Available versions of this document: latest release, release 4.0, release 3.6, release 3.5, nightly master

Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

# Index

## applications

## Index of all things

Name | Application | Object class | Category |
---|---|---|---|

`_4ti2Circuits(Matrix A)` | matroid | Functions | Combinatorics |

`ABSTRACT_OBJECTIVE` | polytope | property of LinearProgram | no category |

`AccurateFloat` | common | Property_types | Basic Types |

`Action` | group | Objects | no category |

`action<action_type>(Any g, Core::BigObject O)` | group | Functions | Utilities |

`action_from_generators(Array<Array<Int>> gens, Group action)` | group | Functions | Utilities |

`action_inv<action_type>(Array<Int> p, Core::BigObject O)` | group | Functions | Utilities |

`action_to_cyclic_notation(PermutationAction a)` | group | Functions | Utilities |

`add(String multi_property_name, Any subobject, Any properties)` | core | method of Core::BigObject | no category |

`add_edge(Int tail_node, Int head_node)` | common | method of Graph | no category |

`add_index(HASH index)` | common | method of PolyDB::Collection | Database Collection Administration |

`add_index_from_property(String property)` | common | method of PolyDB::Collection | Database Collection Administration |

`add_indices(ARRAY index)` | common | method of PolyDB::Collection | Database Collection Administration |

`add_indices_from_property(ARRAY property)` | common | method of PolyDB::Collection | Database Collection Administration |

`add_morphisms(Morphism f, Morphism g)` | tropical | Functions | Morphisms |

`add_node()` | common | method of Graph | no category |

`add_user_to_collection()` | common | method of PolyDB::Client | Database Administration |

`ADJACENCY` | graph | property of Graph | no category |

`adjacency_matrix(Graph graph)` | common | Functions | Graph Operations |

`adjacent_nodes(Int node)` | common | method of Graph | no category |

`AFFINE` | fulton | property of NormalToricVariety | Algebraic Geometry |

`affine_chart(Int chart)` | tropical | method of Cycle | Affine and projective coordinates |

`affine_float_coords(Polytope P)` | polytope | Functions | Coordinate conversions |

`AFFINE_HULL` | fan | property of PolyhedralComplex | Geometry |

`AFFINE_HULL` | polytope | property of PointConfiguration | Geometry |

`AFFINE_HULL` | polytope | property of Polytope | Geometry |

`affine_linear_space<Addition>(Matrix<Rational> lineality, Vector<Rational> translate, Integer weight)` | tropical | Functions | Creation functions for specific cycles |

`affine_representation(Int domain_chart, Int target_chart)` | tropical | method of Morphism | Affine and projective coordinates |

`affine_transform(Cycle<Addition> C, Matrix<Rational> M, Vector<Rational> T)` | tropical | Functions | Basic polyhedral operations |

`affine_transform(Cycle<Addition> C, Morphism<Addition> M)` | tropical | Functions | Basic polyhedral operations |

`AffineLattice<Scalar>` | polytope | Objects | Geometry |

`after(Morphism g)` | tropical | method of Morphism | Morphisms |

`ag23_matroid()` | matroid | Functions | Producing a matroid from scratch |

`ag32_matroid()` | matroid | Functions | Producing a matroid from scratch |

`ag32_prime_matroid()` | matroid | Functions | Producing a matroid from scratch |

`alexander_dual(SimplicialComplex complex)` | topaz | Functions | Producing a new simplicial complex from others |

`all_edges(Int tail_node, Int head_node)` | common | method of Graph | no category |

`all_families()` | tropical | method of LinesInCubic | Lists of lines |

`ALL_GROUP_ELEMENTS` | group | property of Action | Symmetry |

`all_group_elements<Scalar>(MatrixActionOnVectors<Scalar> action)` | group | Functions | Symmetry |

`all_group_elements(PermutationAction a)` | group | Functions | Utilities |

`all_isolated()` | tropical | method of LinesInCubic | Lists of lines |

`all_permutations(Int n)` | common | Functions | Combinatorics |

`all_rows_or_cols` | common | Property_types | Algebraic Types |

`all_spanningtrees(Graph G)` | graph | Functions | Combinatorics |

`all_steiner_points(Polytope P)` | polytope | Functions | Geometry |

`all_subsets_of_k(Any c, Int k)` | common | Functions | Set Operations |

`ALPHA_LATTICE` | fulton | property of VersalComponent | Combinatorics |

`alternating_group(Int d)` | group | Functions | Producing a group |

`ALTSHULER_DET` | fan | property of SubdivisionOfVectors | no category |

`ALTSHULER_DET` | polytope | property of Cone | Combinatorics |

`AMBIENT_DIM` | tropical | property of VoronoiDiagram | no category |

`AMBIENT_DIM()` | fan | method of PolyhedralFan | Geometry |

`AMBIENT_DIM` | fan | property of HyperplaneArrangement | Geometry |

`AMBIENT_DIM` | fan | method of SubdivisionOfPoints | Geometry |

`AMBIENT_DIM()` | fan | method of PolyhedralComplex | Geometry |

`AMBIENT_DIM()` | polytope | method of Cone | Geometry |

`AMBIENT_DIM()` | polytope | method of PointConfiguration | Geometry |

`AMBIENT_DIM()` | polytope | method of Polytope | Geometry |

`ambient_lattice_normalization(Polytope p)` | polytope | Functions | Transformations |

`AMPLE` | fulton | property of TDivisor | Algebraic Geometry |

`anti_diag(Vector d)` | common | Functions | Linear Algebra |

`anti_diag(Matrix m1, Matrix m2)` | common | Functions | Linear Algebra |

`anti_diagonal(Int i)` | common | method of Matrix | no category |

`application(String name)` | core | Functions | Basic |

`apply(Core::BigObject o)` | core | method of Core::RuleChain | no category |

`apply` | common | method of Min | no category |

`apply` | common | method of Max | no category |

`apply_rule(String pattern)` | core | method of Core::BigObject | no category |

`ApproximateSet<Element>` | common | Property_types | Set Types |

`apropos(String pattern)` | core | Functions | Interactive |

`archimedean_solid(String s)` | polytope | Functions | Producing regular polytopes and their generalizations |

`are_in_same_orbit(PermutationAction a, Vector v1, Vector v2)` | group | Functions | Orbits |

`are_permuted(Array a, Array b)` | common | Functions | Combinatorics |

`Array<Element>` | common | Property_types | Basic Types |

`array_family_fixed_edge()` | tropical | method of LinesInCubic | Lists of lines |

`array_family_fixed_vertex()` | tropical | method of LinesInCubic | Lists of lines |

`array_family_moving_edge()` | tropical | method of LinesInCubic | Lists of lines |

`array_family_moving_vertex()` | tropical | method of LinesInCubic | Lists of lines |

`array_isolated_edge()` | tropical | method of LinesInCubic | Lists of lines |

`array_isolated_no_edge()` | tropical | method of LinesInCubic | Lists of lines |

`associahedron(Int d)` | polytope | Functions | Producing a polytope from scratch |

`attach(String name, Any data, String constructor_arg)` | core | method of Core::BigObject | no category |

`AUTOMORPHISM_GROUP` | matroid | property of Matroid | Advanced properties |

`automorphism_group(Graph graph)` | group | Functions | Symmetry |

`automorphism_group(IncidenceMatrix<NonSymmetric> m, Bool on_rows)` | group | Functions | Symmetry |

`automorphisms(Graph graph)` | graph | Functions | Comparing |

`automorphisms(IncidenceMatrix<NonSymmetric> m)` | graph | Functions | Comparing |

`automorphisms(IncidenceMatrix<Symmetric> m)` | graph | Functions | Comparing |

`average(ARRAY array)` | common | Functions | Utilities |

`AVERAGE_DEGREE` | graph | property of Graph | no category |

`back()` | common | method of Set | no category |

`BALANCE` | polytope | property of Polytope | Combinatorics |

`BALANCED` | polytope | property of Polytope | Combinatorics |

`BALANCED_FACES` | tropical | property of Cycle | Weights and lattices |

`BALL` | topaz | property of SimplicialComplex | Topology |

`ball(Int d)` | topaz | Functions | Producing from scratch |

`ball_lifting_lp(GeometricSimplicialComplex c, Int facet_index, Rational conv_eps)` | polytope | Functions | Optimization |

`barycenter(Matrix A)` | common | Functions | Linear Algebra |

`BARYCENTER` | polytope | property of PointConfiguration | Geometry |

`barycentric_subdivision(SimplicialComplex complex)` | topaz | Functions | Producing a new simplicial complex from others |

`barycentric_subdivision(Cone c)` | polytope | Functions | Triangulations, subdivisions and volume |

`BASE` | group | property of PermutationAction | no category |

`BASEPOINT_FREE` | fulton | property of TDivisor | Algebraic Geometry |

`BASES` | matroid | property of Matroid | Axiom systems |

`bases_from_revlex_encoding(String encoding, Int r, Int n)` | matroid | Functions | Other |

`bases_to_revlex_encoding(Array<Set> bases, Int r, Int n)` | matroid | Functions | Other |

`BasicDecoration` | graph | Property_types | Combinatorics |

`basis(Matrix A)` | common | Functions | Linear Algebra |

`BASIS` | ideal | property of Groebner | Commutative algebra |

`BASIS` | polytope | property of AffineLattice | no category |

`BASIS` | polytope | property of GroebnerBasis | no category |

`basis_affine(Matrix A)` | common | Functions | Linear Algebra |

`basis_cols(Matrix A)` | common | Functions | Linear Algebra |

`basis_rows(Matrix A)` | common | Functions | Linear Algebra |

`BB_VISUAL()` | tropical | method of Cycle | Visualization |

`before(Morphism g)` | tropical | method of Morphism | Morphisms |

`BETA_INVARIANT` | matroid | property of Matroid | Advanced properties |

`betti_number()` | topaz | method of HomologyGroup | no category |

`betti_numbers<Coeff>(ChainComplex C)` | topaz | Functions | Topology |

`betti_numbers<Coeff>(SimplicialComplex S)` | topaz | Functions | Topology |

`BICONNECTED_COMPONENTS` | graph | property of Graph | no category |

`billera_lee(Vector<Integer> H)` | polytope | Functions | Producing a polytope from other objects |

`BINARY` | matroid | property of Matroid | Realizability |

`binary_markov_graph(Array<Bool> observation)` | polytope | Functions | Producing a polytope from scratch |

`binary_markov_graph(String observation)` | polytope | Functions | Producing a polytope from scratch |

`BINARY_VECTORS` | matroid | property of Matroid | Realizability |

`binomial(Int n, Int k)` | common | Functions | Combinatorics |

`BINOMIAL_GENERATORS` | fulton | property of BinomialIdeal | no category |

`BinomialIdeal` | fulton | Objects | no category |

`BIPARTITE` | graph | property of Graph | no category |

`BIPARTITE()` | topaz | method of SimplicialComplex | Combinatorics |

`bipyramid(Polytope P, Scalar z, Scalar z_prime)` | polytope | Functions | Producing a polytope from polytopes |

`birkhoff(Int n, Bool even)` | polytope | Functions | Producing a polytope from scratch |

`bistellar_simplification(SimplicialComplex complex)` | topaz | Functions | Producing a new simplicial complex from others |

`Bitset` | common | Property_types | Set Types |

`BITSET_ACTION` | polytope | property of Cone | Symmetry |

`blending(Polytope P1, Int v1, Polytope P2, Int v2)` | polytope | Functions | Producing a polytope from polytopes |

`Bool` | common | Property_types | Basic Types |

`BOTTOM_NODE` | graph | property of Lattice | Combinatorics |

`bound(Polytope P)` | polytope | Functions | Transformations |

`BOUNDARY` | topaz | property of SimplicialComplex | Combinatorics |

`BOUNDARY` | polytope | property of Cone | Combinatorics |

`BOUNDARY` | polytope | property of PointConfiguration | Combinatorics |

`BOUNDARY_LATTICE_POINTS` | polytope | property of Polytope | Lattice points in polytopes |

`boundary_matrix(Int d)` | topaz | method of SimplicialComplex | Combinatorics |

`boundary_matrix(Int d)` | topaz | method of ChainComplex | no category |

`boundary_matrix(Int d, Int t)` | topaz | method of Filtration | no category |

`BOUNDED` | fan | property of PolyhedralComplex | Geometry |

`BOUNDED` | polytope | property of PointConfiguration | Geometry |

`BOUNDED` | polytope | property of Polytope | Geometry |

`BOUNDED_COMPLEX` | polytope | property of Polytope | Unbounded polyhedra |

`BOUNDED_DUAL_GRAPH` | polytope | method of Polytope | Unbounded polyhedra |

`BOUNDED_FACETS()` | polytope | method of Polytope | Unbounded polyhedra |

`BOUNDED_GRAPH` | polytope | method of Polytope | Unbounded polyhedra |

`BOUNDED_HASSE_DIAGRAM` | polytope | method of Polytope | Unbounded polyhedra |

`BOUNDED_VERTICES()` | polytope | method of Polytope | Unbounded polyhedra |

`BOUNDING_BOX` | graph | property of GeometricGraph | no category |

`bounding_box(Matrix m)` | common | Functions | Utilities |

`bounding_box(Int chart)` | tropical | method of Cycle | Visualization |

`bounding_box_facets(Int offset, Int chart)` | tropical | method of Cycle | Visualization |

`bounding_box_facets(Matrix V)` | polytope | Functions | Visualization |

`bounding_facets(Matrix H, Matrix V)` | polytope | Functions | Visualization |

`bs2quotient(Polytope P, SimplicialComplex complex)` | topaz | Functions | Producing a new simplicial complex from others |

`building_set(Array<Set> generators, Int n)` | fan | Functions | Other |

`CachedObjectPointer` | common | Property_types | Artificial |

`CANONICAL` | polytope | property of Polytope | Lattice points in cones |

`canonical_form(Graph g)` | graph | Functions | Comparing |

`canonical_hash(Graph g, Int k)` | graph | Functions | Comparing |

`canonical_hash(IncidenceMatrix M, Int k)` | graph | Functions | Comparing |

`cap_product(CycleGroup<E> cocycles, CycleGroup<E> cycles)` | topaz | Functions | Topology |

`cartesian_product(Cycle cycles)` | tropical | Functions | Basic polyhedral operations |

`CARTIER` | fulton | property of TDivisor | Algebraic Geometry |

`CARTIER_DATA` | fulton | property of TDivisor | Combinatorics |

`cast<Target>(Core::BigObject object)` | common | Functions | Data Conversion |

`catalan_solid(String s)` | polytope | Functions | Producing regular polytopes and their generalizations |

