Index A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | Z A A() (sage.geometry.linear_expression.LinearExpression method) (sage.geometry.polyhedron.double_description.Problem method) (sage.geometry.polyhedron.representation.Hrepresentation method) A_matrix() (sage.geometry.polyhedron.double_description.Problem method) a_maximal_chain() (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) add_cell() (sage.geometry.polyhedral_complex.PolyhedralComplex method) add_hyperplane() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) add_inequality() (sage.geometry.polyhedron.double_description.StandardDoubleDescriptionPair method) adjacency_graph() (sage.geometry.triangulation.element.Triangulation method) adjacency_matrix() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) adjacent() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.representation.Hrepresentation method) (sage.geometry.polyhedron.representation.Vrepresentation method) adjust_options() (sage.geometry.toric_plotter.ToricPlotter method) affine() (sage.geometry.triangulation.base.Point method) affine_hull() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base6.Polyhedron_base6 method) affine_hull_manifold() (sage.geometry.polyhedron.base6.Polyhedron_base6 method) affine_hull_projection() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base6.Polyhedron_base6 method) affine_lattice_polytope() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) affine_space() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) affine_tangent_cone() (sage.geometry.polyhedron.face.PolyhedronFace method) affine_transform() (sage.geometry.lattice_polytope.LatticePolytopeClass method) AffineHullProjectionData (class in sage.geometry.convex_set) AffineSubspace (class in sage.geometry.hyperplane_arrangement.affine_subspace) alexander_whitney() (sage.geometry.polyhedral_complex.PolyhedralComplex method) all_cached_data() (in module sage.geometry.lattice_polytope) all_facet_equations() (in module sage.geometry.lattice_polytope) all_nef_partitions() (in module sage.geometry.lattice_polytope) all_points() (in module sage.geometry.lattice_polytope) all_polars() (in module sage.geometry.lattice_polytope) ambient() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.relative_interior.RelativeInterior method) ambient_dim() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.polyhedron.parent.Polyhedra_base method) (sage.geometry.relative_interior.RelativeInterior method) (sage.geometry.triangulation.base.PointConfiguration_base method) (sage.geometry.voronoi_diagram.VoronoiDiagram method) (sage.rings.polynomial.groebner_fan.PolyhedralCone method) (sage.rings.polynomial.groebner_fan.PolyhedralFan method) ambient_dimension() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) ambient_facet_indices() (sage.geometry.lattice_polytope.LatticePolytopeClass method) ambient_H_indices() (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) (sage.geometry.polyhedron.face.PolyhedronFace method) ambient_Hrepresentation() (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) (sage.geometry.polyhedron.face.PolyhedronFace method) ambient_module() (sage.geometry.linear_expression.LinearExpressionModule method) (sage.geometry.toric_lattice.ToricLattice_ambient method) ambient_ordered_point_indices() (sage.geometry.lattice_polytope.LatticePolytopeClass method) ambient_point_indices() (sage.geometry.lattice_polytope.LatticePolytopeClass method) ambient_ray_indices() (sage.geometry.cone.ConvexRationalPolyhedralCone method) ambient_space() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangements method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.parent.Polyhedra_base method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) ambient_V_indices() (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) (sage.geometry.polyhedron.face.PolyhedronFace method) ambient_vector_space() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.linear_expression.LinearExpressionModule method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.relative_interior.RelativeInterior method) ambient_vertex_indices() (sage.geometry.lattice_polytope.LatticePolytopeClass method) ambient_Vrepresentation() (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) (sage.geometry.polyhedron.face.PolyhedronFace method) AmbientVectorSpace (class in sage.geometry.hyperplane_arrangement.hyperplane) an_affine_basis() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.relative_interior.RelativeInterior method) an_element() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.parent.Polyhedra_base method) (sage.geometry.triangulation.point_configuration.PointConfiguration method) are_adjacent() (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) as_combinatorial_polyhedron() (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) as_polyhedron() (sage.geometry.polyhedron.face.PolyhedronFace method) B b() (sage.geometry.linear_expression.LinearExpression method) (sage.geometry.polyhedron.representation.Hrepresentation method) backend() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.parent.Polyhedra_base method) barycentric_subdivision() (sage.geometry.polyhedron.base.Polyhedron_base method) base_extend() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.parent.Polyhedra_base method) (sage.geometry.toric_lattice.ToricLattice_quotient method) base_projection() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) base_projection_matrix() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) base_rays() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) base_ring() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangements method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.double_description.Problem method) (sage.geometry.triangulation.base.PointConfiguration_base method) (sage.geometry.voronoi_diagram.VoronoiDiagram method) basis() (sage.geometry.linear_expression.LinearExpressionModule method) (sage.geometry.point_collection.PointCollection method) bigraphical() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) bipartite_ribbon_graph() (in module sage.geometry.ribbon_graph) bipyramid() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) Birkhoff_polytope() (sage.geometry.polyhedron.library.Polytopes method) bistellar_flips() (sage.geometry.triangulation.point_configuration.PointConfiguration method) bitruncated_six_hundred_cell() (sage.geometry.polyhedron.library.Polytopes method) boundary() (sage.geometry.ribbon_graph.RibbonGraph method) (sage.geometry.triangulation.element.Triangulation method) boundary_complex() (sage.geometry.polyhedron.base.Polyhedron_base method) boundary_point_indices() (sage.geometry.lattice_polytope.LatticePolytopeClass method) boundary_points() (sage.geometry.lattice_polytope.LatticePolytopeClass method) boundary_polyhedral_complex() (sage.geometry.triangulation.element.Triangulation method) boundary_simplicial_complex() (sage.geometry.triangulation.element.Triangulation method) boundary_subcomplex() (sage.geometry.polyhedral_complex.PolyhedralComplex method) bounded_edges() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) bounded_regions() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) bounding_box() (sage.geometry.polyhedron.base.Polyhedron_base method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) braid() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) buchberger() (sage.rings.polynomial.groebner_fan.GroebnerFan method) buckyball() (sage.geometry.polyhedron.library.Polytopes method) C cantellated_one_hundred_twenty_cell() (sage.geometry.polyhedron.library.Polytopes method) cantellated_six_hundred_cell() (sage.geometry.polyhedron.library.Polytopes method) cantitruncated_one_hundred_twenty_cell() (sage.geometry.polyhedron.library.Polytopes method) cantitruncated_six_hundred_cell() (sage.geometry.polyhedron.library.Polytopes method) cardinality() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.point_collection.PointCollection method) cartesian_product() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.fan.RationalPolyhedralFan method) (sage.geometry.point_collection.PointCollection method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) Catalan() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) cdd_Hrepresentation() (in module sage.geometry.polyhedron.cdd_file_format) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) cdd_Vrepresentation() (in module sage.geometry.polyhedron.cdd_file_format) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) cell_iterator() (sage.geometry.polyhedral_complex.PolyhedralComplex method) cells() (sage.geometry.polyhedral_complex.PolyhedralComplex method) cells_list_to_cells_dict() (in module sage.geometry.polyhedral_complex) cells_sorted() (sage.geometry.polyhedral_complex.PolyhedralComplex method) center() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.polyhedron.base.Polyhedron_base method) centroid() (sage.geometry.polyhedron.base7.Polyhedron_base7 method) chain_complex() (sage.geometry.polyhedral_complex.PolyhedralComplex method) change_ring() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangements method) (sage.geometry.hyperplane_arrangement.hyperplane.AmbientVectorSpace method) (sage.geometry.linear_expression.LinearExpression method) (sage.geometry.linear_expression.LinearExpressionModule method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.parent.Polyhedra_base method) characteristic() (sage.rings.polynomial.groebner_fan.GroebnerFan method) characteristic_polynomial() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) choose_algorithm_to_compute_edges_or_ridges() (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) circuits() (sage.geometry.triangulation.point_configuration.PointConfiguration method) circuits_support() (sage.geometry.triangulation.point_configuration.PointConfiguration method) classify_cone_2d() (in module sage.geometry.cone) closed_faces() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) closure() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.relative_interior.RelativeInterior method) cocharacteristic_polynomial() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) codim() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.convex_set.ConvexSet_base method) codimension() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.convex_set.ConvexSet_base method) codomain_dim() (sage.geometry.polyhedron.lattice_euclidean_group_element.LatticeEuclideanGroupElement method) codomain_fan() (sage.geometry.fan_morphism.FanMorphism method) coefficients() (sage.geometry.linear_expression.LinearExpression method) color_list() (in module