackIdeal": [ 273 "ideal::Ideal" 274 ], 275 "polytope::VoronoiPolyhedron": [ 276 "polytope::Cone", 277 "polytope::Polytope" 278 ], 279 "topaz::GeometricSimplicialComplex": [ 280 "topaz::SimplicialComplex" 281 ], 282 "tropical::CovectorLattice": [ 283 "graph::Graph", 284 "graph::Lattice" 285 ], 286 "tropical::Cycle": [ 287 "fan::PolyhedralComplex", 288 "fan::PolyhedralFan" 289 ], 290 "tropical::Hypersurface": [ 291 "fan::PolyhedralComplex", 292 "fan::PolyhedralFan", 293 "tropical::Cycle" 294 ], 295 "tropical::MatroidRingCycle": [ 296 "fan::PolyhedralComplex", 297 "fan::PolyhedralFan", 298 "tropical::Cycle" 299 ] 300 } 301} 302