`CATENARY_G_INVARIANT` | matroid | property of Matroid | Advanced properties |

`cayley_embedding(Polytope P_0, Polytope P_1, Scalar t_0, Scalar t_1)` | polytope | Functions | Producing a polytope from polytopes |

`cayley_embedding(Array<Polytope> A)` | polytope | Functions | Producing a polytope from polytopes |

`cayley_polytope(Array<Polytope> P_Array)` | polytope | Functions | Producing a polytope from polytopes |

`CD_INDEX()` | polytope | method of Polytope | Combinatorics |

`CD_INDEX_COEFFICIENTS` | polytope | property of Polytope | Combinatorics |

`ceil(Rational a)` | common | Functions | Arithmetic |

`Cell` | topaz | Property_types | Topology |

`cell(Int i)` | fan | method of SubdivisionOfVectors | Geometry |

`cell(Int i)` | fan | method of SubdivisionOfPoints | Geometry |

`CELL_DECOMPOSITION` | fan | property of HyperplaneArrangement | Geometry |

`cell_decomposition_brute_force` | fan | Functions | Geometry |

`cell_from_subdivision(Polytope P, Int cell)` | polytope | Functions | Producing a polytope from polytopes |

`CELL_SIGNATURES` | fan | property of HyperplaneArrangement | Combinatorics |

`cell_to_signature` | fan | method of HyperplaneArrangement | Combinatorics |

`cells()` | topaz | method of Filtration | no category |

`cells_from_subdivision(Polytope<Scalar> P, Set<Int> cells)` | polytope | Functions | Producing a polytope from polytopes |

`center(Polytope P)` | polytope | Functions | Transformations |

`center_distance(Polytope p)` | polytope | Functions | Geometry |

`CENTERED` | polytope | property of PointConfiguration | Geometry |

`CENTERED` | polytope | property of Polytope | Geometry |

`CENTERED_ZONOTOPE` | polytope | property of Polytope | Geometry |

`CENTRALLY_SYMMETRIC` | polytope | property of Polytope | Geometry |

`CENTROID` | polytope | property of Polytope | Geometry |

`cf2rational(Vector<Integer> v)` | fulton | Functions | Continued fractions |

`ChainComplex<MatrixType>` | topaz | Property_types | Topology |

`change_password` | common | method of PolyDB::Client | Database Access |

`CHARACTER` | group | property of Action | Symmetry |

`CHARACTER_TABLE` | group | property of Group | Symmetry |

`CHARACTERISTIC_POLYNOMIAL` | graph | property of Graph | no category |

`check_basis_exchange_axiom(Array<Set> B)` | matroid | Functions | Other |

`check_cycle_equality(Cycle<Addition> X, Cycle<Addition> Y, Bool check_weights)` | tropical | Functions | Basic polyhedral operations |

`check_fan(Matrix rays, IncidenceMatrix cones)` | fan | Functions | Consistency check |

`check_fan_objects<Coord>(Array<Cone> cones)` | fan | Functions | Consistency check |

`check_flat_axiom(Array<Set> F)` | matroid | Functions | Other |

`check_hyperplane_axiom(Array<Set> H)` | matroid | Functions | Other |

`check_inc(Matrix points, Matrix hyperplanes, String sign, Bool verbose)` | polytope | Functions | Consistency check |

`check_poly(IncidenceMatrix VIF)` | polytope | Functions | Consistency check |

`check_transversality(Matroid M)` | matroid | Functions | Advanced properties |

`check_valuated_basis_axioms(Array<Set<Int>> bases, Vector<TropicalNumber<Addition,Scalar>> valuation)` | matroid | Functions | Other |

`check_valuated_circuit_axioms(Matrix<TropicalNumber<Addition,Scalar>> M)` | matroid | Functions | Other |

`CHIROTOPE` | polytope | property of VectorConfiguration | Matroid properties |

`CHIROTOPE` | polytope | property of Polytope | Matroid properties |

`chirotope(Polytope P)` | polytope | Functions | Triangulations, subdivisions and volume |

`chirotope(VectorConfiguration P)` | polytope | Functions | Triangulations, subdivisions and volume |

`chirotope(Polytope P)` | polytope | Functions | Triangulations, subdivisions and volume |

`chirotope(VectorConfiguration P)` | polytope | Functions | Triangulations, subdivisions and volume |

`circuit_completions(Matrix L, Matrix R)` | polytope | Functions | Geometry |

`CIRCUITS` | matroid | property of Matroid | Axiom systems |

`CIRCUITS` | polytope | property of VectorConfiguration | Matroid properties |

`CIRCUITS` | polytope | property of Polytope | Matroid properties |

`circuits2matrix(Set<Pair<Set<Int>,Set<Int>>> co)` | polytope | Functions | Combinatorics |

`clear(Int r, Int c)` | common | method of Matrix | no category |

`clip_graph(Graph G, Matrix V, Matrix BB)` | graph | Functions | Visualization |

`clique_complex(Graph graph)` | topaz | Functions | Producing a simplicial complex from other objects |

`CLOSED_PSEUDO_MANIFOLD` | topaz | property of SimplicialComplex | Topology |

`coarse_covectors(Matrix<TropicalNumber<Addition,Scalar>> points, Matrix<TropicalNumber<Addition,Scalar>> generators)` | tropical | Functions | Tropical covector decomposition |

`coarse_covectors_of_scalar_vertices(Matrix<Scalar> points, Matrix<TropicalNumber<Addition,Scalar>> generators)` | tropical | Functions | Tropical covector decomposition |

`coarsen(Cycle<Addition> complex, Bool testFan)` | tropical | Functions | Basic polyhedral operations |

`cocircuit_equation_of_ridge(Cone C, Set rho)` | polytope | Functions | Combinatorics |

`COCIRCUIT_EQUATIONS` | polytope | property of QuotientSpace | Combinatorics |

`COCIRCUIT_EQUATIONS` | polytope | property of Cone | Combinatorics |

`COCIRCUIT_EQUATIONS` | polytope | property of PointConfiguration | Combinatorics |

`cocircuit_equations(Cone C, Array<Set> interior_ridge_simplices, Array<Set> interior_simplices)` | polytope | Functions | Combinatorics |

`cocircuit_equations_support_reps(Matrix<Scalar> points, Array<Array<Int>> gens, Array<SetType> rirs, Array<SetType> rmis)` | polytope | Functions | Symmetry |

`COCIRCUITS` | matroid | method of Matroid | Axiom systems |

`COCIRCUITS` | polytope | property of VectorConfiguration | Matroid properties |

`COCIRCUITS` | polytope | property of Polytope | Matroid properties |

`COCUBICAL` | polytope | property of Polytope | Combinatorics |

`COCUBICALITY` | polytope | property of Polytope | Combinatorics |

`COCYCLES` | topaz | property of SimplicialComplex | Topology |

`codegree<Scalar>(Cone P)` | polytope | Functions | Combinatorics |

`codegree<Scalar>(PointConfiguration P)` | polytope | Functions | Combinatorics |

`CODIMENSION_ONE_POLYTOPES` | tropical | property of Cycle | Combinatorics |

`coeff()` | topaz | method of CycleGroup | no category |

`COEFFICIENTS` | fulton | property of TDivisor | Combinatorics |

`COEFFICIENTS` | tropical | property of Hypersurface | no category |

`coefficients_as_vector()` | common | method of UniPolynomial | no category |

`coefficients_as_vector()` | common | method of Polynomial | no category |

`COEFFS` | tropical | property of RationalCurve | Combinatorics |

`coherency_index(Polytope p1, Polytope p2, Matrix points, Vector w1, Vector w2)` | polytope | Functions | Triangulations, subdivisions and volume |

`coherency_index(Matrix points, Vector w1, Vector w2)` | polytope | Functions | Triangulations, subdivisions and volume |

`coherency_index(Polytope p1, Polytope p2)` | polytope | Functions | Triangulations, subdivisions and volume |

`COHOMOLOGY` | topaz | property of SimplicialComplex | Topology |

`col(Int i)` | common | method of Matrix | no category |

`col(Int i)` | common | method of IncidenceMatrix | no category |

`col_to_row_action(Matrix M, Array of)` | group | Functions | Symmetry |

`collect(Element e)` | common | method of Set | no category |

`COLOOPS` | matroid | method of Matroid | Axiom systems |

`Color` | common | Property_types | Visualization |

`colored_ball_from_colored_sphere(SimplicialComplex complex)` | topaz | Functions | Producing a new simplicial complex from others |

`COLORING` | topaz | property of SimplicialComplex | no category |

`COLORING` | topaz | property of SimplicialComplex | Combinatorics |

`cols()` | common | method of Matrix | no category |

`cols()` | common | method of IncidenceMatrix | no category |

`cols` | common | Functions | Data Conversion |

`cols(Matrix A)` | common | Functions | Data Conversion |

`COMBINATORIAL_DIM` | fan | property of PolyhedralFan | Combinatorics |

`COMBINATORIAL_DIM` | polytope | property of Cone | Combinatorics |

`combinatorial_symmetries(PolyhedralFan f)` | fan | Functions | Symmetry |

`combinatorial_symmetries(Polytope p)` | polytope | Functions | Symmetry |

`combinatorial_symmetrized_cocircuit_equations(Cone P, Set<Int> comps)` | polytope | Functions | Symmetry |

`combinatorial_symmetrized_cocircuit_equations(Cone P, Array<SetType> rirs, Array<SetType> rmis, Set<Int> comps)` | polytope | Functions | Symmetry |

`commit` | core | method of Core::BigObject | no category |

`common_refinement(PolyhedralFan f1, PolyhedralFan f2)` | fan | Functions | Producing a fan |

`common_refinement(Matrix points, IncidenceMatrix sub1, IncidenceMatrix sub2, Int dim)` | polytope | Functions | Triangulations, subdivisions and volume |

`common_refinement(Polytope p1, Polytope p2)` | polytope | Functions | Triangulations, subdivisions and volume |

`COMPACTIFICATION` | fan | property of PolyhedralComplex | Combinatorics |

`companion()` | common | method of HermiteNormalForm | no category |

`complement_graph(Graph G)` | graph | Functions | Combinatorics |

`complete(Int n)` | graph | Functions | Producing a graph |

`COMPLETE` | fan | property of PolyhedralFan | Combinatorics |

`complete_bipartite(Int k, Int l)` | graph | Functions | Producing a graph |

`complex_projective_plane()` | topaz | Functions | Producing from scratch |

`COMPLEXITY` | polytope | property of Polytope | Combinatorics |

`compose(Visual::Object vis_obj …)` | common | Functions | Visualization |

`compose(Visual::Container vis_container, Visual::Object vis_obj …)` | common | Functions | Visualization |

`COMPRESSED` | polytope | property of Polytope | Lattice points in cones |

`concat_rows(Matrix A)` | common | Functions | Data Conversion |

`cone(SimplicialComplex complex, Int k)` | topaz | Functions | Producing a new simplicial complex from others |

`cone(Int i)` | fan | method of PolyhedralFan | Combinatorics |

`Cone<Scalar>` | polytope | Objects | no category |

`CONE_AMBIENT_DIM` | polytope | property of Cone | Geometry |

`CONE_AMBIENT_DIM` | polytope | property of Polytope | Geometry |

`CONE_DIM` | polytope | property of Cone | Geometry |

`CONE_DIM` | polytope | property of Polytope | Geometry |

`cone_of_tubing(Graph G, Graph T)` | fan | Functions | Other |

`cone_representative(Int i)` | fan | method of PolyhedralFan | Symmetry |

`CONES` | fan | property of PolyhedralFan | Combinatorics |

`cones_action(PolyhedralFan f, Int k)` | fan | Functions | Symmetry |

`CONES_COMBINATORIAL_DIMS` | fan | property of PolyhedralFan | Combinatorics |

`CONES_DIMS()` | fan | method of PolyhedralFan | Combinatorics |

`CONES_ORBIT_SIZES` | fan | property of PolyhedralFan | Symmetry |

`CONES_REPS` | fan | property of PolyhedralFan | Symmetry |

`congruent(Polytope P1, Polytope P2)` | polytope | Functions | Comparing |

`conjugacy_class<Element>(Action action, Element e)` | group | Functions | Symmetry |

`conjugacy_class<Scalar>(MatrixActionOnVectors<Scalar> action, Matrix<Scalar> e)` | group | Functions | Symmetry |

`CONJUGACY_CLASS_REPRESENTATIVES` | group | property of Action | Symmetry |

`CONJUGACY_CLASS_SIZES` | group | property of Group | Symmetry |

`CONJUGACY_CLASSES` | group | property of Action | Symmetry |

`CONNECTED` | graph | property of Graph | no category |

`CONNECTED()` | topaz | method of SimplicialComplex | Topology |

`CONNECTED` | matroid | property of Matroid | Advanced properties |

`CONNECTED_COMPONENTS` | graph | property of Graph | no category |

`CONNECTED_COMPONENTS()` | topaz | method of SimplicialComplex | Combinatorics |

`CONNECTED_COMPONENTS` | matroid | property of Matroid | Advanced properties |

`connected_sum(SimplicialComplex complex1, SimplicialComplex complex2, Int f1, Int f2)` | topaz | Functions | Producing a new simplicial complex from others |

`CONNECTIVITY` | graph | property of Graph | no category |

`connectivity(Graph<Undirected> graph)` | graph | Functions | Combinatorics |

`CONNECTIVITY()` | topaz | method of SimplicialComplex | Combinatorics |

`CONNECTIVITY()` | polytope | method of Cone | Combinatorics |

`constant_coefficient()` | common | method of UniPolynomial | no category |

`constant_coefficient()` | common | method of Polynomial | no category |

`CONSTRUCTION()` | polytope | method of Visual::SchlegelDiagram | no category |

`Container` | common | Property_types | Artificial |

`containing_normal_cone(Cone P, Vector q)` | polytope | Functions | Geometry |

`containing_outer_cone(Polytope P, Vector q)` | polytope | Functions | Geometry |

`contains(Element e)` | common | method of Set | no category |

`contains(Vector<Scalar> v)` | polytope | method of Cone | Geometry |

`contains_in_interior(Vector<Scalar> v)` | polytope | method of Cone | Geometry |

`contains_monomial(String s)` | ideal | method of Ideal | no category |

`contains_point(Cycle A, Vector<Rational> point)` | tropical | Functions | Basic polyhedral operations |