sage.geometry.toric_plotter) column_matrix() (sage.geometry.point_collection.PointCollection method) combinatorial_automorphism_group() (sage.geometry.polyhedron.base4.Polyhedron_base4 method) combinatorial_face_to_polyhedral_face() (in module sage.geometry.polyhedron.face) combinatorial_polyhedron() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) CombinatorialFace (class in sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face) CombinatorialPolyhedron (class in sage.geometry.polyhedron.combinatorial_polyhedron.base) common_refinement() (sage.geometry.fan.RationalPolyhedralFan method) complex() (sage.geometry.fan.RationalPolyhedralFan method) compute_dimension() (sage.geometry.polyhedron.combinatorial_polyhedron.list_of_faces.ListOfFaces method) Cone() (in module sage.geometry.cone) cone() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) (sage.rings.polynomial.groebner_fan.InitialForm method) cone_containing() (sage.geometry.fan.RationalPolyhedralFan method) cone_lattice() (sage.geometry.fan.RationalPolyhedralFan method) Cone_of_fan (class in sage.geometry.fan) cones() (sage.geometry.fan.RationalPolyhedralFan method) (sage.rings.polynomial.groebner_fan.PolyhedralFan method) connected_component() (sage.geometry.polyhedral_complex.PolyhedralComplex method) connected_components() (sage.geometry.polyhedral_complex.PolyhedralComplex method) ConnectedTriangulationsIterator (class in sage.geometry.triangulation.base) constant_term() (sage.geometry.linear_expression.LinearExpression method) construct_free_chain() (in module sage.geometry.hyperplane_arrangement.check_freeness) construction() (sage.geometry.toric_lattice.ToricLattice_generic method) contained_simplex() (sage.geometry.triangulation.point_configuration.PointConfiguration method) contains() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.fan.RationalPolyhedralFan method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) (sage.geometry.polyhedron.representation.Equation method) (sage.geometry.polyhedron.representation.Inequality method) contains_origin() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) contract_edge() (sage.geometry.ribbon_graph.RibbonGraph method) convex_hull() (in module sage.geometry.lattice_polytope) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) (sage.geometry.triangulation.point_configuration.PointConfiguration method) ConvexRationalPolyhedralCone (class in sage.geometry.abc) (class in sage.geometry.cone) ConvexSet_base (class in sage.geometry.convex_set) ConvexSet_closed (class in sage.geometry.convex_set) ConvexSet_compact (class in sage.geometry.convex_set) ConvexSet_open (class in sage.geometry.convex_set) ConvexSet_relatively_open (class in sage.geometry.convex_set) coord_index_of() (sage.geometry.polyhedron.plot.Projection method) coord_indices_of() (sage.geometry.polyhedron.plot.Projection method) coordinate() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) coordinate_vector() (sage.geometry.toric_lattice.ToricLattice_quotient method) coordinates_of() (sage.geometry.polyhedron.plot.Projection method) count() (sage.geometry.polyhedron.representation.PolyhedronRepresentation method) Coxeter() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) create_key() (sage.geometry.toric_lattice.ToricLatticeFactory method) create_object() (sage.geometry.toric_lattice.ToricLatticeFactory method) cross_polytope() (in module sage.geometry.lattice_polytope) (sage.geometry.polyhedron.library.Polytopes method) cross_positive_operators_gens() (sage.geometry.cone.ConvexRationalPolyhedralCone method) cube() (sage.geometry.polyhedron.library.Polytopes method) cuboctahedron() (sage.geometry.polyhedron.library.Polytopes method) current() (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_geom method) cyclic_polytope() (sage.geometry.polyhedron.library.Polytopes method) cyclic_sort_vertices_2d() (in module sage.geometry.polyhedron.plot) D defining_polynomial() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) degree_on_basis() (sage.geometry.polyhedron.modules.formal_polyhedra_module.FormalPolyhedraModule method) deletion() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) Delta() (sage.geometry.lattice_polytope.NefPartition method) Delta_polar() (sage.geometry.lattice_polytope.NefPartition method) Deltas() (sage.geometry.lattice_polytope.NefPartition method) dense_coefficient_list() (sage.geometry.linear_expression.LinearExpression method) derivation_module_basis() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) derivation_module_free_chain() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) dilation() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) (sage.geometry.relative_interior.RelativeInterior method) dim() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.point_collection.PointCollection method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) (sage.geometry.polyhedron.double_description.Problem method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.relative_interior.RelativeInterior method) (sage.geometry.triangulation.base.PointConfiguration_base method) (sage.rings.polynomial.groebner_fan.PolyhedralCone method) (sage.rings.polynomial.groebner_fan.PolyhedralFan method) dimension() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.hyperplane_arrangement.affine_subspace.AffineSubspace method) (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.hyperplane_arrangement.hyperplane.AmbientVectorSpace method) (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) (sage.geometry.point_collection.PointCollection method) (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) (sage.geometry.toric_lattice.ToricLattice_quotient method) dimension_of_homogeneity_space() (sage.rings.polynomial.groebner_fan.GroebnerFan method) direct_sum() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) (sage.geometry.toric_lattice.ToricLattice_generic method) discard_faces() (in module sage.geometry.fan) discrete_complementarity_set() (sage.geometry.cone.ConvexRationalPolyhedralCone method) disjoint_union() (sage.geometry.polyhedral_complex.PolyhedralComplex method) distance() (sage.geometry.triangulation.point_configuration.PointConfiguration method) distance_affine() (sage.geometry.triangulation.point_configuration.PointConfiguration method) distance_between_regions() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) distance_enumerator() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) distance_FS() (sage.geometry.triangulation.point_configuration.PointConfiguration method) distances() (sage.geometry.lattice_polytope.LatticePolytopeClass method) dodecahedron() (sage.geometry.polyhedron.library.Polytopes method) does_backend_handle_base_ring() (in module sage.geometry.polyhedron.parent) domain_dim() (sage.geometry.polyhedron.lattice_euclidean_group_element.LatticeEuclideanGroupElement method) domain_fan() (sage.geometry.fan_morphism.FanMorphism method) DoubleDescriptionPair (class in sage.geometry.polyhedron.double_description) doubly_indexed_whitney_number() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) dual (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base attribute) (sage.geometry.polyhedron.combinatorial_polyhedron.polyhedron_face_lattice.PolyhedronFaceLattice attribute) dual() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.lattice_polytope.NefPartition method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) (sage.geometry.toric_lattice.ToricLattice_ambient method) (sage.geometry.toric_lattice.ToricLattice_quotient method) (sage.geometry.toric_lattice.ToricLattice_sublattice_with_basis method) dual_lattice() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) dual_module() (sage.geometry.point_collection.PointCollection method) E edge_polytope() (sage.geometry.polyhedron.library.Polytopes static method) edges() (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) ehrhart_polynomial() (sage.geometry.polyhedron.base_QQ.Polyhedron_QQ method) (sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ method) ehrhart_quasipolynomial() (sage.geometry.polyhedron.base_QQ.Polyhedron_QQ method) ehrhart_series() (sage.geometry.polyhedron.backend_normaliz.Polyhedron_QQ_normaliz method) Element (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangements attribute) (sage.geometry.hyperplane_arrangement.hyperplane.AmbientVectorSpace attribute) (sage.geometry.linear_expression.LinearExpressionModule attribute) (sage.geometry.newton_polygon.ParentNewtonPolygon attribute) (sage.geometry.polyhedron.parent.Polyhedra_field attribute) (sage.geometry.polyhedron.parent.Polyhedra_normaliz attribute) (sage.geometry.polyhedron.parent.Polyhedra_number_field attribute) (sage.geometry.polyhedron.parent.Polyhedra_polymake attribute) (sage.geometry.polyhedron.parent.Polyhedra_QQ_cdd attribute) (sage.geometry.polyhedron.parent.Polyhedra_QQ_normaliz attribute) (sage.geometry.polyhedron.parent.Polyhedra_QQ_ppl attribute) (sage.geometry.polyhedron.parent.Polyhedra_RDF_cdd attribute) (sage.geometry.polyhedron.parent.Polyhedra_ZZ_normaliz attribute) (sage.geometry.polyhedron.parent.Polyhedra_ZZ_ppl attribute) (sage.geometry.toric_lattice.ToricLattice_ambient attribute) (sage.geometry.toric_lattice.ToricLattice_generic attribute) (sage.geometry.toric_lattice.ToricLattice_quotient attribute) (sage.geometry.triangulation.point_configuration.PointConfiguration attribute) embed() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.fan.RationalPolyhedralFan method) embed_in_reflexive_polytope() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) empty() (sage.geometry.polyhedron.parent.Polyhedra_base method) enumerate_simplices() (sage.geometry.triangulation.element.Triangulation method) Equation (class in sage.geometry.polyhedron.representation) EQUATION (sage.geometry.polyhedron.representation.PolyhedronRepresentation attribute) equation_generator() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) equations() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) equations_list() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) essentialization() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) eval() (sage.geometry.polyhedron.representation.Hrepresentation method) evaluate() (sage.geometry.linear_expression.LinearExpression method) evaluated_on() (sage.geometry.polyhedron.representation.Line method) (sage.geometry.polyhedron.representation.Ray method) (sage.geometry.polyhedron.representation.Vertex method) exclude_points() (sage.geometry.triangulation.point_configuration.PointConfiguration method) exploded_plot() (in module sage.geometry.polyhedral_complex) extrude_edge() (sage.geometry.ribbon_graph.RibbonGraph