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