`CONTINUED_FRACTION` | fulton | property of CyclicQuotient | Input properties |

`CONTINUED_FRACTION` | fulton | property of VersalComponent | Combinatorics |

`contract_edge(Int node1, Int node2)` | common | method of Graph | no category |

`contraction(Matroid m, Set<Int> S)` | matroid | Functions | Producing a matroid from matroids |

`contraction(Matroid m, Int x)` | matroid | Functions | Producing a matroid from matroids |

`contraction(VectorConfiguration C, Int v)` | polytope | Functions | Combinatorics |

`conv(Array<Polytope> P_Array)` | polytope | Functions | Producing a polytope from polytopes |

`convert_to<Target>(` | common | Functions | Data Conversion |

`convert_to<Target>(Vector v)` | common | Functions | Data Conversion |

`convert_to<Target>(Matrix m)` | common | Functions | Data Conversion |

`convert_to<Target>(Polynomial m)` | common | Functions | Data Conversion |

`convert_to<Target>(UniPolynomial m)` | common | Functions | Data Conversion |

`convert_to<Coord>(Cone c)` | polytope | Functions | Coordinate conversions |

`convert_to<Coord>(Polytope P)` | polytope | Functions | Coordinate conversions |

`CONVEX` | fan | property of SubdivisionOfVectors | Geometry |

`CONVEX` | polytope | property of PointConfiguration | Geometry |

`CONVEX_HULL` | polytope | property of PointConfiguration | Geometry |

`COORDINATE_ACTION` | fan | property of PolyhedralComplex | Symmetry |

`COORDINATE_ACTION` | polytope | property of Polytope | Symmetry |

`COORDINATE_LABELS` | polytope | property of Cone | Visualization |

`COORDINATES` | graph | property of GeometricGraph | no category |

`coordinates` | common | method of Plucker | no category |

`COORDINATES` | topaz | property of GeometricSimplicialComplex | no category |

`Core::BigObject` | core | Objects | no category |

`Core::RuleChain` | core | Objects | no category |

`core_point_algo(Polytope p, Rational optLPvalue)` | polytope | Functions | Optimization |

`core_point_algo_Rote(Polytope p, Rational optLPvalue)` | polytope | Functions | Optimization |

`COTRANSVERSAL` | matroid | method of Matroid | Advanced properties |

`count(HASH query)` | common | method of PolyDB::Collection | Database Query Operations |

`count_distinct(HASH query, String property)` | common | method of PolyDB::Collection | Database Query Operations |

`count_mn_cones(Int n, Int k)` | tropical | Functions | Moduli of rational curves |

`count_mn_rays(Int n)` | tropical | Functions | Moduli of rational curves |

`CovectorDecoration` | tropical | Property_types | no category |

`CovectorLattice` | tropical | Objects | Combinatorics |

`COVECTORS` | tropical | property of CovectorLattice | Combinatorics |

`covectors(Matrix<TropicalNumber<Addition,Scalar>> points, Matrix<TropicalNumber<Addition,Scalar>> generators)` | tropical | Functions | Tropical covector decomposition |

`covectors_of_scalar_vertices(Matrix<Scalar> points, Matrix<TropicalNumber<Addition,Scalar>> generators)` | tropical | Functions | Tropical covector decomposition |

`covering_relations(Graph<Directed> P)` | graph | Functions | Posets |

`coxeter_group(String type)` | polytope | Functions | Producing other objects |

`CP_INDICES` | polytope | property of Polytope | no category |

`CQS_MATRIX` | fulton | property of VersalComponent | Combinatorics |

`cramer(Matrix A, Vector b)` | common | Functions | Linear Algebra |

`cramer(Matrix<TropicalNumber> matrix)` | tropical | Functions | Tropical operations |

`create_database_admin()` | common | method of PolyDB::Client | Database Administration |

`create_permissive_schema(Any object …)` | core | Functions | Schemas |

`create_restrictive_schema(Any object)` | core | Functions | Schemas |

`create_user()` | common | method of PolyDB::Client | Database Administration |

`CRITICAL_FACE_VECTOR` | topaz | property of MorseMatching | no category |

`CRITICAL_FACES` | topaz | property of MorseMatching | no category |

`cross<Scalar>(Int d, Scalar scale)` | polytope | Functions | Producing regular polytopes and their generalizations |

`cross_variety<Addition>(Int n, Int k, Rational h, Integer weight)` | tropical | Functions | Creation functions for specific cycles |

`crosscut_complex(Polytope p)` | polytope | Functions | Producing other objects |

`CRUST_GRAPH` | polytope | property of VoronoiPolyhedron | no category |

`CS_PERMUTATION` | polytope | property of Polytope | Geometry |

`cs_quotient(Polytope P)` | polytope | Functions | Quotient spaces |

`cube<Scalar>(Int d, Scalar x_up, Scalar x_low)` | polytope | Functions | Producing regular polytopes and their generalizations |

`cube_complex(Array<Int> x)` | topaz | Functions | Producing from scratch |

`cube_group(Int d)` | group | Functions | Producing a group |

`CUBIC` | tropical | property of LinesInCubic | Defining properties |

`CUBICAL` | polytope | property of Polytope | Combinatorics |

`CUBICAL_H_VECTOR` | polytope | property of Polytope | Combinatorics |

`CUBICALITY` | polytope | property of Polytope | Combinatorics |

`cuboctahedron()` | polytope | Functions | Producing regular polytopes and their generalizations |

`CURVE_EDGE_LENGTHS()` | tropical | method of Cycle | Weights and lattices |

`cutting_functions(Cycle<Addition> F, Vector<Integer> weight_aim)` | tropical | Functions | Inverse problems |

`Cycle<Addition>` | tropical | Objects | no category |

`cycle_graph(Int n)` | graph | Functions | Producing a graph |

`CycleGroup<Scalar>` | topaz | Property_types | Topology |

`CYCLES` | topaz | property of SimplicialComplex | Topology |

`cyclic<Addition>(Int d, Int n)` | tropical | Functions | Producing a tropical polytope |

`cyclic(Int d, Int n)` | polytope | Functions | Producing a polytope from scratch |

`cyclic_caratheodory(Int d, Int n)` | polytope | Functions | Producing a polytope from scratch |

`cyclic_group(Int d)` | group | Functions | Producing a group |

`CyclicQuotient` | fulton | Objects | no category |

`cylinder_2()` | polytope | Functions | Quotient spaces |

`davis_manifold()` | polytope | Functions | Quotient spaces |

`DCEL_DATA` | topaz | property of HyperbolicSurface | no category |

`decomposition_polytope(Cycle A)` | tropical | Functions | Weight space |

`DECORATION` | graph | property of Lattice | Combinatorics |

`deg()` | common | method of UniPolynomial | no category |

`deg()` | common | method of Polynomial | no category |

`DEGENERATE` | fulton | property of NormalToricVariety | Algebraic Geometry |

`degree(Int node)` | common | method of Graph | no category |

`DEGREE` | tropical | property of Cycle | Intersection theory |

`degree(Cycle A)` | tropical | Functions | Intersection theory |

`DEGREE` | group | property of Action | Symmetry |

`degree<Scalar>(PointConfiguration P)` | polytope | Functions | Combinatorics |

`DEGREE_ONE_GENERATORS` | polytope | property of Cone | Lattice points in cones |

`DEGREE_SEQUENCE` | graph | property of Graph | no category |

`DELAUNAY_DIAGRAM` | polytope | property of VoronoiPolyhedron | no category |

`DELAUNAY_GRAPH` | polytope | property of VoronoiPolyhedron | no category |

`DELAUNAY_TRIANGULATION` | polytope | property of VoronoiPolyhedron | no category |

`delaunay_triangulation(VoronoiPolyhedron V)` | polytope | Functions | Triangulations, subdivisions and volume |

`delete_all_edges(Int tail_node, Int head_node)` | common | method of Graph | no category |

`delete_edge` | common | method of Graph | no category |

`delete_node(Int node)` | common | method of Graph | no category |

`delete_user(String user)` | common | method of PolyDB::Client | Database Administration |

`deletion(SimplicialComplex complex, Set<Int> face)` | topaz | Functions | Producing a new simplicial complex from others |

`deletion(Matroid m, Set<Int> S)` | matroid | Functions | Producing a matroid from matroids |

`deletion(Matroid m, Int x)` | matroid | Functions | Producing a matroid from matroids |

`deletion(VectorConfiguration C, Int v)` | polytope | Functions | Combinatorics |

`delocalize()` | tropical | method of Cycle | Local computations |

`delpezzo(Int d, Scalar scale)` | polytope | Functions | Producing a polytope from scratch |

`denominator(Rational a)` | common | Functions | Arithmetic |

`denominator(RationalFunction f)` | common | Functions | Arithmetic |

`denominator(PuiseuxFraction f)` | common | Functions | Arithmetic |

`DENOMINATOR` | tropical | property of RationalFunction | Defining morphisms and functions |

`dense(Vector v)` | common | Functions | Data Conversion |

`dense(Matrix m)` | common | Functions | Data Conversion |

`dense<Element>(SparseVector<Element> v)` | common | Functions | Data Conversion |

`dense<Element>(SparseMatrix<Element> m)` | common | Functions | Data Conversion |

`dense(IncidenceMatrix m)` | common | Functions | Data Conversion |

`dense(Set s, Int dim)` | common | Functions | Data Conversion |

`DEPTH` | ideal | property of Ideal | Commutative algebra |

`description` | core | method of Core::BigObject | no category |

`det(Matrix<` | common | Functions | Linear Algebra |

`diag(Vector d)` | common | Functions | Linear Algebra |

`diag(Matrix m1, Matrix m2)` | common | Functions | Linear Algebra |

`diagonal(Int i)` | common | method of Matrix | no category |

`DIAMETER` | graph | property of Graph | no category |

`DIAMETER()` | polytope | method of Cone | Backward compatibility |

`dihedral_angle(Vector<Scalar> H1, Vector<Scalar> H2)` | polytope | Functions | Geometry |

`DIHEDRAL_ANGLES` | polytope | property of Polytope | Geometry |

`dihedral_group(Int o)` | group | Functions | Producing a group |

`dim()` | common | method of Vector | no category |

`dim()` | common | method of Graph | no category |

`dim` | tropical | method of CovectorLattice | Combinatorics |

`dim` | topaz | method of SimplicialComplex | no category |

`DIM` | topaz | property of SimplicialComplex | Combinatorics |

`dim()` | topaz | method of ChainComplex | no category |

`dim()` | topaz | method of Filtration | no category |

`dim()` | fan | method of PolyhedralFan | Combinatorics |

`DIM()` | fan | method of PolyhedralFan | Geometry |

`DIM` | fan | method of SubdivisionOfPoints | Geometry |

`DIM()` | fan | method of PolyhedralComplex | Geometry |

`DIM` | ideal | property of Ideal | Commutative algebra |

`DIM` | polytope | property of QuotientSpace | Combinatorics |

`dim()` | polytope | method of Cone | Combinatorics |

`DIM()` | polytope | method of Cone | Geometry |

`DIM()` | polytope | method of PointConfiguration | Geometry |

`DIM()` | polytope | method of Polytope | Geometry |

`DIMENSION` | fulton | property of VersalComponent | Combinatorics |

`DIMS` | graph | property of Lattice | Combinatorics |

`direct_sum(Matroid m_1, Matroid m_2)` | matroid | Functions | Producing a matroid from matroids |

`Directed` | common | Property_types | Artificial |

`DIRECTED_BOUNDED_GRAPH` | polytope | property of LinearProgram | no category |

`DIRECTED_GRAPH` | polytope | property of LinearProgram | no category |

`DIRECTED_GRAPH(LinearProgram lp)` | polytope | method of Visual::Polytope | no category |

`DIRECTED_GRAPH(LinearProgram lp)` | polytope | method of Visual::PolytopeGraph | no category |

`DIRECTED_GRAPH(LinearProgram lp)` | polytope | method of Visual::SchlegelDiagram | no category |

`DirectedMulti` | common | Property_types | Artificial |

`disable_rules(String pattern)` | core | method of Core::BigObject | no category |

`disable_rules(String pattern)` | core | Functions | Basic |

`disjoint_union(SimplicialComplex complex1, SimplicialComplex complex2)` | topaz | Functions | Producing a new simplicial complex from others |

`distance_matrix(Matrix S, CODE d)` | common | Functions | Utilities |

`distinct(HASH query, String property)` | common | method of PolyDB::Collection | Database Query Operations |

`Div<Scalar>` | common | Property_types | Arithmetic |

`div(` | common | Functions | Arithmetic |

`div_exact(Int a)` | common | method of Matrix | no category |

`div_exact(Int a)` | common | method of Vector | no category |

`div_exact(Integer a, Integer b)` | common | Functions | Arithmetic |

`division` | ideal | method of Groebner | no category |

`DIVISOR` | fulton | property of NormalToricVariety | Algebraic Geometry |

`divisor(Cycle C, RationalFunction F)` | tropical | Functions | Divisor computation |

`divisor_nr(Cycle C, RationalFunction F)` | tropical | Functions | Divisor computation |

`dodecahedron()` | polytope | Functions | Producing regular polytopes and their generalizations |

`DOMAIN` | tropical | property of RationalFunction | Defining morphisms and functions |

`DOMAIN` | tropical | property of Morphism | Defining morphisms and functions |

`DOMAIN_NAME` | group | property of Action | Symmetry |

`DOME` | tropical | property of Hypersurface | no category |

`DOME` | tropical | property of Polytope | Geometry |

`dont_save` | core | method of Core::BigObject | no category |

`DUAL` | matroid | property of Matroid | Duality |

`dual(Matroid m)` | matroid | Functions | Producing a matroid from matroids |

`dual(ValuatedMatroid<Addition,Scalar> M)` | matroid | Functions | Producing a matroid from matroids |

`dual_addition_version(Polytope<Addition,Scalar> polytope, Bool strong_conversion)` | tropical | Functions | Conversion of tropical addition |

`dual_addition_version(TropicalNumber<Addition,Scalar> number, Bool strong_conversion)` | tropical | Functions | Conversion of tropical addition |

`dual_addition_version(Vector<TropicalNumber<Addition,Scalar>> vector, Bool strong_conversion)` | tropical | Functions | Conversion of tropical addition |

`dual_addition_version(Matrix<TropicalNumber<Addition,Scalar>> matrix, Bool strong_conversion)` | tropical | Functions | Conversion of tropical addition |

`dual_addition_version(Polynomial<TropicalNumber<Addition,Scalar>> polynomial, Bool strong_conversion)` | tropical | Functions | Conversion of tropical addition |

`dual_addition_version(Cycle<Addition> cycle, Bool strong_conversion)` | tropical | Functions | Conversion of tropical addition |