method) F f_vector() (sage.geometry.fan.RationalPolyhedralFan method) (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.rings.polynomial.groebner_fan.PolyhedralFan method) face_by_face_lattice_index() (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) face_codimension() (sage.geometry.triangulation.point_configuration.PointConfiguration method) face_fan() (sage.geometry.polyhedron.base.Polyhedron_base method) face_generator() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) face_interior() (sage.geometry.triangulation.point_configuration.PointConfiguration method) face_iter() (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) face_lattice() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base4.Polyhedron_base4 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) face_poset() (sage.geometry.polyhedral_complex.PolyhedralComplex method) face_product() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) face_semigroup_algebra() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) face_split() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) face_truncation() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) face_vector() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) FaceFan() (in module sage.geometry.fan) FaceIterator (class in sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator) FaceIterator_base (class in sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator) FaceIterator_geom (class in sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator) faces() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base3.Polyhedron_base3 method) facet_adjacency_matrix() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) facet_constant() (sage.geometry.lattice_polytope.LatticePolytopeClass method) facet_constants() (sage.geometry.lattice_polytope.LatticePolytopeClass method) facet_graph() (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) facet_normal() (sage.geometry.lattice_polytope.LatticePolytopeClass method) facet_normals() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) facet_of() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) facets() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.rings.polynomial.groebner_fan.PolyhedralCone method) facets_tuple_to_bit_rep_of_facets() (in module sage.geometry.polyhedron.combinatorial_polyhedron.conversions) facets_tuple_to_bit_rep_of_Vrep() (in module sage.geometry.polyhedron.combinatorial_polyhedron.conversions) factor() (sage.geometry.fan_morphism.FanMorphism method) Fan() (in module sage.geometry.fan) fan() (sage.geometry.triangulation.element.Triangulation method) Fan2d() (in module sage.geometry.fan) fan_2d_cyclically_ordered_rays() (in module sage.geometry.fan_isomorphism) fan_2d_echelon_form() (in module sage.geometry.fan_isomorphism) fan_2d_echelon_forms() (in module sage.geometry.fan_isomorphism) fan_isomorphic_necessary_conditions() (in module sage.geometry.fan_isomorphism) fan_isomorphism_generator() (in module sage.geometry.fan_isomorphism) FanMorphism (class in sage.geometry.fan_morphism) FanNotIsomorphicError farthest_point() (sage.geometry.triangulation.point_configuration.PointConfiguration method) felsner_matrix() (sage.geometry.pseudolines.PseudolineArrangement method) fibration_generator() (sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) find_isomorphism() (in module sage.geometry.fan_isomorphism) (sage.geometry.polyhedron.ppl_lattice_polygon.LatticePolygon_PPL_class method) find_translation() (sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ method) first_coordinate_plane() (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) fixed_subpolytope() (sage.geometry.polyhedron.base_QQ.Polyhedron_QQ method) fixed_subpolytopes() (sage.geometry.polyhedron.base_QQ.Polyhedron_QQ method) flag_f_vector() (sage.geometry.polyhedron.base4.Polyhedron_base4 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) flow_polytope() (sage.geometry.polyhedron.library.Polytopes static method) FormalPolyhedraModule (class in sage.geometry.polyhedron.modules.formal_polyhedra_module) G G_semiorder() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) G_Shi() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) Gale_transform() (sage.geometry.fan.RationalPolyhedralFan method) gale_transform() (sage.geometry.polyhedron.base6.Polyhedron_base6 method) Gale_transform() (sage.geometry.triangulation.point_configuration.PointConfiguration method) gale_transform_to_polytope() (in module sage.geometry.polyhedron.library) gale_transform_to_primal() (in module sage.geometry.polyhedron.library) gen() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangements method) (sage.geometry.linear_expression.LinearExpressionModule method) generalized_permutahedron() (sage.geometry.polyhedron.library.Polytopes method) generating_cone() (sage.geometry.fan.RationalPolyhedralFan method) generating_cones() (sage.geometry.fan.RationalPolyhedralFan method) generating_function_of_integral_points() (in module sage.geometry.polyhedron.generating_function) (sage.geometry.polyhedron.base2.Polyhedron_base2 method) gens() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangements method) (sage.geometry.linear_expression.LinearExpressionModule method) (sage.geometry.toric_lattice.ToricLattice_quotient method) genus() (sage.geometry.ribbon_graph.RibbonGraph method) get_face() (sage.geometry.polyhedron.combinatorial_polyhedron.polyhedron_face_lattice.PolyhedronFaceLattice method) get_integral_point() (sage.geometry.polyhedron.base2.Polyhedron_base2 method) gfan() (sage.rings.polynomial.groebner_fan.GroebnerFan method) gkz_phi() (sage.geometry.triangulation.element.Triangulation method) Gosset_3_21() (sage.geometry.polyhedron.library.Polytopes method) grand_antiprism() (sage.geometry.polyhedron.library.Polytopes method) graph() (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base4.Polyhedron_base4 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) graphical() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) great_rhombicuboctahedron() (sage.geometry.polyhedron.library.Polytopes method) greatest_common_subface_of_Hrep() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) groebner_cone() (sage.rings.polynomial.groebner_fan.ReducedGroebnerBasis method) GroebnerFan (class in sage.rings.polynomial.groebner_fan) H h_star_vector() (sage.geometry.polyhedron.base2.Polyhedron_base2 method) has_good_reduction() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) has_IP_property() (sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) hasse_diagram() (sage.geometry.polyhedron.base4.Polyhedron_base4 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) Hilbert_basis() (sage.geometry.cone.ConvexRationalPolyhedralCone method) Hilbert_coefficients() (sage.geometry.cone.ConvexRationalPolyhedralCone method) hilbert_series() (sage.geometry.polyhedron.backend_normaliz.Polyhedron_QQ_normaliz method) hodge_numbers() (sage.geometry.lattice_polytope.NefPartition method) homogeneity_space() (sage.rings.polynomial.groebner_fan.GroebnerFan method) homogeneous_vector() (sage.geometry.polyhedron.representation.Line method) (sage.geometry.polyhedron.representation.Ray method) (sage.geometry.polyhedron.representation.Vertex method) homology_basis() (sage.geometry.ribbon_graph.RibbonGraph method) Hrep2Vrep (class in sage.geometry.polyhedron.double_description_inhomogeneous) Hrep_generator() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) Hrepresentation (class in sage.geometry.polyhedron.representation) Hrepresentation() (sage.geometry.polyhedron.backend_ppl.Polyhedron_ppl method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) Hrepresentation_space() (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.parent.Polyhedra_base method) Hrepresentation_str() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) Hstar_function() (sage.geometry.polyhedron.base_QQ.Polyhedron_QQ method) hypercube() (sage.geometry.polyhedron.library.Polytopes method) Hyperplane (class in sage.geometry.hyperplane_arrangement.hyperplane) hyperplane_arrangement() (sage.geometry.polyhedron.base.Polyhedron_base method) HyperplaneArrangementElement (class in sage.geometry.hyperplane_arrangement.arrangement) HyperplaneArrangementLibrary (class in sage.geometry.hyperplane_arrangement.library) HyperplaneArrangements (class in sage.geometry.hyperplane_arrangement.arrangement) hyperplanes() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) hypersimplex() (sage.geometry.polyhedron.library.Polytopes method) I icosahedron() (sage.geometry.polyhedron.library.Polytopes method) icosidodecahedron() (sage.geometry.polyhedron.library.Polytopes method) icosidodecahedron_V2() (sage.geometry.polyhedron.library.Polytopes method) ideal() (sage.rings.polynomial.groebner_fan.GroebnerFan method) (sage.rings.polynomial.groebner_fan.ReducedGroebnerBasis method) ideal_to_gfan_format() (in module sage.rings.polynomial.groebner_fan) identity() (sage.geometry.polyhedron.plot.Projection method) ignore_subfaces() (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) ignore_supfaces() (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) image (sage.geometry.convex_set.AffineHullProjectionData attribute) image_cone() (sage.geometry.fan_morphism.FanMorphism method) incidence_matrix() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) incidence_matrix_to_bit_rep_of_facets() (in module sage.geometry.polyhedron.combinatorial_polyhedron.conversions) incidence_matrix_to_bit_rep_of_Vrep() (in module sage.geometry.polyhedron.combinatorial_polyhedron.conversions) incident() (sage.geometry.polyhedron.representation.Hrepresentation method) (sage.geometry.polyhedron.representation.Vrepresentation method) include_points() (sage.geometry.toric_plotter.ToricPlotter method) index() (sage.geometry.fan_morphism.FanMorphism method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.point_collection.PointCollection method) (sage.geometry.polyhedron.representation.PolyhedronRepresentation method) (sage.geometry.triangulation.base.Point method) inequalities() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) inequalities_list() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) Inequality (class in sage.geometry.polyhedron.representation) INEQUALITY (sage.geometry.polyhedron.representation.PolyhedronRepresentation attribute) inequality_generator() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) initial_form_systems() (sage.rings.polynomial.groebner_fan.TropicalPrevariety method) initial_forms() (sage.rings.polynomial.groebner_fan.InitialForm method) initial_pair() (sage.geometry.polyhedron.double_description.Problem