`dual_addition_version(MatroidRingCycle<Addition> M)` | tropical | Functions | Conversion of tropical addition |

`DUAL_BIPARTITE()` | topaz | method of SimplicialComplex | Combinatorics |

`DUAL_BOUNDED_H_VECTOR` | polytope | property of Polytope | Combinatorics |

`DUAL_CONNECTED()` | topaz | method of SimplicialComplex | Topology |

`DUAL_CONNECTED_COMPONENTS()` | topaz | method of SimplicialComplex | Combinatorics |

`DUAL_CONNECTIVITY()` | topaz | method of SimplicialComplex | Combinatorics |

`DUAL_CONNECTIVITY()` | polytope | method of Cone | Combinatorics |

`DUAL_CONTINUED_FRACTION` | fulton | property of CyclicQuotient | Input properties |

`DUAL_DIAMETER()` | polytope | method of Cone | Backward compatibility |

`DUAL_EVEN()` | polytope | method of Cone | Combinatorics |

`dual_faces()` | graph | method of Lattice | Combinatorics |

`DUAL_GRAPH` | topaz | property of SimplicialComplex | Combinatorics |

`DUAL_GRAPH` | fan | property of PolyhedralFan | Combinatorics |

`DUAL_GRAPH` | polytope | property of Cone | Combinatorics |

`DUAL_GRAPH` | polytope | property of Polytope | Combinatorics |

`DUAL_GRAPH_SIGNATURE()` | topaz | method of SimplicialComplex | Combinatorics |

`DUAL_GRAPH_SIGNATURE()` | polytope | method of Cone | Topology |

`DUAL_H_VECTOR` | polytope | property of Polytope | Combinatorics |

`dual_linear_program(Polytope P, Bool maximize)` | polytope | Functions | Producing a polytope from polytopes |

`DUAL_MAX_CLIQUES()` | topaz | method of SimplicialComplex | Combinatorics |

`DUAL_SUBDIVISION` | tropical | property of Hypersurface | Combinatorics |

`dual_subdivision()` | tropical | method of Hypersurface | Combinatorics |

`DUAL_TREE` | fan | property of PlanarNet | Combinatorics |

`DUAL_TRIANGLE_FREE()` | polytope | method of Cone | Backward compatibility |

`dualOutitudePolynomials(Array<Array<Int>> dcel_data)` | topaz | Functions | Other |

`dwarfed_cube(Int d)` | polytope | Functions | Producing a polytope from scratch |

`dwarfed_product_polygons(Int d, Int s)` | polytope | Functions | Producing a polytope from scratch |

`edge(Int tail_node, Int head_node)` | common | method of Graph | no category |

`edge(Int from, Int to)` | common | method of EdgeHashMap | no category |

`edge(Int from, Int to)` | common | method of EdgeMap | no category |

`EDGE_COLORS()` | polytope | method of Visual::PolytopeGraph | no category |

`EDGE_COLORS` | polytope | property of Polytope | no category |

`edge_contraction(SimplicialComplex complex)` | topaz | Functions | Producing a new simplicial complex from others |

`EDGE_DIRECTIONS` | polytope | property of Polytope | no category |

`EDGE_DIRECTIONS` | polytope | property of Polytope | Geometry |

`edge_exists(Int tail_node, Int head_node)` | common | method of Graph | no category |

`edge_lengths(Graph<Directed> G, Matrix coords)` | graph | Functions | Other |

`EDGE_LENGTHS` | polytope | property of Polytope | no category |

`edge_middle(Polytope P)` | polytope | Functions | Producing a polytope from polytopes |

`EDGE_ORIENTABLE` | polytope | property of Polytope | Combinatorics |

`edge_orientable(Polytope P)` | polytope | Functions | Other |

`EDGE_ORIENTATION` | polytope | property of Polytope | Combinatorics |

`EDGE_WEIGHTS` | topaz | property of SimplicialComplex | no category |

`EdgeHashMap<Dir, Element>` | common | Property_types | Graph Types |

`EdgeIterator` | common | Property_types | Artificial |

`EdgeList` | common | Property_types | Artificial |

`EdgeMap<Dir, Element>` | common | Property_types | Graph Types |

`EDGES()` | graph | method of Graph | Combinatorics |

`edges()` | common | method of Graph | no category |

`edges(Graph graph)` | common | Functions | Graph Operations |

`EFFECTIVE` | fulton | property of TDivisor | Algebraic Geometry |

`EFFECTIVE_CONE` | fulton | property of NormalToricVariety | Algebraic Geometry |

`EHRHART_POLYNOMIAL` | polytope | property of Polytope | Lattice points in cones |

`EHRHART_POLYNOMIAL_COEFF()` | polytope | method of Polytope | Lattice points in cones |

`EHRHART_QUASI_POLYNOMIAL` | polytope | property of Polytope | Lattice points in cones |

`eigenvalues(Matrix<Float> A)` | common | Functions | Linear Algebra |

`EIGENVALUES_LAPLACIAN` | graph | property of Graph | no category |

`eigenvalues_laplacian(Graph G)` | graph | Functions | Combinatorics |

`eigenvalues_laplacian(Graph G)` | graph | Functions | Combinatorics |

`elem(Int r, Int c)` | common | method of Matrix | no category |

`elem(Int r, Int c)` | common | method of IncidenceMatrix | no category |

`eliminate_denominators(Vector v)` | common | Functions | Lattice Tools |

`eliminate_denominators_entire(Matrix v)` | common | Functions | Lattice Tools |

`eliminate_denominators_entire_affine(Matrix v)` | common | Functions | Lattice Tools |

`eliminate_denominators_in_rows(Matrix M)` | common | Functions | Lattice Tools |

`embed(Int nvars)` | common | method of Polynomial | no category |

`empty_cycle<Addition>(Int ambient_dim)` | tropical | Functions | Creation functions for specific cycles |

`ENVELOPE` | tropical | property of Polytope | Geometry |

`EPSILON` | polytope | property of Cone | Geometry |

`equal_bases(Matrix M1, Matrix M2)` | common | Functions | Linear Algebra |

`equal_polyhedra(Polytope P1, Polytope P2)` | polytope | Functions | Comparing |

`EQUATIONS` | polytope | property of Cone | Input property |

`EQUATIONS` | polytope | property of Polytope | Input property |

`EQUATIONS_GENERATORS` | group | property of Action | Symmetry |

`erase(Set f)` | common | method of FacetList | no category |

`erase(Int from, Int to)` | common | method of EdgeHashMap | no category |

`eraseSubsets(Set s)` | common | method of FacetList | no category |

`eraseSupersets(Set s)` | common | method of FacetList | no category |

`ESSENTIALLY_GENERIC` | polytope | property of Cone | Combinatorics |

`EULER_CHARACTERISTIC` | topaz | property of SimplicialComplex | Topology |

`evaluate(Coefficient x, Exponent exp)` | common | method of UniPolynomial | no category |

`evaluate(PuiseuxFraction f, ` | common | Functions | no category |

`evaluate(Matrix m, Coefficient x, Int exp)` | common | Functions | no category |

`evaluate(Vector v, Coefficient x, Int exp)` | common | Functions | no category |

`evaluate_float(Float x)` | common | method of UniPolynomial | no category |

`evaluate_float(PuiseuxFraction f, Float x)` | common | Functions | no category |

`evaluate_float(Matrix m, Float x)` | common | Functions | no category |

`evaluate_float(Vector v, Float x)` | common | Functions | no category |

`evaluation_map<Addition>(Int n, Matrix<Rational> Delta, Int i)` | tropical | Functions | Moduli of rational curves |

`evaluation_map<Addition>(Int n, Int r, Int d, Int i)` | tropical | Functions | Moduli of rational curves |

`EVEN()` | polytope | method of Cone | Combinatorics |

`EXCESS_FACET_DEGREE` | polytope | property of Cone | Combinatorics |

`EXCESS_RAY_DEGREE` | polytope | property of Cone | Combinatorics |

`EXCESS_VERTEX_DEGREE` | polytope | property of Polytope | Combinatorics |

`exit` | core | Functions | Interactive |

`EXPLICIT_ORBIT_REPRESENTATIVE_MATRIX` | group | property of Action | Symmetry |

`EXPLICIT_ORBIT_REPRESENTATIVES` | group | property of Action | Symmetry |

`explicit_zonotope(Matrix zones)` | polytope | Functions | Producing a polytope from scratch |

`export_configured(String filename)` | core | Functions | Interactive |

`ext_gcd(` | common | Functions | Arithmetic |

`extend_application(String extension, String app_name)` | core | Functions | Interactive |

`ExtGCD<Scalar>` | common | Property_types | Arithmetic |

`F2_VECTOR` | topaz | property of SimplicialComplex | Combinatorics |

`F2_VECTOR` | fan | property of PolyhedralFan | Combinatorics |

`F2_VECTOR` | polytope | property of Cone | Combinatorics |

`F2_VECTOR` | polytope | property of Polytope | Combinatorics |

`f8_matroid()` | matroid | Functions | Producing a matroid from scratch |

`F_VECTOR` | topaz | property of SimplicialComplex | Combinatorics |

`F_VECTOR` | matroid | property of Matroid | Advanced properties |

`F_VECTOR` | fan | property of PolyhedralFan | Combinatorics |

`F_VECTOR` | polytope | property of QuotientSpace | Combinatorics |

`F_VECTOR` | polytope | property of Cone | Combinatorics |

`F_VECTOR` | polytope | property of Polytope | Combinatorics |

`fac(Int n)` | common | Functions | Arithmetic |

`face()` | graph | method of BasicDecoration | no category |

`face(Cone P, Set S)` | polytope | Functions | Producing a polytope from polytopes |

`face_fan<Coord>(Polytope p, Vector v)` | fan | Functions | Producing a fan |

`face_fan<Coord>(Polytope p)` | fan | Functions | Producing a fan |

`FACE_ORBITS` | polytope | property of QuotientSpace | Combinatorics |

`face_pair(Cone P, Set S)` | polytope | Functions | Other |

`FACE_SIMPLICITY` | polytope | property of Polytope | Combinatorics |

`FACES` | graph | property of Lattice | Combinatorics |

`FACES(String PROPERTY_NAME)` | topaz | method of Visual::SimplicialComplex | no category |

`FACES(Array<Set> faces)` | topaz | method of Visual::SimplicialComplexLattice | no category |

`faces()` | topaz | method of CycleGroup | no category |

`FACES` | polytope | property of QuotientSpace | Combinatorics |

`faces_of_dim(Cone c)` | polytope | method of Cone | Combinatorics |

`faces_of_dim(PointConfiguration p)` | polytope | method of PointConfiguration | Combinatorics |

`FACET` | polytope | property of SchlegelDiagram | no category |

`facet(Cone P, Int facet)` | polytope | Functions | Producing a polytope from polytopes |

`facet_arrangement` | fan | Functions | Producing a hyperplane arrangement |

`FACET_DEGREES()` | polytope | method of Cone | Combinatorics |

`FACET_LABELS` | polytope | property of Cone | Visualization |

`FACET_LABELS` | polytope | property of Polytope | Visualization |

`facet_normal(Int i, Int j)` | tropical | method of Cycle | Combinatorics |

`FACET_NORMALS` | fan | property of PolyhedralFan | Geometry |

`FACET_NORMALS_ACTION` | group | property of Group | Symmetry |

`FACET_NORMALS_BY_PAIRS` | tropical | property of Cycle | Combinatorics |

`FACET_POINT` | polytope | property of SchlegelDiagram | no category |

`FACET_POINT_LATTICE_DISTANCES(Vector<Rational> v)` | polytope | method of Polytope | Lattice points in cones |

`FACET_SIZES` | polytope | property of Cone | Combinatorics |

`facet_to_infinity(Polytope P, Int i)` | polytope | Functions | Producing a polytope from polytopes |

`FACET_TRIANGULATIONS` | polytope | property of Cone | no category |

`FACET_TRIANGULATIONS` | polytope | property of PointConfiguration | Triangulation and volume |

`FACET_VERTEX_LATTICE_DISTANCES` | polytope | property of Polytope | Lattice points in cones |

`FACET_VOLUMES` | polytope | property of Polytope | Geometry |

`FACET_WIDTH` | polytope | property of Polytope | Lattice points in cones |

`FACET_WIDTHS` | polytope | property of Polytope | Lattice points in cones |

`FacetList` | common | Property_types | Set Types |

`FACETS` | topaz | property of SimplicialComplex | Combinatorics |

`FACETS` | polytope | property of Cone | Geometry |

`FACETS_ACTION` | group | property of Group | Symmetry |

`FACETS_GENERATORS` | group | property of Action | Symmetry |

`FACETS_THRU_INPUT_RAYS` | polytope | property of Cone | Geometry |

`FACETS_THRU_POINTS` | polytope | property of Polytope | Geometry |

`FACETS_THRU_RAYS` | polytope | property of Cone | Combinatorics |

`FACETS_THRU_VERTICES` | polytope | property of Polytope | Combinatorics |

`FAN_AMBIENT_DIM` | fan | property of PolyhedralFan | Geometry |

`fan_decomposition(Cycle<Addition> C)` | tropical | Functions | Basic polyhedral operations |

`FAN_DIM` | fan | property of PolyhedralFan | Geometry |

`FANO` | fulton | property of NormalToricVariety | Algebraic Geometry |

`fano_matroid()` | matroid | Functions | Producing a matroid from scratch |

`fano_simplex(Int d)` | polytope | Functions | Producing a polytope from scratch |

`FAR_FACE` | polytope | property of Polytope | Unbounded polyhedra |

`FAR_HYPERPLANE` | polytope | property of Polytope | Geometry |

`FAR_POINTS` | polytope | property of PointConfiguration | Geometry |

`FAR_PSEUDOVERTICES` | tropical | property of Polytope | Geometry |

`FAR_VERTICES` | fan | property of PolyhedralComplex | Geometry |

`FATNESS` | polytope | property of Polytope | Combinatorics |

`FEASIBLE` | tropical | property of Polytope | Geometry |

`FEASIBLE` | polytope | property of Polytope | Geometry |

`fiber_polytope(PointConfiguration pc, PointConfiguration pc)` | polytope | Functions | Triangulations, subdivisions and volume |

`fiber_polytope(PointConfiguration pc, Polytope pc)` | polytope | Functions | Triangulations, subdivisions and volume |

`fiber_polytope(PointConfiguration P, Matrix pi)` | polytope | Functions | Triangulations, subdivisions and volume |

`fibonacci(Int n)` | common | Functions | Combinatorics |

`fibonacci2(Int n)` | common | Functions | Combinatorics |

`fibonacci_numbers(Int m)` | common | Functions | Utilities |

`Filtration<MatrixType>` | topaz | Property_types | Topology |

`find(HASH query)` | common | method of PolyDB::Collection | Database Query Operations |

`find(Set f)` | common | method of FacetList | no category |

`find(Int from, Int to)` | common | method of EdgeHashMap | no category |

`find_facet_vertex_permutations(SimplicialComplex complex1, SimplicialComplex complex2)` | topaz | Functions | Comparing |

`find_facet_vertex_permutations(Cone P1, Cone P2)` | polytope | Functions | Comparing |

`find_lattice_permutation(Lattice L1, Lattice L2, Permutation permutation)` | graph | Functions | Combinatorics |

`find_node_permutation(Graph graph1, Graph graph2)` | graph | Functions | Comparing |

`find_one(HASH query)` | common | method of PolyDB::Collection | Database Query Operations |

`find_permutation(Array a, Array b)` | common | Functions | Combinatorics |

`find_row_col_permutation(IncidenceMatrix<NonSymmetric> m1, IncidenceMatrix<NonSymmetric> m2)` | graph | Functions | Comparing |

`find_transitive_lp_sol(Matrix Inequalities)` | polytope | Functions | Optimization |

`findSubsets(Set s)` | common | method of FacetList | no category |

`findSupersets(Set s)` | common | method of FacetList | no category |

`FLAG_VECTOR` | polytope | property of Cone | Combinatorics |

`FLAPS` | fan | property of PlanarNet | Combinatorics |

`FLAPS()` | fan | method of Visual::PlanarNet | no category |

`Flexible` | common | Property_types | Visualization |

`flip_tube(Graph G, Graph T, Int t)` | fan | Functions | Other |

`FLIP_WORDS` | topaz | property of HyperbolicSurface | no category |

`flips_to_canonical_triangulation(Array<Array<Int>> DCEL_data, Vector<Rational> A_coords)` | topaz | Functions | Other |

`Float` | common | Property_types | Basic Types |

`floor(Rational a)` | common | Functions | Arithmetic |

`flow_polytope<Scalar>(Graph<Directed> G, EdgeMap<Directed,Scalar> Arc_Bounds, Int source, Int sink)` | polytope | Functions | Producing a polytope from graphs |

`flow_polytope<Scalar>(Graph<Directed> G, Array<Scalar> Arc_Bounds, Int source, Int sink)` | polytope | Functions | Producing a polytope from graphs |

`FOLDABLE` | topaz | property of SimplicialComplex | Combinatorics |

`FOLDABLE_COCIRCUIT_EQUATIONS` | polytope | property of Cone | Combinatorics |

`foldable_max_signature_ilp(Int d, Matrix points, Rational volume, SparseMatrix cocircuit_equations)` | polytope | Functions | Triangulations, subdivisions and volume |

`FOLDABLE_MAX_SIGNATURE_UPPER_BOUND` | polytope | property of Polytope | Combinatorics |

`foldable_max_signature_upper_bound(Int d, Matrix points, Rational volume, SparseMatrix cocircuit_equations)` | polytope | Functions | Triangulations, subdivisions and volume |

`foldable_prism(GeometricSimplicialComplex complex)` | topaz | Functions | Producing a new simplicial complex from others |

`forgetful_map<Addition>(Int n, Set<Int> S)` | tropical | Functions | Moduli of rational curves |

`form()` | common | method of SmithNormalForm | no category |

`found_application(String extension, String app_name)` | core | Functions | Interactive |

`found_extension(String dirname)` | core | Functions | Interactive |

`fractional_cut_polytope(Graph G)` | polytope | Functions | Producing a polytope from graphs |

`fractional_knapsack(Vector<Rational> b)` | polytope | Functions | Producing a polytope from scratch |

`fractional_matching_polytope(Graph G)` | polytope | Functions | Producing a polytope from graphs |

`free_extension(Matroid M)` | matroid | Functions | Producing a matroid from matroids |

`free_sum(Polytope P1, Polytope P2)` | polytope | Functions | Producing a polytope from polytopes |

`free_sum(VectorConfiguration P1, VectorConfiguration P2)` | polytope | Functions | Producing a vector configuration |

`free_sum_decomposition(Polytope P)` | polytope | Functions | Producing a polytope from polytopes |

`free_sum_decomposition_indices(Polytope P)` | polytope | Functions | Producing a polytope from polytopes |

`front()` | common | method of Set | no category |

`FTR_CYCLIC_NORMAL` | polytope | property of Cone | Visualization |

`FTV_CYCLIC_NORMAL` | polytope | property of Polytope | Visualization |

`FULL_DIM` | fan | property of PolyhedralFan | Geometry |

`FULL_DIM` | fan | property of SubdivisionOfVectors | Geometry |

`FULL_DIM` | polytope | property of VectorConfiguration | Geometry |

`FULL_DIM` | polytope | property of Cone | Geometry |

`fundamental2gap(String filename)` | topaz | method of SimplicialComplex | Topology |

`FUNDAMENTAL_GROUP` | topaz | property of SimplicialComplex | Topology |

`FUNDAMENTAL_GROUP_GEN_LABELS` | topaz | property of SimplicialComplex | Topology |

`g()` | common | method of ExtGCD | no category |

`G_DIM` | topaz | property of GeometricSimplicialComplex | no category |

`G_INVARIANT` | matroid | property of Matroid | Advanced properties |

`G_VECTOR` | polytope | property of Polytope | Combinatorics |

`GALE()` | polytope | method of Polytope | Visualization |

`GALE_TRANSFORM` | polytope | property of VectorConfiguration | Geometry |

`GALE_TRANSFORM` | polytope | property of Polytope | Geometry |

`GALE_VERTICES` | polytope | property of Polytope | Visualization |

`gc_closure(Polytope P)` | polytope | Functions | Producing a polytope from polytopes |

`gcd(Int a, Int b)` | common | Functions | Arithmetic |

`gcd(Vector<` | common | Functions | Arithmetic |

`gcd(UniPolynomial p, UniPolynomial q)` | common | Functions | Arithmetic |

`generalized_johnson_graph(Int n, Int k, Int i)` | graph | Functions | Producing a graph |

`generating_polyhedron_facets(PolyhedralFan P)` | fan | Functions | Geometry |

`GENERATING_POLYTOPE` | fulton | property of NormalToricVariety | Basic properties |

`GENERATORS` | group | property of Action | Symmetry |

`GENERATORS` | ideal | property of Ideal | Input properties |

`GENUS` | tropical | method of Hypersurface | Topology |

`GENUS` | topaz | property of SimplicialComplex | Topology |

`GeometricGraph<Scalar>` | graph | Objects | Combinatorics |

`GeometricSimplicialComplex<Scalar>` | topaz | Objects | no category |

`geomview(Visual::Object vis_obj …)` | common | Functions | Visualization |

`get_attachment(String name)` | core | method of Core::BigObject | no category |

`get_collection(String name)` | common | method of PolyDB::Client | Database Access |

`get_map()` | graph | method of InverseRankMap | Combinatorics |

`get_schedule(String property_name)` | core | method of Core::BigObject | no category |

`get_schema()` | common | method of PolyDB::Collection | Database Access |

`get_users(ARRAY usernames)` | common | method of PolyDB::Client | Database Administration |

`get_var_names` | common | method of UniPolynomial | no category |

`get_var_names` | common | method of Polynomial | no category |

`get_var_names()` | common | Functions | Arithmetic |

`GF2` | common | Property_types | Basic Types |

`gfan_secondary_fan(Matrix M)` | fan | Functions | Producing a fan |

`gfan_secondary_fan(PointConfiguration P)` | fan | Functions | Producing a fan |

`gfan_tropicalbruteforce(Ideal I)` | tropical | Functions | gfan |

`gfan_tropicalhypersurface(Polynomial<Rational> p)` | tropical | Functions | gfan |

`gfan_tropicalintersection(Ideal I)` | tropical | Functions | gfan |

`gfan_tropicalvariety_of_prime(Ideal I)` | tropical | Functions | gfan |

`give(String property_name, Any multi_choice)` | core | method of Core::BigObject | no category |

`gkz_dome(Int k, Int depth)` | topaz | method of HyperbolicSurface | Other |

`GKZ_VECTOR` | polytope | property of PointConfiguration | Triangulation and volume |

`GKZ_VECTOR` | polytope | property of Polytope | Triangulation and volume |

`GKZ_VECTORS(Int depth)` | topaz | method of HyperbolicSurface | Other |

`goldfarb(Int d, Scalar e, Scalar g)` | polytope | Functions | Producing a polytope from scratch |

`goldfarb_sit(Int d, Scalar eps, Scalar delta)` | polytope | Functions | Producing a polytope from scratch |

`GORENSTEIN` | fan | property of PolyhedralFan | Toric Varieties |

`GORENSTEIN` | polytope | property of Polytope | Lattice points in cones |

`GORENSTEIN_CONE` | polytope | property of Cone | Lattice points in cones |

`GORENSTEIN_INDEX` | polytope | property of Polytope | Lattice points in cones |

`GORENSTEIN_VECTOR` | polytope | property of Polytope | Lattice points in cones |

`Graph<Dir>` | graph | Objects | Combinatorics |

`Graph<Dir>` | common | Property_types | Graph Types |

`GRAPH` | tropical | property of RationalCurve | Combinatorics |

`GRAPH` | topaz | property of SimplicialComplex | Combinatorics |

`GRAPH` | fan | property of PolyhedralFan | Combinatorics |

`GRAPH` | polytope | property of Cone | Combinatorics |

`GRAPH` | polytope | property of PointConfiguration | Combinatorics |

`GRAPH` | polytope | property of Polytope | Combinatorics |

`GRAPH` | polytope | property of Polytope | Combinatorics |

`graph_associahedron_fan(Graph G)` | fan | Functions | Producing a fan |

`GRAPH_EDGE_LENGTHS` | tropical | property of RationalCurve | Combinatorics |

`graph_from_cycles` | graph | Functions | no category |

`graph_from_edges(Array<Set<Int>> edges)` | graph | Functions | Other |

`graph_homomorphisms(Graph G, Graph H)` | graph | Functions | Combinatorics |

`GRAPH_SIGNATURE()` | topaz | method of SimplicialComplex | Combinatorics |

`GRAPH_SIGNATURE()` | polytope | method of Cone | Topology |

`GraphMap<Dir, Element>` | common | Property_types | Graph Types |

`graphviz(Visual::Object vis_obj …)` | graph | Functions | Visualization |

`GROEBNER` | ideal | property of Ideal | Commutative algebra |

`Groebner` | ideal | Objects | no category |

`GROEBNER_BASIS` | polytope | property of Polytope | Lattice points in cones |

`groebner_fan(Ideal I)` | fan | Functions | Producing a fan |

`GroebnerBasis` | polytope | Objects | Lattice points in cones |

`GROUP` | topaz | property of SimplicialComplex | Symmetry |

`Group` | group | Objects | no category |

`GROUP` | fan | property of PolyhedralFan | Symmetry |

`GROUP` | fan | property of PolyhedralComplex | Symmetry |

`GROUP` | polytope | property of VectorConfiguration | Symmetry |

`GROUP` | polytope | property of Cone | Symmetry |

`GROUP` | polytope | property of PointConfiguration | Symmetry |

`GROUP` | polytope | property of Polytope | Symmetry |

`group_from_cyclic_notation0(String generators)` | group | Functions | Producing a group |

`group_from_cyclic_notation1(String generators)` | group | Functions | Producing a group |

`group_from_permlib_cyclic_notation(Array<String> gens, Int degree)` | group | Functions | Producing a group |

`group_left_multiplication_table(Group G)` | group | Functions | Symmetry |

`group_right_multiplication_table(Group G)` | group | Functions | Symmetry |

`gudkov_curve()` | tropical | Functions | no category |

`h_induced_quotient(SimplicialComplex C, Set<Int> vertices)` | topaz | Functions | Producing a new simplicial complex from others |

`H_STAR_VECTOR` | polytope | property of Cone | Lattice points in cones |

`H_VECTOR` | topaz | property of SimplicialComplex | Combinatorics |

`H_VECTOR` | matroid | property of Matroid | Advanced properties |

`H_VECTOR` | polytope | property of Polytope | Combinatorics |

`hadamard_product(Matrix M1, Matrix M2)` | common | Functions | Linear Algebra |

`halfspace_subdivision<Addition>(Rational a, Vector<Rational> g, Integer w)` | tropical | Functions | Creation functions for specific cycles |

`harnack_curve(Int d)` | tropical | Functions | no category |

`has_gaps()` | common | method of Graph | no category |

`HashMap<Key, Value>` | common | Property_types | Set Types |

`HashSet<Element>` | common | Property_types | Set Types |

`HASSE_DIAGRAM` | topaz | property of SimplicialComplex | Combinatorics |

`HASSE_DIAGRAM` | fan | property of PolyhedralFan | Combinatorics |

`HASSE_DIAGRAM` | polytope | property of Cone | Combinatorics |

`HASSE_DIAGRAM` | polytope | property of Polytope | Combinatorics |

`hd_embedder(Array label_width)` | graph | Functions | Visualization |

`help(String item)` | core | Functions | Interactive |

`hermite_normal_form(Matrix M)` | common | Functions | Linear Algebra |

`HermiteNormalForm<Scalar>` | common | Property_types | Linear Algebra |

`higgs_lift(Matroid M)` | matroid | Functions | Producing a matroid from matroids |

`HILBERT_BASIS()` | polytope | method of Cone | Lattice points in cones |

`HILBERT_BASIS_GENERATORS` | polytope | property of Cone | Lattice points in cones |

`HILBERT_POLYNOMIAL` | ideal | property of Ideal | Commutative algebra |

`HILBERT_SERIES` | polytope | property of Cone | Lattice points in cones |

`hirzebruch_surface(Integer r)` | fulton | Functions | Producing a normal toric variety |

`histogram(ARRAY data)` | common | Functions | Utilities |

`history` | core | Functions | Interactive |

`hnf()` | common | method of HermiteNormalForm | no category |

`hom_poset(Graph<Directed> P, Graph<Directed> Q)` | graph | Functions | Posets |

`hom_poset(Array<Array<Int>> homs, Graph<Directed> Q)` | graph | Functions | Posets |