method) InitialForm (class in sage.rings.polynomial.groebner_fan) inner_product_matrix() (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) int_to_simplex() (sage.geometry.triangulation.base.PointConfiguration_base method) integral_hull() (sage.geometry.polyhedron.backend_normaliz.Polyhedron_normaliz method) integral_length() (in module sage.geometry.cone) integral_points() (sage.geometry.polyhedron.backend_normaliz.Polyhedron_QQ_normaliz method) (sage.geometry.polyhedron.base2.Polyhedron_base2 method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) integral_points_count() (sage.geometry.polyhedron.base2.Polyhedron_base2 method) (sage.geometry.polyhedron.base_QQ.Polyhedron_QQ method) integral_points_generators() (sage.geometry.polyhedron.backend_normaliz.Polyhedron_QQ_normaliz method) integral_points_not_interior_to_facets() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) IntegralRayCollection (class in sage.geometry.cone) integrate() (sage.geometry.polyhedron.base7.Polyhedron_base7 method) interactive() (sage.rings.polynomial.groebner_fan.GroebnerFan method) (sage.rings.polynomial.groebner_fan.ReducedGroebnerBasis method) interior() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.relative_interior.RelativeInterior method) interior_contains() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.representation.Equation method) (sage.geometry.polyhedron.representation.Inequality method) interior_facets() (sage.geometry.triangulation.element.Triangulation method) interior_point_indices() (sage.geometry.lattice_polytope.LatticePolytopeClass method) interior_points() (sage.geometry.lattice_polytope.LatticePolytopeClass method) internal_ray() (sage.rings.polynomial.groebner_fan.InitialForm method) intersection() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.hyperplane_arrangement.affine_subspace.AffineSubspace method) (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) (sage.geometry.toric_lattice.ToricLattice_generic method) intersection_poset() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) is_affine() (sage.geometry.triangulation.base.PointConfiguration_base method) is_bipyramid() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) is_birational() (sage.geometry.fan_morphism.FanMorphism method) is_bounded() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) is_bundle() (sage.geometry.fan_morphism.FanMorphism method) is_cell() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_central() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) is_closed() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.convex_set.ConvexSet_closed method) (sage.geometry.convex_set.ConvexSet_open method) (sage.geometry.relative_interior.RelativeInterior method) is_combinatorially_isomorphic() (sage.geometry.polyhedron.base4.Polyhedron_base4 method) is_compact() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.convex_set.ConvexSet_compact method) (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.face.PolyhedronFace method) is_complete() (sage.geometry.fan.RationalPolyhedralFan method) is_Cone() (in module sage.geometry.cone) is_connected() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_convex() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_dominant() (sage.geometry.fan_morphism.FanMorphism method) is_effective() (sage.geometry.polyhedron.base_QQ.Polyhedron_QQ method) is_empty() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) is_equation() (sage.geometry.polyhedron.representation.Equation method) (sage.geometry.polyhedron.representation.Hrepresentation method) is_equivalent() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.fan.RationalPolyhedralFan method) is_essential() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) is_extremal() (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) is_face_of() (sage.geometry.cone.ConvexRationalPolyhedralCone method) is_facet_defining_inequality() (sage.geometry.polyhedron.representation.Inequality method) is_Fan() (in module sage.geometry.fan) is_fibration() (sage.geometry.fan_morphism.FanMorphism method) is_finite() (sage.geometry.convex_set.ConvexSet_base method) is_formal() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) is_free() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) is_full_dimensional() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) is_full_space() (sage.geometry.cone.ConvexRationalPolyhedralCone method) is_H() (sage.geometry.polyhedron.representation.Hrepresentation method) is_immutable() (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) is_incident() (sage.geometry.polyhedron.representation.Hrepresentation method) (sage.geometry.polyhedron.representation.Vrepresentation method) is_inequality() (sage.geometry.polyhedron.representation.Hrepresentation method) (sage.geometry.polyhedron.representation.Inequality method) is_injective() (sage.geometry.fan_morphism.FanMorphism method) is_inscribed() (sage.geometry.polyhedron.base.Polyhedron_base method) is_integral() (sage.geometry.polyhedron.representation.Vertex method) is_isomorphic() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.fan.RationalPolyhedralFan method) (sage.geometry.polyhedron.ppl_lattice_polygon.LatticePolygon_PPL_class method) is_lattice_polytope() (sage.geometry.polyhedron.base2.Polyhedron_base2 method) (sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ method) is_LatticePolytope() (in module sage.geometry.lattice_polytope) is_lawrence_polytope() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) is_line() (sage.geometry.polyhedron.representation.Line method) (sage.geometry.polyhedron.representation.Vrepresentation method) is_linear() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) is_maximal_cell() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_minkowski_summand() (sage.geometry.polyhedron.base.Polyhedron_base method) is_mutable() (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) is_NefPartition() (in module sage.geometry.lattice_polytope) is_neighborly() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) is_open() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.convex_set.ConvexSet_closed method) (sage.geometry.convex_set.ConvexSet_open method) (sage.geometry.convex_set.ConvexSet_relatively_open method) is_PointCollection() (in module sage.geometry.point_collection) is_polyhedral_fan() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_Polyhedron() (in module sage.geometry.polyhedron.base) is_prism() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) is_proper() (sage.geometry.cone.ConvexRationalPolyhedralCone method) is_pure() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_pyramid() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) is_ray() (sage.geometry.polyhedron.representation.Ray method) (sage.geometry.polyhedron.representation.Vrepresentation method) is_reflexive() (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ method) is_relatively_open() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.convex_set.ConvexSet_compact method) (sage.geometry.convex_set.ConvexSet_relatively_open method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.face.PolyhedronFace method) is_self_dual() (sage.geometry.polyhedron.base4.Polyhedron_base4 method) is_separating_hyperplane() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) is_simple() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) is_simplex() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) is_simplicial() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.fan.RationalPolyhedralFan method) (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.rings.polynomial.groebner_fan.PolyhedralFan method) is_simplicial_complex() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_simplicial_fan() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_smooth() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.fan.RationalPolyhedralFan method) is_solid() (sage.geometry.cone.ConvexRationalPolyhedralCone method) is_strictly_convex() (sage.geometry.cone.ConvexRationalPolyhedralCone method) is_subcomplex() (sage.geometry.polyhedral_complex.PolyhedralComplex method) is_subface() (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) is_surjective() (sage.geometry.fan_morphism.FanMorphism method) is_ToricLattice() (in module sage.geometry.toric_lattice) is_ToricLatticeQuotient() (in module sage.geometry.toric_lattice) is_torsion_free() (sage.geometry.toric_lattice.ToricLattice_quotient method) is_trivial() (sage.geometry.cone.ConvexRationalPolyhedralCone method) is_universe() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.convex_set.ConvexSet_compact method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.relative_interior.RelativeInterior method) is_V() (sage.geometry.polyhedron.representation.Vrepresentation method) is_vertex() (sage.geometry.polyhedron.representation.Vertex method) (sage.geometry.polyhedron.representation.Vrepresentation method) Ish() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) IshB() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) isomorphism() (sage.geometry.fan.RationalPolyhedralFan method) J join() (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) join_of_Vrep() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) K kernel_fan() (sage.geometry.fan_morphism.FanMorphism method) Kirkman_icosahedron() (sage.geometry.polyhedron.library.Polytopes method) L label_list() (in module sage.geometry.toric_plotter) last_slope() (sage.geometry.newton_polygon.NewtonPolygon_element method) lattice() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) lattice_automorphism_group() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) lattice_dim() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) lattice_from_incidences() (in module sage.geometry.hasse_diagram) lattice_polytope() (sage.geometry.polyhedron.base2.Polyhedron_base2 method) LatticeEuclideanGroupElement (class in sage.geometry.polyhedron.lattice_euclidean_group_element) LatticePolygon_PPL_class (class in sage.geometry.polyhedron.ppl_lattice_polygon) LatticePolytope (class in sage.geometry.abc) LatticePolytope() (in module sage.geometry.lattice_polytope) LatticePolytope_PPL() (in module sage.geometry.polyhedron.ppl_lattice_polytope) LatticePolytope_PPL_class (class in sage.geometry.polyhedron.ppl_lattice_polytope) LatticePolytopeClass (class in sage.geometry.lattice_polytope) LatticePolytopeError LatticePolytopeNoEmbeddingError LatticePolytopesNotIsomorphicError lawrence_extension() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) lawrence_polytope() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) least_common_superface_of_Vrep() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) legend_3d() (in module sage.geometry.hyperplane_arrangement.plot) less_generators() (in module sage.geometry.hyperplane_arrangement.check_freeness) lexicographic_triangulation() (sage.geometry.triangulation.point_configuration.PointConfiguration method) Line (class in sage.geometry.polyhedron.representation) LINE (sage.geometry.polyhedron.representation.PolyhedronRepresentation attribute) line_generator() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.face.PolyhedronFace method) lineality() (sage.geometry.cone.ConvexRationalPolyhedralCone method) lineality_dim() (sage.rings.polynomial.groebner_fan.PolyhedralCone method) (sage.rings.polynomial.groebner_fan.PolyhedralFan method) linear_equivalence_ideal() (sage.geometry.fan.RationalPolyhedralFan method) linear_part() (sage.geometry.hyperplane_arrangement.affine_subspace.AffineSubspace method) (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) linear_part_projection() (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) linear_subspace() (sage.geometry.cone.ConvexRationalPolyhedralCone method) linear_transformation() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) (sage.geometry.relative_interior.RelativeInterior method) LinearExpression (class in sage.geometry.linear_expression) LinearExpressionModule (class in sage.geometry.linear_expression) linearly_independent_vertices() (sage.geometry.lattice_polytope.LatticePolytopeClass method) lines() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.face.PolyhedronFace method) lines_list() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) linial() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) list() (sage.geometry.polyhedron.parent.Polyhedra_base method) ListOfFaces (class in sage.geometry.polyhedron.combinatorial_polyhedron.list_of_faces) lyapunov_like_basis() (sage.geometry.cone.ConvexRationalPolyhedralCone method) lyapunov_rank() (sage.geometry.cone.ConvexRationalPolyhedralCone method) M make_generic() (sage.geometry.ribbon_graph.RibbonGraph method) make_parent() (in module sage.geometry.hyperplane_arrangement.library) make_ribbon() (in module sage.geometry.ribbon_graph) make_simplicial() (sage.geometry.fan.RationalPolyhedralFan method) matrix() (sage.geometry.point_collection.PointCollection method) (sage.geometry.polyhedron.combinatorial_polyhedron.list_of_faces.ListOfFaces method) matrix_space() (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) matroid() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) max_degree() (in module sage.rings.polynomial.groebner_fan) maximal_cell_iterator() (sage.geometry.polyhedral_complex.PolyhedralComplex method) maximal_cells() (sage.geometry.polyhedral_complex.PolyhedralComplex method) maximal_cells_sorted() (sage.geometry.polyhedral_complex.PolyhedralComplex method) maximal_cones() (sage.rings.polynomial.groebner_fan.PolyhedralFan method) maximal_total_degree_of_a_groebner_basis() (sage.rings.polynomial.groebner_fan.GroebnerFan method) meet_of_Hrep() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) minimal_generated_number() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) minimal_total_degree_of_a_groebner_basis() (sage.rings.polynomial.groebner_fan.GroebnerFan method) minkowski_decompositions() (sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ method) minkowski_difference() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) minkowski_sum() (in module sage.geometry.lattice_polytope) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) mixed_volume() (sage.rings.polynomial.groebner_fan.GroebnerFan method) module sage.geometry.abc sage.geometry.cone sage.geometry.cone_catalog sage.geometry.convex_set sage.geometry.fan sage.geometry.fan_isomorphism sage.geometry.fan_morphism sage.geometry.hasse_diagram sage.geometry.hyperplane_arrangement.affine_subspace sage.geometry.hyperplane_arrangement.arrangement sage.geometry.hyperplane_arrangement.check_freeness sage.geometry.hyperplane_arrangement.hyperplane sage.geometry.hyperplane_arrangement.library sage.geometry.hyperplane_arrangement.plot sage.geometry.integral_points sage.geometry.lattice_polytope sage.geometry.linear_expression sage.geometry.newton_polygon sage.geometry.point_collection sage.geometry.polyhedral_complex sage.geometry.polyhedron.backend_cdd sage.geometry.polyhedron.backend_cdd_rdf sage.geometry.polyhedron.backend_field sage.geometry.polyhedron.backend_normaliz sage.geometry.polyhedron.backend_number_field sage.geometry.polyhedron.backend_polymake sage.geometry.polyhedron.backend_ppl sage.geometry.polyhedron.base sage.geometry.polyhedron.base0 sage.geometry.polyhedron.base1 sage.geometry.polyhedron.base2 sage.geometry.polyhedron.base3 sage.geometry.polyhedron.base4 sage.geometry.polyhedron.base5 sage.geometry.polyhedron.base6 sage.geometry.polyhedron.base7 sage.geometry.polyhedron.base_QQ sage.geometry.polyhedron.base_RDF sage.geometry.polyhedron.base_ZZ sage.geometry.polyhedron.cdd_file_format sage.geometry.polyhedron.combinatorial_polyhedron.base sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face sage.geometry.polyhedron.combinatorial_polyhedron.conversions sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator sage.geometry.polyhedron.combinatorial_polyhedron.list_of_faces sage.geometry.polyhedron.combinatorial_polyhedron.polyhedron_face_lattice sage.geometry.polyhedron.constructor sage.geometry.polyhedron.double_description sage.geometry.polyhedron.double_description_inhomogeneous sage.geometry.polyhedron.face sage.geometry.polyhedron.generating_function sage.geometry.polyhedron.lattice_euclidean_group_element sage.geometry.polyhedron.library sage.geometry.polyhedron.modules.formal_polyhedra_module sage.geometry.polyhedron.palp_database sage.geometry.polyhedron.parent sage.geometry.polyhedron.plot sage.geometry.polyhedron.ppl_lattice_polygon sage.geometry.polyhedron.ppl_lattice_polytope sage.geometry.polyhedron.representation sage.geometry.pseudolines sage.geometry.relative_interior sage.geometry.ribbon_graph sage.geometry.toric_lattice sage.geometry.toric_plotter sage.geometry.triangulation.base sage.geometry.triangulation.element sage.geometry.triangulation.point_configuration sage.geometry.voronoi_diagram sage.rings.polynomial.groebner_fan module() (sage.geometry.point_collection.PointCollection method) monomial_coefficients() (sage.geometry.linear_expression.LinearExpression method) mu() (sage.geometry.ribbon_graph.RibbonGraph method) N n_ambient_Hrepresentation() (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) (sage.geometry.polyhedron.face.PolyhedronFace method) n_ambient_Vrepresentation() (sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face.CombinatorialFace method) (sage.geometry.polyhedron.face.PolyhedronFace method) n_bounded_regions() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) n_equations() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) n_facets() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) n_Hrepresentation() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) n_hyperplanes() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) n_inequalities() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) n_integral_points() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) n_lines() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.face.PolyhedronFace method) n_maximal_cells() (sage.geometry.polyhedral_complex.PolyhedralComplex method) n_points() (sage.geometry.triangulation.base.PointConfiguration_base method) n_rays() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.face.PolyhedronFace method) n_regions() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) n_skeleton() (sage.geometry.polyhedral_complex.PolyhedralComplex method) n_vertices() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) n_Vrepresentation() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) nabla() (sage.geometry.lattice_polytope.NefPartition method) nabla_polar() (sage.geometry.lattice_polytope.NefPartition method) nablas() (sage.geometry.lattice_polytope.NefPartition method) nef_partitions() (sage.geometry.lattice_polytope.LatticePolytopeClass method) nef_x() (sage.geometry.lattice_polytope.LatticePolytopeClass method) NefPartition (class in sage.geometry.lattice_polytope) neighborliness() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) neighbors() (sage.geometry.polyhedron.representation.Hrepresentation method) (sage.geometry.polyhedron.representation.Vrepresentation method) NewtonPolygon_element (class in sage.geometry.newton_polygon) next() (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) nfacets() (sage.geometry.lattice_polytope.LatticePolytopeClass method) ngenerating_cones() (sage.geometry.fan.RationalPolyhedralFan method) ngens() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangements method) (sage.geometry.linear_expression.LinearExpressionModule method) nonnegative_orthant() (in module sage.geometry.cone_catalog) normal() (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) normal_cone() (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.triangulation.element.Triangulation method) normal_fan() (sage.geometry.polyhedron.base.Polyhedron_base method) normal_form() (sage.geometry.lattice_polytope.LatticePolytopeClass method) NormalFan() (in module sage.geometry.fan) normalize() (sage.geometry.ribbon_graph.RibbonGraph method) normalize_rays() (in module sage.geometry.cone) nparts() (sage.geometry.lattice_polytope.NefPartition method) npoints() (sage.geometry.lattice_polytope.LatticePolytopeClass method) nrays() (sage.geometry.cone.IntegralRayCollection method) number_boundaries() (sage.geometry.ribbon_graph.RibbonGraph method) number_of_reduced_groebner_bases() (sage.rings.polynomial.groebner_fan.GroebnerFan method) number_of_variables() (sage.rings.polynomial.groebner_fan.GroebnerFan method) nvertices() (sage.geometry.lattice_polytope.LatticePolytopeClass method) O octahedron() (sage.geometry.polyhedron.library.Polytopes method) omnitruncated_one_hundred_twenty_cell() (sage.geometry.polyhedron.library.Polytopes method) omnitruncated_six_hundred_cell() (sage.geometry.polyhedron.library.Polytopes method) one_hundred_twenty_cell() (sage.geometry.polyhedron.library.Polytopes method) one_point_suspension() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) only_subfaces() (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) only_supfaces() (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) options() (in module sage.geometry.toric_plotter) ordered_vertices() (sage.geometry.polyhedron.ppl_lattice_polygon.LatticePolygon_PPL_class