`HOMOGENEOUS` | ideal | property of Ideal | Commutative algebra |

`HOMOGENEOUS` | polytope | property of Cone | Lattice points in cones |

`HOMOGENEOUS_COORDINATE_ACTION` | group | property of Group | Symmetry |

`HOMOLOGY` | topaz | property of SimplicialComplex | Topology |

`homology(Array<Set<Int>> complex, Bool co)` | topaz | Functions | Topology |

`homology(ChainComplex CC, Bool co)` | topaz | Functions | Topology |

`HOMOLOGY` | fan | property of PolyhedralFan | Topology |

`homology_and_cycles(Array<Set<Int>> complex, Bool co)` | topaz | Functions | Topology |

`homology_and_cycles(ChainComplex<SparseMatrix<Integer>> CC, Bool co)` | topaz | Functions | Topology |

`homology_flint(Array<Set<Int>> complex, Bool co)` | topaz | Functions | Topology |

`homology_flint(ChainComplex CC, Bool co)` | topaz | Functions | Topology |

`HomologyGroup<Scalar>` | topaz | Property_types | Topology |

`householder_trafo(Vector<Float> b)` | common | Functions | Linear Algebra |

`HSV` | common | Property_types | Visualization |

`hurwitz_cycle<Addition>(Int k, Vector<Int> degree, Vector<Rational> points)` | tropical | Functions | Hurwitz cycles |

`hurwitz_marked_cycle<Addition>(Int k, Vector<Int> degree, Vector<Rational> pullback_points)` | tropical | Functions | Hurwitz cycles |

`hurwitz_pair<Addition>(Int k, Vector<Int> degree, Vector<Rational> points)` | tropical | Functions | Hurwitz cycles |

`hurwitz_pair_local<Addition>(Int k, Vector<Int> degree, RationalCurve local_curve)` | tropical | Functions | Hurwitz cycles |

`hurwitz_subdivision<Addition>(Int k, Vector<Int> degree, Vector<Rational> points)` | tropical | Functions | Hurwitz cycles |

`HyperbolicSurface` | topaz | Objects | no category |

`hyperplane<Addition>(Vector<TropicalNumber<Addition>> coeffs)` | tropical | Functions | Producing a tropical hypersurface |

`HYPERPLANE_LABELS` | fan | property of HyperplaneArrangement | no category |

`HyperplaneArrangement<Scalar>` | fan | Objects | Geometry |

`HYPERPLANES` | fan | property of HyperplaneArrangement | Geometry |

`hypersimplex<Addition>(Int d, Int k)` | tropical | Functions | Producing a tropical polytope |

`hypersimplex(Int k, Int d)` | polytope | Functions | Producing a polytope from scratch |

`hypersimplex_vertex_splits(Int k, Int d)` | fan | Functions | Producing a hyperplane arrangement |

`Hypersurface<Addition>` | tropical | Objects | no category |

`hypertruncated_cube<Scalar>(Int d, Scalar k, Scalar lambda)` | polytope | Functions | Producing a polytope from scratch |

`icosahedron()` | polytope | Functions | Producing regular polytopes and their generalizations |

`icosidodecahedron()` | polytope | Functions | Producing regular polytopes and their generalizations |

`Ideal` | ideal | Objects | no category |

`IDENTICALLY_SELF_DUAL` | matroid | property of Matroid | Advanced properties |

`IDENTIFICATION_ACTION` | polytope | property of QuotientSpace | Basic properties |

`IMAGES` | group | property of Action | Symmetry |

`implicit_character(ImplicitActionOnSets A)` | group | Functions | Symmetry |

`IMPLICIT_SET_ACTION` | group | property of Group | Symmetry |

`ImplicitActionOnSets` | group | Objects | no category |

`import_extension(String dirname, String options)` | core | Functions | Interactive |

`in_adjacent_nodes(Int node)` | common | method of Graph | no category |

`in_degree(Int node)` | common | method of Graph | no category |

`in_edges(Int node)` | common | method of Graph | no category |

`incidence_matrix(Graph G)` | graph | Functions | Combinatorics |

`incidence_matrix(Graph G)` | graph | Functions | Combinatorics |

`IncidenceMatrix<Sym>` | common | Property_types | Set Types |

`incl(Set s1, Set s2)` | common | Functions | Set Operations |

`include(String rulefile)` | core | Functions | Basic |

`included_polyhedra(Polytope P1, Polytope P2)` | polytope | Functions | Comparing |

`independence_complex(Matroid matroid)` | topaz | Functions | Producing a simplicial complex from other objects |

`index_matrix(SparseMatrix m)` | common | Functions | Data Conversion |

`index_of(Array<Set<Int>> array)` | common | Functions | Utilities |

`INDEX_OF` | group | property of Action | Symmetry |

`indices` | common | method of PolyDB::Collection | Database Collection Administration |

`indices(SparseVector v)` | common | Functions | Data Conversion |

`induce_implicit_action(PermutationAction original_action, String property)` | group | Functions | Symmetry |

`induce_set_action(Cone c, PermutationAction a, String domain)` | group | Functions | Symmetry |

`induced_action(PermutationAction a, Array<Set<Int>> domain)` | group | Functions | Symmetry |

`INDUCED_FROM` | group | property of Action | Symmetry |

`induced_lattice_basis(Polytope p)` | polytope | Functions | Geometry |

`induced_permutations(Array<Array<Int>> gens, Matrix M)` | group | Functions | Symmetry |

`induced_permutations(Array<Matrix<Scalar>> gens, Matrix M)` | group | Functions | Symmetry |

`induced_permutations(Array<Array<Int>> gens, Array<DomainType> S)` | group | Functions | Symmetry |

`induced_permutations(Array<Array<Int>> a, IncidenceMatrix M)` | group | Functions | Symmetry |

`induced_permutations_set_set(Array<Array<Int>> gens, Array<Set<Set>> domain)` | group | Functions | Symmetry |

`induced_rep(Cone C, PermutationActionOnSets A, Array<Int> g)` | group | Functions | Symmetry |

`induced_subcomplex(SimplicialComplex complex, Set<Int> vertices)` | topaz | Functions | Producing a new simplicial complex from others |

`induced_subdivision<Scalar>(VectorConfiguration<Scalar> pc, Matrix<Scalar> R, Set I)` | fan | Functions | Geometry |

`induced_subdivision` | fan | Functions | Geometry |

`induced_subgraph(Graph graph, Set set)` | common | Functions | Graph Operations |

`INEQUALITIES` | tropical | property of Polytope | Input property |

`INEQUALITIES` | polytope | property of Cone | Input property |

`INEQUALITIES` | polytope | property of Polytope | Input property |

`INEQUALITIES_ACTION` | group | property of Group | Symmetry |

`INEQUALITIES_GENERATORS` | group | property of Action | Symmetry |

`INEQUALITIES_THRU_RAYS` | polytope | property of Cone | Geometry |

`INEQUALITIES_THRU_VERTICES` | polytope | property of Polytope | Geometry |

`INEQUALITY_LABELS` | polytope | property of Cone | Visualization |

`INEQUALITY_LABELS` | polytope | property of Polytope | Visualization |

`inf` | common | method of Float | no category |

`inf` | common | method of Rational | no category |

`inf` | common | method of Integer | no category |

`info()` | common | method of PolyDB::Client | Database Access |

`initial_form(Vector<Exponent> v)` | common | method of Polynomial | no category |

`INITIAL_FORMS` | ideal | property of Groebner | Commutative algebra |

`INITIAL_IDEAL` | ideal | property of Groebner | Commutative algebra |

`initiate_collection()` | common | method of PolyDB::Client | Database Administration |

`inner_cone(Cone p, Set<Int> F)` | polytope | Functions | Producing a cone |

`INNER_DESCRIPTION()` | polytope | method of Polytope | Geometry |

`INNER_POINT` | polytope | property of SchlegelDiagram | no category |

`inner_point(Matrix points)` | polytope | Functions | Optimization |

`INPUT_COEFFS` | tropical | property of RationalCurve | Input property |

`INPUT_CONES` | fan | property of PolyhedralFan | Input property |

`INPUT_CONES_ACTION` | group | property of Group | Symmetry |

`INPUT_CONES_REPS` | fan | property of PolyhedralFan | Input property |

`INPUT_FACES` | topaz | property of SimplicialComplex | Input property |

`INPUT_LINEALITY` | fan | property of PolyhedralFan | Input property |

`INPUT_LINEALITY` | polytope | property of Cone | Input property |

`INPUT_LINEALITY_GENERATORS` | group | property of Action | Symmetry |

`INPUT_POLYTOPES` | fan | property of PolyhedralComplex | Input property |

`INPUT_POLYTOPES_ACTION` | fan | property of PolyhedralComplex | Symmetry |

`INPUT_POLYTOPES_REPS` | fan | property of PolyhedralComplex | Symmetry |

`INPUT_RAY_LABELS` | fan | property of PolyhedralFan | Visualization |

`INPUT_RAY_LABELS` | polytope | property of Cone | Visualization |

`INPUT_RAYS` | fan | property of PolyhedralFan | Input property |

`INPUT_RAYS` | polytope | property of Cone | Input property |

`INPUT_RAYS_ACTION` | group | property of Group | Symmetry |

`INPUT_RAYS_GENERATORS` | group | property of Action | Symmetry |

`INPUT_RAYS_IN_FACETS` | polytope | property of Cone | Geometry |

`INPUT_RAYS_REPS` | fan | property of PolyhedralFan | Input property |

`INPUT_SETS` | tropical | property of RationalCurve | Input property |

`INPUT_STRING` | tropical | property of RationalCurve | Input property |

`insert(Core::BigObject one)` | common | method of PolyDB::Collection | Database Collection Administration |

`insert(Set f)` | common | method of FacetList | no category |

`insert_leaves(RationalCurve curve, Vector<Int> nodes)` | tropical | Functions | Abstract rational curves |

`insert_rays(Cycle<Addition> F, Matrix<Rational> R)` | tropical | Functions | Basic polyhedral operations |

`insertMax(Set f)` | common | method of FacetList | no category |

`insertMin(Set f)` | common | method of FacetList | no category |

`Int` | common | Property_types | Basic Types |

`Integer` | common | Property_types | Basic Types |

`integer_hull(Polytope P)` | polytope | Functions | Producing a polytope from polytopes |

`integer_points_bbox(Polytope<Scalar> P)` | polytope | Functions | Geometry |

`INTEGER_VARIABLES` | polytope | property of MixedIntegerLinearProgram | no category |

`INTEGRAL` | fulton | property of TDivisor | Algebraic Geometry |

`interior_and_boundary_ridges(Polytope P)` | polytope | Functions | Triangulations, subdivisions and volume |

`INTERIOR_LATTICE_POINTS` | polytope | property of Polytope | Lattice points in polytopes |

`INTERIOR_RIDGE_SIMPLICES` | polytope | property of Cone | Combinatorics |

`INTERIOR_RIDGE_SIMPLICES` | polytope | property of PointConfiguration | Combinatorics |

`internal_activity()` | matroid | Functions | Other |

`intersect(Cycle X, Cycle Y)` | tropical | Functions | Intersection theory |

`intersect_check_transversality(Cycle X, Cycle Y, Bool ensure_transversality)` | tropical | Functions | Intersection theory |

`intersect_container(Cycle cycle, Cycle container, Bool forceLatticeComputation)` | tropical | Functions | Basic polyhedral operations |

`intersect_in_smooth_surface(Cycle<Addition> surface, Cycle<Addition> A, Cycle<Addition> B)` | tropical | Functions | Intersection theory |

`intersection(Matroid M)` | matroid | Functions | Producing a matroid from matroids |

`intersection(PolyhedralFan F, Matrix H)` | fan | Functions | Producing a fan |

`intersection(Cone C …)` | polytope | Functions | Producing a polytope from polytopes |

`INTERSECTION_COMPLEX` | fan | property of PolyhedralFan | Topology |

`intersection_extremals(Matrix<TropicalNumber> G, Vector<TropicalNumber> a, Vector<TropicalNumber> b)` | tropical | Functions | Tropical operations |

`INTERSECTION_FORM` | topaz | property of SimplicialComplex | Topology |

`IntersectionForm` | topaz | Property_types | Topology |

`inv(Matrix A)` | common | Functions | Linear Algebra |

`invalid_node(Int node)` | common | method of Graph | no category |

`invariant_polynomials(MatrixActionOnVectors a, Int d)` | group | Functions | Symmetry |

`INVERSE_RANK_MAP` | graph | property of Lattice | Combinatorics |

`InverseRankMap<SeqType>` | graph | Property_types | Combinatorics |

`IRREDUCIBLE_DECOMPOSITION` | group | property of Action | Symmetry |

`irreducible_decomposition<Scalar>(Vector<Scalar> character, Group G)` | group | Functions | Symmetry |

`is_B_nested(Set<Set> check_me, PowerSet B)` | fan | Functions | Other |

`IS_BALANCED` | tropical | property of Cycle | Weights and lattices |

`is_balanced(Cycle C)` | tropical | Functions | Weights and lattices |

`is_building_set(PowerSet check_me, Int n)` | fan | Functions | Other |

`is_contained(Matrix<TropicalNumber> apices, Array<Set<Int>> sectors)` | tropical | Functions | Tropical operations |

`is_empty` | tropical | Functions | Degeneracy tests |

`is_fan(Bool allow_translations)` | tropical | method of Cycle | Basic polyhedral operations |

`is_generalized_shelling(Array<Set> FaceList)` | topaz | Functions | Other |

`IS_GLOBALLY_AFFINE_LINEAR` | tropical | property of Morphism | Defining morphisms and functions |

`IS_GLOBALLY_DEFINED` | tropical | property of RationalFunction | Defining morphisms and functions |

`is_integral(Vector v)` | common | Functions | Lattice Tools |

`is_integral(Matrix m)` | common | Functions | Lattice Tools |

`IS_IRREDUCIBLE` | tropical | property of Cycle | Weights and lattices |

`is_isomorphic_to(Matroid M)` | matroid | method of Matroid | Advanced properties |

`is_modular_cut(Matroid M, Array<Set> C)` | matroid | Functions | Other |

`is_nested_matroid(Matroid M)` | matroid | Functions | Advanced properties |

`is_nonnegative(ARRAY data)` | common | Functions | Utilities |

`is_one(` | common | Functions | Arithmetic |

`is_regular(Matrix points, Array<Set<Int>> subdiv)` | polytope | Functions | Triangulations, subdivisions and volume |

`is_smooth(Cycle<Addition> a)` | tropical | Functions | Matroids |

`is_subdivision(Matrix points, Array<Set<Int>> faces)` | polytope | Functions | Triangulations, subdivisions and volume |

`is_unimodal(ARRAY data)` | common | Functions | Utilities |

`is_vertex_decomposition(SimplicialComplex complex, Array<Int> vertices)` | topaz | Functions | Other |