method) oriented_boundary() (sage.geometry.fan.RationalPolyhedralFan method) origin() (sage.geometry.lattice_polytope.LatticePolytopeClass method) orlik_solomon_algebra() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) orlik_terao_algebra() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) orthogonal_projection() (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) orthogonal_sublattice() (sage.geometry.cone.ConvexRationalPolyhedralCone method) outer_normal() (sage.geometry.polyhedron.representation.Inequality method) output_format() (sage.geometry.point_collection.PointCollection static method) P P (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_geom attribute) pair_class (sage.geometry.polyhedron.double_description.Problem attribute) (sage.geometry.polyhedron.double_description.StandardAlgorithm attribute) PALPreader (class in sage.geometry.polyhedron.palp_database) parallelotope() (sage.geometry.polyhedron.library.Polytopes method) parent() (sage.geometry.lattice_polytope.LatticePolytopeClass method) ParentNewtonPolygon (class in sage.geometry.newton_polygon) part() (sage.geometry.lattice_polytope.NefPartition method) part_of() (sage.geometry.lattice_polytope.NefPartition method) part_of_point() (sage.geometry.lattice_polytope.NefPartition method) parts() (sage.geometry.lattice_polytope.NefPartition method) pentakis_dodecahedron() (sage.geometry.polyhedron.library.Polytopes method) permutahedron() (sage.geometry.polyhedron.library.Polytopes method) permutations() (sage.geometry.pseudolines.PseudolineArrangement method) permutations_to_matrices() (sage.geometry.polyhedron.base.Polyhedron_base method) PivotedInequalities (class in sage.geometry.polyhedron.double_description_inhomogeneous) placing_triangulation() (sage.geometry.triangulation.point_configuration.PointConfiguration method) plot() (in module sage.geometry.hyperplane_arrangement.plot) (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.fan.RationalPolyhedralFan method) (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) (sage.geometry.newton_polygon.NewtonPolygon_element method) (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base6.Polyhedron_base6 method) (sage.geometry.polyhedron.ppl_lattice_polygon.LatticePolygon_PPL_class method) (sage.geometry.toric_lattice.ToricLattice_ambient method) (sage.geometry.toric_lattice.ToricLattice_sublattice_with_basis method) (sage.geometry.triangulation.element.Triangulation method) (sage.geometry.triangulation.point_configuration.PointConfiguration method) (sage.geometry.voronoi_diagram.VoronoiDiagram method) plot3d() (sage.geometry.lattice_polytope.LatticePolytopeClass method) plot_generators() (sage.geometry.toric_plotter.ToricPlotter method) plot_hyperplane() (in module sage.geometry.hyperplane_arrangement.plot) plot_labels() (sage.geometry.toric_plotter.ToricPlotter method) plot_lattice() (sage.geometry.toric_plotter.ToricPlotter method) plot_points() (sage.geometry.toric_plotter.ToricPlotter method) plot_ray_labels() (sage.geometry.toric_plotter.ToricPlotter method) plot_rays() (sage.geometry.toric_plotter.ToricPlotter method) plot_walls() (sage.geometry.toric_plotter.ToricPlotter method) poincare_polynomial() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) Point (class in sage.geometry.triangulation.base) point() (sage.geometry.hyperplane_arrangement.affine_subspace.AffineSubspace method) (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.triangulation.base.PointConfiguration_base method) point_configuration() (sage.geometry.triangulation.base.Point method) (sage.geometry.triangulation.element.Triangulation method) PointCollection (class in sage.geometry.point_collection) PointConfiguration (class in sage.geometry.triangulation.point_configuration) PointConfiguration_base (class in sage.geometry.triangulation.base) points() (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.triangulation.base.PointConfiguration_base method) (sage.geometry.voronoi_diagram.VoronoiDiagram method) pointsets_mod_automorphism() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) polar() (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) (sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) polar_P1xP1_polytope() (in module sage.geometry.polyhedron.ppl_lattice_polygon) polar_P2_112_polytope() (in module sage.geometry.polyhedron.ppl_lattice_polygon) polar_P2_polytope() (in module sage.geometry.polyhedron.ppl_lattice_polygon) poly_x() (sage.geometry.lattice_polytope.LatticePolytopeClass method) Polyhedra() (in module sage.geometry.polyhedron.parent) Polyhedra_base (class in sage.geometry.polyhedron.parent) Polyhedra_field (class in sage.geometry.polyhedron.parent) Polyhedra_normaliz (class in sage.geometry.polyhedron.parent) Polyhedra_number_field (class in sage.geometry.polyhedron.parent) Polyhedra_polymake (class in sage.geometry.polyhedron.parent) Polyhedra_QQ_cdd (class in sage.geometry.polyhedron.parent) Polyhedra_QQ_normaliz (class in sage.geometry.polyhedron.parent) Polyhedra_QQ_ppl (class in sage.geometry.polyhedron.parent) Polyhedra_RDF_cdd (class in sage.geometry.polyhedron.parent) Polyhedra_ZZ_normaliz (class in sage.geometry.polyhedron.parent) Polyhedra_ZZ_ppl (class in sage.geometry.polyhedron.parent) polyhedral_complex() (sage.geometry.triangulation.element.Triangulation method) PolyhedralComplex (class in sage.geometry.polyhedral_complex) PolyhedralCone (class in sage.rings.polynomial.groebner_fan) PolyhedralFan (class in sage.rings.polynomial.groebner_fan) polyhedralfan() (sage.rings.polynomial.groebner_fan.GroebnerFan method) Polyhedron (class in sage.geometry.abc) Polyhedron() (in module sage.geometry.polyhedron.constructor) polyhedron() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.polyhedron.representation.PolyhedronRepresentation method) Polyhedron_base (class in sage.geometry.polyhedron.base) Polyhedron_base0 (class in sage.geometry.polyhedron.base0) Polyhedron_base1 (class in sage.geometry.polyhedron.base1) Polyhedron_base2 (class in sage.geometry.polyhedron.base2) Polyhedron_base3 (class in sage.geometry.polyhedron.base3) Polyhedron_base4 (class in sage.geometry.polyhedron.base4) Polyhedron_base5 (class in sage.geometry.polyhedron.base5) Polyhedron_base6 (class in sage.geometry.polyhedron.base6) Polyhedron_base7 (class in sage.geometry.polyhedron.base7) Polyhedron_cdd (class in sage.geometry.polyhedron.backend_cdd) Polyhedron_field (class in sage.geometry.polyhedron.backend_field) Polyhedron_normaliz (class in sage.geometry.polyhedron.backend_normaliz) Polyhedron_number_field (class in sage.geometry.polyhedron.backend_number_field) Polyhedron_polymake (class in sage.geometry.polyhedron.backend_polymake) Polyhedron_ppl (class in sage.geometry.polyhedron.backend_ppl) Polyhedron_QQ (class in sage.geometry.polyhedron.base_QQ) Polyhedron_QQ_cdd (class in sage.geometry.polyhedron.backend_cdd) Polyhedron_QQ_normaliz (class in sage.geometry.polyhedron.backend_normaliz) Polyhedron_QQ_polymake (class in sage.geometry.polyhedron.backend_polymake) Polyhedron_QQ_ppl (class in sage.geometry.polyhedron.backend_ppl) Polyhedron_RDF (class in sage.geometry.polyhedron.base_RDF) Polyhedron_RDF_cdd (class in sage.geometry.polyhedron.backend_cdd_rdf) Polyhedron_ZZ (class in sage.geometry.polyhedron.base_ZZ) Polyhedron_ZZ_normaliz (class in sage.geometry.polyhedron.backend_normaliz) Polyhedron_ZZ_polymake (class in sage.geometry.polyhedron.backend_polymake) Polyhedron_ZZ_ppl (class in sage.geometry.polyhedron.backend_ppl) PolyhedronFace (class in sage.geometry.polyhedron.face) PolyhedronFaceLattice (class in sage.geometry.polyhedron.combinatorial_polyhedron.polyhedron_face_lattice) PolyhedronRepresentation (class in sage.geometry.polyhedron.representation) Polytopes (class in sage.geometry.polyhedron.library) poset_of_regions() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) positive_circuits() (sage.geometry.triangulation.point_configuration.PointConfiguration method) positive_integer_relations() (in module sage.geometry.lattice_polytope) positive_operators_gens() (sage.geometry.cone.ConvexRationalPolyhedralCone method) prefix_check() (in module sage.rings.polynomial.groebner_fan) preimage_cones() (sage.geometry.fan_morphism.FanMorphism method) preimage_fan() (sage.geometry.fan_morphism.FanMorphism method) primitive() (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) primitive_collections() (sage.geometry.fan.RationalPolyhedralFan method) primitive_eulerian_polynomial() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) primitive_preimage_cones() (sage.geometry.fan_morphism.FanMorphism method) prism() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) Problem (class in sage.geometry.polyhedron.double_description) product() (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) project_points() (in module sage.geometry.polyhedron.library) Projection (class in sage.geometry.polyhedron.plot) projection() (sage.geometry.polyhedron.base6.Polyhedron_base6 method) projection_func_identity() (in module sage.geometry.polyhedron.plot) projection_linear_map (sage.geometry.convex_set.AffineHullProjectionData attribute) projection_translation (sage.geometry.convex_set.AffineHullProjectionData attribute) ProjectionFuncSchlegel (class in sage.geometry.polyhedron.plot) ProjectionFuncStereographic (class in sage.geometry.polyhedron.plot) projective() (sage.geometry.triangulation.base.Point method) PseudolineArrangement (class in sage.geometry.pseudolines) pushing_triangulation() (sage.geometry.triangulation.point_configuration.PointConfiguration method) pyramid() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.combinatorial_polyhedron.list_of_faces.ListOfFaces method) Q quotient() (sage.geometry.toric_lattice.ToricLattice_generic method) R R_by_sign() (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) radius() (sage.geometry.polyhedron.base.Polyhedron_base method) radius_square() (sage.geometry.polyhedron.base.Polyhedron_base method) random_cone() (in module sage.geometry.cone) random_element() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.linear_expression.LinearExpressionModule method) random_inequalities() (in module sage.geometry.polyhedron.double_description) random_integral_point() (sage.geometry.polyhedron.base2.Polyhedron_base2 method) rank() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.toric_lattice.ToricLattice_quotient method) RationalPolyhedralFan (class in sage.geometry.fan) Ray (class in sage.geometry.polyhedron.representation) RAY (sage.geometry.polyhedron.representation.PolyhedronRepresentation attribute) ray() (sage.geometry.cone.IntegralRayCollection method) ray_generator() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.face.PolyhedronFace method) rays() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.rings.polynomial.groebner_fan.InitialForm method) (sage.rings.polynomial.groebner_fan.PolyhedralFan method) rays_list() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) read_all_polytopes() (in module sage.geometry.lattice_polytope) read_palp_matrix() (in module sage.geometry.lattice_polytope) read_palp_point_collection() (in module sage.geometry.point_collection) rearrangement() (in module sage.geometry.cone_catalog) rectified_one_hundred_twenty_cell() (sage.geometry.polyhedron.library.Polytopes method) rectified_six_hundred_cell() (sage.geometry.polyhedron.library.Polytopes method) recycle() (sage.geometry.polyhedron.parent.Polyhedra_base method) reduced() (sage.geometry.ribbon_graph.RibbonGraph method) reduced_affine() (sage.geometry.triangulation.base.Point method) reduced_affine_vector() (sage.geometry.triangulation.base.Point method) reduced_affine_vector_space() (sage.geometry.triangulation.base.PointConfiguration_base method) reduced_groebner_bases() (sage.rings.polynomial.groebner_fan.GroebnerFan method) reduced_projective() (sage.geometry.triangulation.base.Point method) reduced_projective_vector() (sage.geometry.triangulation.base.Point method) reduced_projective_vector_space() (sage.geometry.triangulation.base.PointConfiguration_base method) ReducedGroebnerBasis (class in sage.rings.polynomial.groebner_fan) Reflexive4dHodge (class in sage.geometry.polyhedron.palp_database) ReflexivePolytope() (in module sage.geometry.lattice_polytope) ReflexivePolytopes() (in module sage.geometry.lattice_polytope) region_containing_point() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) regions() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.voronoi_diagram.VoronoiDiagram method) regular_polygon() (sage.geometry.polyhedron.library.Polytopes method) relative_boundary_cells() (sage.geometry.polyhedral_complex.PolyhedralComplex method) relative_interior() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.relative_interior.RelativeInterior method) relative_interior_contains() (sage.geometry.cone.ConvexRationalPolyhedralCone method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) relative_interior_point() (sage.rings.polynomial.groebner_fan.PolyhedralCone method) relative_orthogonal_quotient() (sage.geometry.cone.ConvexRationalPolyhedralCone method) relative_quotient() (sage.geometry.cone.ConvexRationalPolyhedralCone method) relative_star_generators() (sage.geometry.fan_morphism.FanMorphism method) RelativeInterior (class in sage.geometry.relative_interior) remove_cell() (sage.geometry.polyhedral_complex.PolyhedralComplex method) render() (sage.rings.polynomial.groebner_fan.GroebnerFan method) render3d() (sage.rings.polynomial.groebner_fan.GroebnerFan method) render_0d() (sage.geometry.polyhedron.plot.Projection method) render_1d() (sage.geometry.polyhedron.plot.Projection method) render_2d() (sage.geometry.polyhedron.plot.Projection method) render_3d() (sage.geometry.polyhedron.plot.Projection method) render_fill_2d() (sage.geometry.polyhedron.plot.Projection method) render_line_1d() (sage.geometry.polyhedron.plot.Projection method) render_outline_2d() (sage.geometry.polyhedron.plot.Projection method) render_points_1d() (sage.geometry.polyhedron.plot.Projection method) render_points_2d() (sage.geometry.polyhedron.plot.Projection method) render_solid() (sage.geometry.polyhedron.base6.Polyhedron_base6 method) render_solid_3d() (sage.geometry.polyhedron.plot.Projection method) render_vertices_3d() (sage.geometry.polyhedron.plot.Projection method) render_wireframe() (sage.geometry.polyhedron.base6.Polyhedron_base6 method) render_wireframe_3d() (sage.geometry.polyhedron.plot.Projection method) repr_pretty() (in module sage.geometry.polyhedron.representation) (sage.geometry.polyhedron.representation.Hrepresentation method) representative_point() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.relative_interior.RelativeInterior method) reset() (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_base method) (sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator.FaceIterator_geom method) reset_options() (in module sage.geometry.toric_plotter) restrict_to_connected_triangulations() (sage.geometry.triangulation.point_configuration.PointConfiguration method) restrict_to_fine_triangulations() (sage.geometry.triangulation.point_configuration.PointConfiguration method) restrict_to_regular_triangulations() (sage.geometry.triangulation.point_configuration.PointConfiguration method) restrict_to_star_triangulations() (sage.geometry.triangulation.point_configuration.PointConfiguration method) restricted_automorphism_group() (sage.geometry.polyhedron.base4.Polyhedron_base4 method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) (sage.geometry.triangulation.point_configuration.PointConfiguration method) restriction() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) reverse() (sage.geometry.newton_polygon.NewtonPolygon_element method) rho() (sage.geometry.ribbon_graph.RibbonGraph method) rhombic_dodecahedron() (sage.geometry.polyhedron.library.Polytopes method) rhombicosidodecahedron() (sage.geometry.polyhedron.library.Polytopes method) RibbonGraph (class in sage.geometry.ribbon_graph) ridges() (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) ring() (sage.rings.polynomial.groebner_fan.GroebnerFan method) ring_to_gfan_format() (in module sage.rings.polynomial.groebner_fan) run() (sage.geometry.polyhedron.double_description.StandardAlgorithm method) runcinated_one_hundred_twenty_cell() (sage.geometry.polyhedron.library.Polytopes method) runcitruncated_one_hundred_twenty_cell() (sage.geometry.polyhedron.library.Polytopes method) runcitruncated_six_hundred_cell() (sage.geometry.polyhedron.library.Polytopes method) S sage.geometry.abc module sage.geometry.cone module sage.geometry.cone_catalog module sage.geometry.convex_set module sage.geometry.fan module sage.geometry.fan_isomorphism module sage.geometry.fan_morphism module sage.geometry.hasse_diagram module sage.geometry.hyperplane_arrangement.affine_subspace module sage.geometry.hyperplane_arrangement.arrangement module sage.geometry.hyperplane_arrangement.check_freeness module sage.geometry.hyperplane_arrangement.hyperplane module sage.geometry.hyperplane_arrangement.library module sage.geometry.hyperplane_arrangement.plot module sage.geometry.integral_points module sage.geometry.lattice_polytope module sage.geometry.linear_expression module sage.geometry.newton_polygon module sage.geometry.point_collection module sage.geometry.polyhedral_complex module sage.geometry.polyhedron.backend_cdd module sage.geometry.polyhedron.backend_cdd_rdf module sage.geometry.polyhedron.backend_field module sage.geometry.polyhedron.backend_normaliz module sage.geometry.polyhedron.backend_number_field module sage.geometry.polyhedron.backend_polymake module sage.geometry.polyhedron.backend_ppl module sage.geometry.polyhedron.base module sage.geometry.polyhedron.base0 module sage.geometry.polyhedron.base1 module sage.geometry.polyhedron.base2 module sage.geometry.polyhedron.base3 module sage.geometry.polyhedron.base4 module sage.geometry.polyhedron.base5 module sage.geometry.polyhedron.base6 module sage.geometry.polyhedron.base7 module sage.geometry.polyhedron.base_QQ module sage.geometry.polyhedron.base_RDF module sage.geometry.polyhedron.base_ZZ module sage.geometry.polyhedron.cdd_file_format module sage.geometry.polyhedron.combinatorial_polyhedron.base module sage.geometry.polyhedron.combinatorial_polyhedron.combinatorial_face module sage.geometry.polyhedron.combinatorial_polyhedron.conversions module sage.geometry.polyhedron.combinatorial_polyhedron.face_iterator module sage.geometry.polyhedron.combinatorial_polyhedron.list_of_faces module sage.geometry.polyhedron.combinatorial_polyhedron.polyhedron_face_lattice module sage.geometry.polyhedron.constructor module sage.geometry.polyhedron.double_description module sage.geometry.polyhedron.double_description_inhomogeneous module sage.geometry.polyhedron.face module sage.geometry.polyhedron.generating_function module sage.geometry.polyhedron.lattice_euclidean_group_element module sage.geometry.polyhedron.library module sage.geometry.polyhedron.modules.formal_polyhedra_module module sage.geometry.polyhedron.palp_database module sage.geometry.polyhedron.parent module sage.geometry.polyhedron.plot module sage.geometry.polyhedron.ppl_lattice_polygon module sage.geometry.polyhedron.ppl_lattice_polytope module sage.geometry.polyhedron.representation module sage.geometry.pseudolines module sage.geometry.relative_interior module sage.geometry.ribbon_graph module sage.geometry.toric_lattice module sage.geometry.toric_plotter module sage.geometry.triangulation.base module sage.geometry.triangulation.element module sage.geometry.triangulation.point_configuration module sage.geometry.voronoi_diagram module sage.rings.polynomial.groebner_fan module saturation() (sage.geometry.toric_lattice.ToricLattice_generic method) schlegel() (sage.geometry.polyhedron.plot.Projection method) schlegel_projection() (sage.geometry.polyhedron.base6.Polyhedron_base6 method) schur() (in module sage.geometry.cone_catalog) secondary_polytope() (sage.geometry.triangulation.point_configuration.PointConfiguration method) section_linear_map (sage.geometry.convex_set.AffineHullProjectionData attribute) section_translation (sage.geometry.convex_set.AffineHullProjectionData attribute) sector() (in module sage.geometry.toric_plotter) semigroup_generators() (sage.geometry.cone.ConvexRationalPolyhedralCone method) semiorder() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) set() (sage.geometry.point_collection.PointCollection method) set_engine() (sage.geometry.triangulation.point_configuration.PointConfiguration class method) set_immutable() (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.backend_ppl.Polyhedron_ppl method) (sage.geometry.toric_lattice.ToricLattice_quotient_element method) set_palp_dimension() (in module sage.geometry.lattice_polytope) set_rays() (sage.geometry.toric_plotter.ToricPlotter method) SetOfAllLatticePolytopesClass (class in sage.geometry.lattice_polytope) Shi() (sage.geometry.hyperplane_arrangement.library.HyperplaneArrangementLibrary method) show() (sage.geometry.polyhedron.base6.Polyhedron_base6 method) (sage.geometry.pseudolines.PseudolineArrangement method) show3d() (sage.geometry.lattice_polytope.LatticePolytopeClass method) sigma() (sage.geometry.ribbon_graph.RibbonGraph