`is_zero(` | common | Functions | Arithmetic |

`isa(Any type)` | core | method of Core::BigObject | no category |

`isfinite(` | common | Functions | Arithmetic |

`isinf(` | common | Functions | Arithmetic |

`isomorphic(IncidenceMatrix IncidenceMatrix1, IncidenceMatrix IncidenceMatrix2)` | graph | Functions | Comparing |

`isomorphic(Graph graph1, Graph graph2)` | graph | Functions | Comparing |

`isomorphic(SimplicialComplex complex1, SimplicialComplex complex2)` | topaz | Functions | Comparing |

`isomorphic(Cone P1, Cone P2)` | polytope | Functions | Comparing |

`isotypic_basis(Group G, PermutationActionOnSets A, Int i)` | group | Functions | Symmetry |

`isotypic_basis(Group G, PermutationAction A, Int i)` | group | Functions | Symmetry |

`isotypic_basis<Scalar>(Group G, MatrixActionOnVectors<Scalar> A, Int i)` | group | Functions | Symmetry |

`ISOTYPIC_COMPONENTS` | polytope | property of SymmetrizedCocircuitEquations | no category |

`isotypic_configuration(Polytope P, Int i)` | polytope | Functions | Symmetry |

`isotypic_projector(Group G, PermutationAction A, Int i)` | group | Functions | Symmetry |

`isotypic_projector<Scalar>(Group G, MatrixActionOnVectors<Scalar> A, Int i)` | group | Functions | Symmetry |

`isotypic_supports(PermutationActionOnSets a, Array<Set> A)` | group | Functions | Symmetry |

`isotypic_supports(PermutationActionOnSets a, SparseMatrix M)` | group | Functions | Symmetry |

`iterated_barycentric_subdivision(SimplicialComplex complex, Int k)` | topaz | Functions | Producing a new simplicial complex from others |

`iterated_barycentric_subdivision(Cone c, Int n)` | polytope | Functions | Triangulations, subdivisions and volume |

`ITERATED_DELAUNAY_GRAPH` | polytope | property of VoronoiPolyhedron | no category |

`ITERATED_VORONOI_GRAPH` | polytope | property of VoronoiPolyhedron | no category |

`Iterator<Element>` | common | Property_types | Artificial |

`j_matroid()` | matroid | Functions | Producing a matroid from scratch |

`javaview(Visual::Object vis_obj …)` | common | Functions | Visualization |

`johnson_graph(Int n, Int k)` | graph | Functions | Producing a graph |

`johnson_solid(Int n)` | polytope | Functions | Producing regular polytopes and their generalizations |

`johnson_solid(String s)` | polytope | Functions | Producing regular polytopes and their generalizations |

`join_complexes(SimplicialComplex complex1, SimplicialComplex complex2)` | topaz | Functions | Producing a new simplicial complex from others |

`join_polytopes(Polytope P1, Polytope P2)` | polytope | Functions | Producing a polytope from polytopes |

`jreality(Visual::Object vis_obj …)` | common | Functions | Visualization |

`k1()` | common | method of ExtGCD | no category |

`k2()` | common | method of ExtGCD | no category |

`k_cyclic(Int n, Vector s)` | polytope | Functions | Producing a polytope from scratch |

`k_skeleton(SimplicialComplex complex, Int k)` | topaz | Functions | Producing a new simplicial complex from others |

`k_skeleton(GeometricSimplicialComplex complex, Int k)` | topaz | Functions | Producing a new simplicial complex from others |

`k_skeleton<Coord>(PolyhedralFan F, Int k)` | fan | Functions | Producing a fan |

`klee_minty_cube(Int d, Scalar e)` | polytope | Functions | Producing a polytope from scratch |

`klein_bottle()` | topaz | Functions | Producing from scratch |

`kneser_graph(Int n, Int k)` | graph | Functions | Producing a graph |

`KNOT` | topaz | property of SimplicialComplex | Topology |

`l8_matroid()` | matroid | Functions | Producing a matroid from scratch |

`labeled(Vector data, Array<String> elem_labels)` | common | Functions | Formatting |

`labeled_vertices(String label …)` | topaz | method of SimplicialComplex | Combinatorics |

`labeled_vertices(String label …)` | polytope | method of Polytope | Geometry |

`LABELS` | matroid | property of Matroid | Other |

`LABELS` | fan | property of SubdivisionOfVectors | Visualization |

`LABELS` | polytope | property of VectorConfiguration | Visualization |

`LAMINAR` | matroid | property of Matroid | Advanced properties |

`laplacian(Graph G)` | graph | Functions | Combinatorics |

`laplacian(Graph G)` | graph | Functions | Combinatorics |

`latex(Matrix data, Array<String> elem_labels)` | common | Functions | Formatting |

`Lattice<Decoration, SeqType>` | graph | Objects | Combinatorics |

`LATTICE()` | polytope | method of Visual::Polytope | no category |

`LATTICE` | polytope | property of Polytope | Geometry |

`LATTICE_ACCUMULATED_EDGE_LENGTHS` | polytope | property of Polytope | Lattice points in cones |

`lattice_automorphisms_smooth_polytope(Polytope P)` | polytope | Functions | Symmetry |

`LATTICE_BASES` | tropical | property of Cycle | Weights and lattices |

`lattice_basis(Matrix<Integer> A)` | common | Functions | Linear Algebra |

`LATTICE_BASIS` | polytope | property of Polytope | Lattice points in cones |

`lattice_bipyramid(Polytope P, Vector v, Vector v_prime, Rational z, Rational z_prime)` | polytope | Functions | Producing a polytope from polytopes |

`LATTICE_CODEGREE` | polytope | property of Polytope | Lattice points in cones |

`LATTICE_COLORED()` | polytope | method of Visual::Polytope | no category |

`LATTICE_DEGREE` | polytope | property of Polytope | Lattice points in cones |

`LATTICE_EDGE_LENGTHS` | polytope | property of Polytope | Lattice points in cones |

`LATTICE_EMPTY` | polytope | property of Polytope | Lattice points in cones |

`LATTICE_GENERATORS` | tropical | property of Cycle | Weights and lattices |

`LATTICE_HOLLOW` | polytope | method of Polytope | no category |

`lattice_index(Matrix<Integer> m)` | tropical | Functions | Lattices |

`lattice_isomorphic_smooth_polytopes(Polytope P1, Polytope P2)` | polytope | Functions | Comparing |

`lattice_normal(Int i, Int j)` | tropical | method of Cycle | Weights and lattices |

`LATTICE_NORMAL_FCT_VECTOR` | tropical | property of Cycle | Weights and lattices |

`LATTICE_NORMAL_SUM` | tropical | property of Cycle | Weights and lattices |

`LATTICE_NORMAL_SUM_FCT_VECTOR` | tropical | property of Cycle | Weights and lattices |

`LATTICE_NORMALS` | tropical | property of Cycle | Weights and lattices |

`lattice_of_chains(Lattice<Decoration> lattice)` | graph | Functions | Combinatorics |

`LATTICE_OF_CYCLIC_FLATS` | matroid | property of Matroid | Axiom systems |

`LATTICE_OF_FLATS` | matroid | property of Matroid | Axiom systems |

`LATTICE_POINTS()` | polytope | method of Polytope | Lattice points in polytopes |

`LATTICE_POINTS_GENERATORS` | polytope | property of Polytope | Lattice points in polytopes |

`lattice_pyramid(Polytope P, Rational z, Vector v)` | polytope | Functions | Producing a polytope from polytopes |

`LATTICE_VOLUME` | polytope | property of Polytope | Lattice points in cones |

`LATTICE_WIDTH` | polytope | property of Polytope | Lattice points in cones |

`LATTICE_WIDTH_DIRECTION` | polytope | property of Polytope | Lattice points in cones |

`lawrence(Cone P)` | polytope | Functions | Producing a polytope from polytopes |

`lawrence_matrix(Matrix M)` | polytope | Functions | Other |

`LayeredPermutationAction` | group | Objects | no category |

`lc()` | common | method of UniPolynomial | no category |

`lc()` | common | method of Polynomial | no category |

`lcm(Int a, Int b)` | common | Functions | Arithmetic |

`lcm(Vector<` | common | Functions | Arithmetic |

`lecture_hall_simplex(Int d)` | polytope | Functions | Producing a polytope from scratch |

`LEDA_graph(Graph G)` | graph | Functions | Visualization |

`left_companion()` | common | method of SmithNormalForm | no category |

`left_companion()` | common | method of SingularValueDecomposition | no category |

`lex_extension(Matroid M, Array<Set> C)` | matroid | Functions | Producing a matroid from matroids |

`lex_maximal` | group | method of PermutationAction | Orbits |

`lex_min_representative(Group G, Set S)` | group | Functions | Symmetry |

`lex_minimal` | group | method of PermutationAction | Orbits |

`lex_ordered(FacetList f)` | common | Functions | Data Conversion |

`lifted_pluecker(Matrix<TropicalNumber<Addition>> V)` | tropical | Functions | Other |

`LIFTING` | fulton | property of RationalDivisorClassGroup | Algebraic Geometry |

`lin_solve(Matrix A, Vector b)` | common | Functions | Linear Algebra |

`line_graph(Graph G)` | graph | Functions | Combinatorics |

`LINEALITY_DIM` | fan | property of PolyhedralFan | Geometry |

`LINEALITY_DIM` | polytope | property of Cone | Geometry |

`lineality_space(Matrix A)` | common | Functions | Linear Algebra |

`LINEALITY_SPACE` | fan | property of PolyhedralFan | Geometry |

`LINEALITY_SPACE` | fan | property of HyperplaneArrangement | Geometry |

`LINEALITY_SPACE` | polytope | property of Cone | Geometry |

`LINEALITY_SPACE_GENERATORS` | group | property of Action | Symmetry |

`LINEALITY_VALUES` | tropical | property of RationalFunction | Defining morphisms and functions |

`LINEALITY_VALUES` | tropical | property of Morphism | Defining morphisms and functions |

`LINEAR_OBJECTIVE` | polytope | property of MixedIntegerLinearProgram | no category |

`LINEAR_OBJECTIVE` | polytope | property of LinearProgram | no category |

`linear_space(ValuatedMatroid<Addition,Rational> A)` | tropical | Functions | Tropical linear spaces |

`LINEAR_SPAN` | fan | property of SubdivisionOfVectors | Geometry |

`LINEAR_SPAN` | polytope | property of VectorConfiguration | Geometry |

`LINEAR_SPAN` | polytope | property of Cone | Geometry |

`LINEAR_SPAN_NORMALS` | fan | property of PolyhedralFan | Geometry |

`linear_symmetries` | polytope | Functions | Symmetry |

`linear_symmetries(Matrix m)` | polytope | Functions | Symmetry |

`LinearProgram<Scalar>` | polytope | Objects | Optimization |

`lines_in_cubic(Polynomial<TropicalNumber<Addition>> p)` | tropical | Functions | Lines in surfaces |

`LinesInCubic<Addition>` | tropical | Objects | no category |

`link_complex(SimplicialComplex complex, Set<Int> face)` | topaz | Functions | Producing a new simplicial complex from others |

`list` | core | method of Core::RuleChain | no category |

`List<Element>` | common | Property_types | Basic Types |

`list_attachments` | core | method of Core::BigObject | no category |

`list_collections(String section)` | common | method of PolyDB::Client | Database Access |

`LIST_FAMILY_FIXED_EDGE` | tropical | property of LinesInCubic | Lists of lines |

`LIST_FAMILY_FIXED_VERTEX` | tropical | property of LinesInCubic | Lists of lines |

`LIST_FAMILY_MOVING_EDGE` | tropical | property of LinesInCubic | Lists of lines |

`LIST_FAMILY_MOVING_VERTEX` | tropical | property of LinesInCubic | Lists of lines |

`LIST_ISOLATED_EDGE` | tropical | property of LinesInCubic | Lists of lines |

`LIST_ISOLATED_NO_EDGE` | tropical | property of LinesInCubic | Lists of lines |

`list_names` | core | method of Core::BigObject | no category |

`list_new_properties` | core | method of Core::RuleChain | no category |

`list_properties(Bool deep)` | core | method of Core::BigObject | no category |

`list_sections(String section)` | common | method of PolyDB::Client | Database Access |

`lm()` | common | method of Polynomial | no category |

`load(String filename)` | core | Functions | Basic |

`load_commands(String filename)` | core | Functions | Interactive |

`load_data(String filename)` | core | Functions | Basic |

`load_schema(String filename)` | core | Functions | Schemas |

`load_singular_library(String s)` | ideal | Functions | Singular interface |

`local_codim_one(Cycle<Addition> complex, Int face)` | tropical | Functions | Local computations |

`local_m0n<Addition>(RationalCurve R …)` | tropical | Functions | Moduli of rational curves |

`local_point(Cycle<Addition> complex, Vector<Rational> v)` | tropical | Functions | Local computations |

`local_restrict(Cycle<Addition> complex, IncidenceMatrix cones)` | tropical | Functions | Local computations |

`LOCAL_RESTRICTION` | tropical | property of Cycle | Local computations |

`local_var_names(String names …)` | common | Functions | Arithmetic |

`local_vertex(Cycle<Addition> complex, Int ray)` | tropical | Functions | Local computations |

`LocalFloatEpsilon` | common | Property_types | Artificial |

`LOCALLY_STRONGLY_CONNECTED` | topaz | property of SimplicialComplex | Topology |

`long_and_winding(Int r)` | polytope | Functions | Producing a polytope from scratch |

`lookup(String property_name, Any multi_choice)` | core | method of Core::BigObject | no category |

`LOOPS` | matroid | property of Matroid | Advanced properties |

`lower_deg()` | common | method of UniPolynomial | no category |

`lower_lattice_points` | fulton | Functions | Commutative Algebra |

`LP` | polytope | property of Polytope | Optimization |

`lp2poly<Scalar>(String file, Vector testvec, String prefix)` | polytope | Functions | Optimization |

`m0n<Addition>(Int n)` | tropical | Functions | Moduli of rational curves |

`m_sequence(Vector<Int> h)` | polytope | Functions | Other |

`MAHLER_VOLUME` | polytope | property of Polytope | Triangulation and volume |

`make_hyperplanes_unique_in_support` | fan | Functions | no category |

`make_totally_dual_integral(Polytope P)` | polytope | Functions | Producing a polytope from polytopes |

`MANIFOLD` | topaz | property of SimplicialComplex | Topology |

`Map<Key, Value>` | common | Property_types | Set Types |

`mapping_polytope(Polytope P1, Polytope P2)` | polytope | Functions | Producing a polytope from polytopes |