method) sign_vector() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) simplex() (sage.geometry.polyhedron.library.Polytopes method) simplex_to_int() (sage.geometry.triangulation.base.PointConfiguration_base method) simplicial_complex() (sage.geometry.triangulation.element.Triangulation method) simpliciality() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) simplicity() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) six_hundred_cell() (sage.geometry.polyhedron.library.Polytopes method) skeleton() (sage.geometry.lattice_polytope.LatticePolytopeClass method) skeleton_points() (sage.geometry.lattice_polytope.LatticePolytopeClass method) skeleton_show() (sage.geometry.lattice_polytope.LatticePolytopeClass method) skip_palp_matrix() (in module sage.geometry.lattice_polytope) slack_matrix() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) slopes() (sage.geometry.newton_polygon.NewtonPolygon_element method) small_rhombicuboctahedron() (sage.geometry.polyhedron.library.Polytopes method) snub_cube() (sage.geometry.polyhedron.library.Polytopes method) snub_dodecahedron() (sage.geometry.polyhedron.library.Polytopes method) solid_restriction() (sage.geometry.cone.ConvexRationalPolyhedralCone method) some_elements() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.parent.Polyhedra_base method) span() (sage.geometry.cone.IntegralRayCollection method) (sage.geometry.toric_lattice.ToricLattice_generic method) span_of_basis() (sage.geometry.toric_lattice.ToricLattice_generic method) stack() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) stacking_locus() (sage.geometry.polyhedron.face.PolyhedronFace method) StandardAlgorithm (class in sage.geometry.polyhedron.double_description) StandardDoubleDescriptionPair (class in sage.geometry.polyhedron.double_description) Stanley_Reisner_ideal() (sage.geometry.fan.RationalPolyhedralFan method) star_center() (sage.geometry.triangulation.point_configuration.PointConfiguration method) star_generator_indices() (sage.geometry.fan.Cone_of_fan method) star_generators() (sage.geometry.fan.Cone_of_fan method) stereographic() (sage.geometry.polyhedron.plot.Projection method) stratify() (sage.geometry.polyhedral_complex.PolyhedralComplex method) strict_quotient() (sage.geometry.cone.ConvexRationalPolyhedralCone method) sub_polytope_generator() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) sub_polytopes() (sage.geometry.polyhedron.ppl_lattice_polygon.LatticePolygon_PPL_class method) sub_reflexive_polygons() (in module sage.geometry.polyhedron.ppl_lattice_polygon) subdirect_sum() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) subdivide() (sage.geometry.fan.RationalPolyhedralFan method) (sage.geometry.polyhedral_complex.PolyhedralComplex method) sublattice() (sage.geometry.cone.ConvexRationalPolyhedralCone method) sublattice_complement() (sage.geometry.cone.ConvexRationalPolyhedralCone method) sublattice_quotient() (sage.geometry.cone.ConvexRationalPolyhedralCone method) subpolygons_of_polar_P1xP1() (in module sage.geometry.polyhedron.ppl_lattice_polygon) subpolygons_of_polar_P2() (in module sage.geometry.polyhedron.ppl_lattice_polygon) subpolygons_of_polar_P2_112() (in module sage.geometry.polyhedron.ppl_lattice_polygon) support_contains() (sage.geometry.fan.RationalPolyhedralFan method) symmetric_edge_polytope() (sage.geometry.polyhedron.library.Polytopes static method) symmetric_space() (sage.geometry.hyperplane_arrangement.hyperplane.AmbientVectorSpace method) T tetrahedron() (sage.geometry.polyhedron.library.Polytopes method) tikz() (sage.geometry.polyhedron.base6.Polyhedron_base6 method) (sage.geometry.polyhedron.plot.Projection method) to_linear_program() (sage.geometry.polyhedron.base.Polyhedron_base method) to_RationalPolyhedralFan() (sage.rings.polynomial.groebner_fan.PolyhedralFan method) to_symmetric_space() (sage.geometry.hyperplane_arrangement.hyperplane.Hyperplane method) toric_variety() (sage.geometry.fan.RationalPolyhedralFan method) ToricLattice_ambient (class in sage.geometry.toric_lattice) ToricLattice_generic (class in sage.geometry.toric_lattice) ToricLattice_quotient (class in sage.geometry.toric_lattice) ToricLattice_quotient_element (class in sage.geometry.toric_lattice) ToricLattice_sublattice (class in sage.geometry.toric_lattice) ToricLattice_sublattice_with_basis (class in sage.geometry.toric_lattice) ToricLatticeFactory (class in sage.geometry.toric_lattice) ToricPlotter (class in sage.geometry.toric_plotter) translation() (sage.geometry.convex_set.ConvexSet_base method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) (sage.geometry.relative_interior.RelativeInterior method) transpositions() (sage.geometry.pseudolines.PseudolineArrangement method) traverse_boundary() (sage.geometry.lattice_polytope.LatticePolytopeClass method) triangulate() (sage.geometry.polyhedron.base7.Polyhedron_base7 method) (sage.geometry.triangulation.point_configuration.PointConfiguration method) Triangulation (class in sage.geometry.triangulation.element) triangulation_render_2d() (in module sage.geometry.triangulation.element) triangulation_render_3d() (in module sage.geometry.triangulation.element) triangulations() (sage.geometry.triangulation.point_configuration.PointConfiguration method) triangulations_list() (sage.geometry.triangulation.point_configuration.PointConfiguration method) trivial() (in module sage.geometry.cone_catalog) tropical_basis() (sage.rings.polynomial.groebner_fan.GroebnerFan method) tropical_intersection() (sage.rings.polynomial.groebner_fan.GroebnerFan method) TropicalPrevariety (class in sage.rings.polynomial.groebner_fan) truncated_cube() (sage.geometry.polyhedron.library.Polytopes method) truncated_dodecahedron() (sage.geometry.polyhedron.library.Polytopes method) truncated_icosidodecahedron() (sage.geometry.polyhedron.library.Polytopes method) truncated_octahedron() (sage.geometry.polyhedron.library.Polytopes method) truncated_one_hundred_twenty_cell() (sage.geometry.polyhedron.library.Polytopes method) truncated_six_hundred_cell() (sage.geometry.polyhedron.library.Polytopes method) truncated_tetrahedron() (sage.geometry.polyhedron.library.Polytopes method) truncation() (sage.geometry.polyhedron.base5.Polyhedron_base5 method) twenty_four_cell() (sage.geometry.polyhedron.library.Polytopes method) type() (sage.geometry.polyhedron.representation.Equation method) (sage.geometry.polyhedron.representation.Inequality method) (sage.geometry.polyhedron.representation.Line method) (sage.geometry.polyhedron.representation.Ray method) (sage.geometry.polyhedron.representation.Vertex method) U unbounded_regions() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) union() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.polyhedral_complex.PolyhedralComplex method) union_as_polyhedron() (sage.geometry.polyhedral_complex.PolyhedralComplex method) universe() (sage.geometry.polyhedron.parent.Polyhedra_base method) V varchenko_matrix() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) vector() (sage.geometry.polyhedron.representation.PolyhedronRepresentation method) verify() (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) (sage.geometry.polyhedron.double_description_inhomogeneous.Hrep2Vrep method) (sage.geometry.polyhedron.double_description_inhomogeneous.Vrep2Hrep method) Vertex (class in sage.geometry.polyhedron.representation) VERTEX (sage.geometry.polyhedron.representation.PolyhedronRepresentation attribute) vertex() (sage.geometry.lattice_polytope.LatticePolytopeClass method) vertex_adjacency_matrix() (sage.geometry.polyhedron.base3.Polyhedron_base3 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) vertex_digraph() (sage.geometry.polyhedron.base4.Polyhedron_base4 method) vertex_facet_graph() (sage.geometry.polyhedron.base4.Polyhedron_base4 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) vertex_facet_pairing_matrix() (sage.geometry.lattice_polytope.LatticePolytopeClass method) vertex_generator() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.face.PolyhedronFace method) vertex_graph() (sage.geometry.fan.RationalPolyhedralFan method) (sage.geometry.polyhedron.base4.Polyhedron_base4 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) vertices() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) (sage.geometry.lattice_polytope.LatticePolytopeClass method) (sage.geometry.newton_polygon.NewtonPolygon_element method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) (sage.geometry.polyhedron.face.PolyhedronFace method) (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) vertices_list() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) vertices_matrix() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) vertices_saturating() (sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class method) verts_for_normal() (in module sage.rings.polynomial.groebner_fan) virtual_rays() (sage.geometry.fan.RationalPolyhedralFan method) volume() (sage.geometry.polyhedron.base7.Polyhedron_base7 method) (sage.geometry.triangulation.point_configuration.PointConfiguration method) VoronoiDiagram (class in sage.geometry.voronoi_diagram) Vrep2Hrep (class in sage.geometry.polyhedron.double_description_inhomogeneous) Vrep_generator() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) Vrepresentation (class in sage.geometry.polyhedron.representation) Vrepresentation() (sage.geometry.polyhedron.backend_ppl.Polyhedron_ppl method) (sage.geometry.polyhedron.base0.Polyhedron_base0 method) (sage.geometry.polyhedron.combinatorial_polyhedron.base.CombinatorialPolyhedron method) Vrepresentation_space() (sage.geometry.polyhedron.base1.Polyhedron_base1 method) (sage.geometry.polyhedron.parent.Polyhedra_base method) W wedge() (sage.geometry.polyhedral_complex.PolyhedralComplex method) (sage.geometry.polyhedron.base5.Polyhedron_base5 method) weight_vectors() (sage.rings.polynomial.groebner_fan.GroebnerFan method) whitney_data() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) whitney_number() (sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement method) write_cdd_Hrepresentation() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) write_cdd_Vrepresentation() (sage.geometry.polyhedron.base0.Polyhedron_base0 method) write_for_palp() (sage.geometry.point_collection.PointCollection method) write_palp_matrix() (in module sage.geometry.lattice_polytope) Z Z_operators_gens() (sage.geometry.cone.ConvexRationalPolyhedralCone method) zero() (sage.geometry.polyhedron.parent.Polyhedra_base method) zero_set() (sage.geometry.polyhedron.double_description.DoubleDescriptionPair method) zero_sum_projection() (in module sage.geometry.polyhedron.library) zonotope() (sage.geometry.polyhedron.library.Polytopes method)