`mapvars(Array<Int> indices, Int nvars)` | common | method of Polynomial | no category |

`MASSIVE_GKZ_VECTOR` | polytope | property of PointConfiguration | Triangulation and volume |

`MATCHING` | topaz | property of SimplicialComplex | no category |

`Matrix<Element, Sym>` | common | Property_types | Algebraic Types |

`MATRIX` | tropical | property of Morphism | Defining morphisms and functions |

`MATRIX_ACTION` | fan | property of PolyhedralFan | Symmetry |

`MATRIX_ACTION` | polytope | property of VectorConfiguration | Symmetry |

`MATRIX_ACTION` | polytope | property of Cone | Symmetry |

`MATRIX_ACTION` | polytope | property of PointConfiguration | Symmetry |

`MATRIX_ACTION` | polytope | property of Polytope | Symmetry |

`MATRIX_ACTION_ON_COMPLEX` | fan | property of PolyhedralComplex | Symmetry |

`MatrixActionOnVectors` | group | Objects | no category |

`matrixPair2apexSet(Matrix<TropicalNumber> G, Matrix<TropicalNumber> A)` | tropical | Functions | Tropical operations |

`Matroid` | matroid | Objects | no category |

`matroid_coordinates_from_curve<Addition>(RationalCurve r)` | tropical | Functions | Abstract rational curves |

`matroid_fan<Addition>(Matroid m)` | tropical | Functions | Matroids |

`matroid_fan<Addition>(Matrix<Rational> m)` | tropical | Functions | Matroids |

`matroid_fan_from_flats<Addition>(Matroid A)` | tropical | Functions | Matroids |

`matroid_from_characteristic_vector(Vector<Integer> v, Int r, Int n)` | matroid | Functions | Producing a matroid from other objects |

`matroid_from_cyclic_flats(Array<Set<Int>> F, Array<Set<Int>> R, Int N)` | matroid | Functions | Producing a matroid from other objects |

`matroid_from_fan(Cycle<Addition> A)` | tropical | Functions | Matroids |

`matroid_from_graph(Graph g)` | matroid | Functions | Producing a matroid from other objects |

`matroid_from_matroid_polytope(Polytope p)` | matroid | Functions | Producing a matroid from other objects |

`MATROID_HYPERPLANES` | matroid | property of Matroid | Axiom systems |

`matroid_indices_of_hypersimplex_vertices()` | polytope | Functions | Other |

`matroid_plueckervector(Matroid m)` | matroid | Functions | Other |

`matroid_polytope<Addition, Scalar>(Matroid m, Scalar v)` | tropical | Functions | Producing a tropical polytope |

`matroid_ring_cycle<Addition>(Matroid M, Int scale)` | tropical | Functions | Creation functions for specific cycles |

`matroid_ring_linear_space(MatroidRingCycle L)` | tropical | Functions | Matroid ring cycle arithmetics |

`matroid_ring_product(MatroidRingCycle A, MatroidRingCycle B)` | tropical | Functions | Matroid ring cycle arithmetics |

`matroid_ring_sum(MatroidRingCycle A, MatroidRingCycle B)` | tropical | Functions | Matroid ring cycle arithmetics |

`MatroidRingCycle<Addition>` | tropical | Objects | no category |

`Max` | common | Property_types | Arithmetic |

`max` | common | method of Int | no category |

`MAX_BOUNDARY_SIMPLICES` | polytope | property of Cone | Combinatorics |

`MAX_BOUNDARY_SIMPLICES` | polytope | property of PointConfiguration | Combinatorics |

`MAX_CLIQUES` | graph | property of Graph | no category |

`MAX_CLIQUES()` | topaz | method of SimplicialComplex | Combinatorics |

`max_GC_rank(Int d)` | polytope | Functions | Producing a polytope from scratch |

`MAX_INTERIOR_SIMPLICES` | polytope | property of Cone | Combinatorics |

`MAX_INTERIOR_SIMPLICES` | polytope | property of PointConfiguration | Combinatorics |

`max_interior_simplices(Polytope P)` | polytope | Functions | Triangulations, subdivisions and volume |

`max_interior_simplices(PointConfiguration P)` | polytope | Functions | Triangulations, subdivisions and volume |

`max_metric(Int n)` | fan | Functions | Finite metric spaces |

`MAXIMAL_AT_CODIM_ONE` | tropical | property of Cycle | Combinatorics |

`MAXIMAL_CELLS` | fan | property of SubdivisionOfVectors | Combinatorics |

`maximal_chains_of_lattice(Lattice F)` | graph | Functions | Combinatorics |

`MAXIMAL_CONE_LABELS` | fan | property of PolyhedralFan | Visualization |

`MAXIMAL_CONES` | fan | property of PolyhedralFan | Combinatorics |

`MAXIMAL_CONES_ACTION` | group | property of Group | Symmetry |

`MAXIMAL_CONES_ACTION` | fan | property of PolyhedralFan | Symmetry |

`MAXIMAL_CONES_COMBINATORIAL_DIMS` | fan | property of PolyhedralFan | Combinatorics |

`MAXIMAL_CONES_FACETS` | fan | property of PolyhedralFan | Geometry |

`MAXIMAL_CONES_GENERATORS` | group | property of Action | Symmetry |

`MAXIMAL_CONES_IN_ORBITS` | fan | property of PolyhedralFan | Symmetry |

`MAXIMAL_CONES_INCIDENCES` | fan | property of PolyhedralFan | Combinatorics |

`MAXIMAL_CONES_LINEAR_SPAN_NORMALS` | fan | property of PolyhedralFan | Geometry |

`MAXIMAL_CONES_ORBIT_SIZES` | fan | property of PolyhedralFan | Symmetry |

`MAXIMAL_CONES_REPS` | fan | property of PolyhedralFan | Symmetry |

`MAXIMAL_CONES_REPS_DIMS` | fan | property of PolyhedralFan | Symmetry |

`MAXIMAL_CONES_REPS_FACETS` | fan | property of PolyhedralFan | Symmetry |

`MAXIMAL_CONES_REPS_LINEAR_SPAN_NORMALS` | fan | property of PolyhedralFan | Symmetry |

`MAXIMAL_CONES_THRU_RAYS` | fan | property of PolyhedralFan | Combinatorics |

`MAXIMAL_COVECTOR_CELLS` | tropical | property of Polytope | Combinatorics |

`MAXIMAL_COVECTORS` | tropical | property of Polytope | Combinatorics |

`MAXIMAL_FACE` | polytope | property of LinearProgram | no category |

`MAXIMAL_POLYTOPES` | fan | property of PolyhedralComplex | Combinatorics |

`MAXIMAL_POLYTOPES_ACTION` | fan | property of PolyhedralComplex | Symmetry |

`MAXIMAL_POLYTOPES_AFFINE_HULL_NORMALS` | fan | property of PolyhedralComplex | Geometry |

`MAXIMAL_POLYTOPES_COMBINATORIAL_DIMS` | fan | property of PolyhedralComplex | Combinatorics |

`MAXIMAL_POLYTOPES_FACETS` | fan | property of PolyhedralComplex | Geometry |

`MAXIMAL_POLYTOPES_GENERATORS` | fan | property of PolyhedralComplex | Symmetry |

`MAXIMAL_POLYTOPES_IN_ORBITS` | fan | property of PolyhedralComplex | Symmetry |

`MAXIMAL_POLYTOPES_INCIDENCES` | fan | property of PolyhedralComplex | Combinatorics |

`MAXIMAL_POLYTOPES_ORBIT_SIZES` | fan | property of PolyhedralComplex | Symmetry |

`MAXIMAL_POLYTOPES_REPS` | fan | property of PolyhedralComplex | Symmetry |

`MAXIMAL_POLYTOPES_REPS_AFFINE_SPAN_NORMALS` | fan | property of PolyhedralComplex | Symmetry |

`MAXIMAL_POLYTOPES_REPS_DIMS` | fan | property of PolyhedralComplex | Symmetry |

`MAXIMAL_POLYTOPES_REPS_FACETS` | fan | property of PolyhedralComplex | Symmetry |

`MAXIMAL_POLYTOPES_THRU_VERTICES` | fan | property of PolyhedralComplex | Combinatorics |

`MAXIMAL_SOLUTION` | polytope | property of MixedIntegerLinearProgram | no category |

`MAXIMAL_TRANSVERSAL_PRESENTATION` | matroid | property of Matroid | Advanced properties |

`MAXIMAL_VALUE` | polytope | property of MixedIntegerLinearProgram | no category |

`MAXIMAL_VALUE` | polytope | property of LinearProgram | no category |

`MAXIMAL_VERTEX` | polytope | property of LinearProgram | no category |

`maximum(ARRAY array)` | common | Functions | Utilities |

`median(ARRAY array)` | common | Functions | Utilities |

`metapost(Visual::Object vis_obj …)` | graph | Functions | Visualization |

`metric_extended_tight_span(Matrix<Rational> M)` | fan | Functions | Finite metric spaces |

`metric_tight_span(Matrix<Rational> M)` | fan | Functions | Finite metric spaces |

`metric_vector` | tropical | method of RationalCurve | Conversion |

`MILP` | polytope | property of Polytope | Optimization |

`Min` | common | Property_types | Arithmetic |

`min` | common | method of Int | no category |

`MIN_MAX_FACE(LinearProgram lp)` | polytope | method of Visual::Polytope | no category |

`MIN_MAX_FACE(LinearProgram lp)` | polytope | method of Visual::PolytopeLattice | no category |

`MIN_MAX_FACE(LinearProgram lp)` | polytope | method of Visual::PolytopeGraph | no category |

`MIN_MAX_FACE(LinearProgram lp)` | polytope | method of Visual::SchlegelDiagram | no category |

`min_metric(Int n)` | fan | Functions | Finite metric spaces |

`MIN_WEIGHTS` | fan | property of SubdivisionOfVectors | Geometry |

`minimal_base(Matroid matroid, Vector weights)` | matroid | Functions | Other |

`MINIMAL_FACE` | polytope | property of LinearProgram | no category |

`MINIMAL_NON_FACES` | topaz | property of SimplicialComplex | Combinatorics |

`MINIMAL_NON_FACES` | polytope | property of Polytope | Combinatorics |

`MINIMAL_SOLUTION` | polytope | property of MixedIntegerLinearProgram | no category |

`MINIMAL_VALUE` | polytope | property of MixedIntegerLinearProgram | no category |

`MINIMAL_VALUE` | polytope | property of LinearProgram | no category |

`MINIMAL_VERTEX` | polytope | property of LinearProgram | no category |

`MINIMAL_VERTEX_ANGLE` | polytope | property of Polytope | Geometry |

`minimal_vertex_angle(Polytope P)` | polytope | Functions | Geometry |

`minimum(ARRAY array)` | common | Functions | Utilities |

`MINKOWSKI_CONE` | polytope | property of Polytope | Geometry |

`MINKOWSKI_CONE_COEFF(Vector<Rational> coeff)` | polytope | method of Polytope | Geometry |

`MINKOWSKI_CONE_POINT(Vector<Rational> point)` | polytope | method of Polytope | Geometry |

`minkowski_sum(TropicalNumber<Addition,Scalar> lambda, Polytope<Addition,Scalar> P, TropicalNumber<Addition,Scalar> mu, Polytope<Addition,Scalar> Q)` | tropical | Functions | Producing a tropical polytope |

`minkowski_sum(PointConfiguration P1, PointConfiguration P2)` | polytope | Functions | Producing a point configuration |

`minkowski_sum(Scalar lambda, PointConfiguration P1, Scalar mu, PointConfiguration P2)` | polytope | Functions | Producing a point configuration |

`minkowski_sum(Polytope P1, Polytope P2)` | polytope | Functions | Producing a polytope from polytopes |

`minkowski_sum(Scalar lambda, Polytope P1, Scalar mu, Polytope P2)` | polytope | Functions | Producing a polytope from polytopes |

`minkowski_sum_fukuda(Array<Polytope> summands)` | polytope | Functions | Producing a polytope from polytopes |

`minor(Set r, Set c)` | common | method of Matrix | no category |

`minor(Set r, Set c)` | common | method of IncidenceMatrix | no category |

`minus_inf` | common | method of Float | no category |

`minus_inf` | common | method of Rational | no category |

`minus_inf` | common | method of Integer | no category |

`MIXED_GRAPH` | topaz | property of SimplicialComplex | Visualization |

`mixed_graph(SimplicialComplex complex)` | topaz | Functions | Other |

`mixed_integer_hull(Polytope P, Array<Int> int_coords)` | polytope | Functions | Producing a polytope from polytopes |

`mixed_subdivision(Polytope P_0, Polytope P_1, Array<Set> VIF, Scalar t_0, Scalar t_1)` | fan | Functions | Producing a polyhedral complex |

`mixed_subdivision(Int m, Polytope C, Array<Set> a)` | fan | Functions | Producing a polyhedral complex |

`mixed_subdivision(Array<Polytope> A, Array<Set> VIF)` | fan | Functions | Producing a polyhedral complex |

`mixed_volume(Polytope<Scalar> P1, Polytope<Scalar> P2, Polytope<Scalar> Pn)` | polytope | Functions | Triangulations, subdivisions and volume |

`MixedIntegerLinearProgram<Scalar>` | polytope | Objects | Optimization |

`MODULE_GENERATORS` | fulton | property of NormalToricVariety | Combinatorics |

`MOEBIUS_STRIP_EDGES` | polytope | property of Polytope | Combinatorics |

`MOEBIUS_STRIP_QUADS` | polytope | property of Polytope | Combinatorics |

`MONOID_GRADING` | polytope | property of Cone | Lattice points in cones |

`monomial` | common | method of UniPolynomial | no category |

`monomial(Int var_index, Int n_vars)` | common | method of Polynomial | no category |

`MONOMIAL` | ideal | property of Ideal | Commutative algebra |

`monomial_cone_lattice(Matrix M)` | tropical | Functions | Tropical operations |

`monomial_dual_description(Matrix monomial_generators)` | tropical | Functions | Tropical operations |

`monomials<Coefficient, Exponent>(Int n)` | common | Functions | Arithmetic |

`MONOMIALS` | tropical | property of Hypersurface | no category |

`monomials_as_matrix()` | common | method of Polynomial | no category |

`monomials_as_vector()` | common | method of UniPolynomial | no category |

`moore_penrose_inverse(Matrix M)` | common | Functions | Linear Algebra |

`MORI_CONE` | fulton | property of NormalToricVariety | Algebraic Geometry |

`Morphism<Addition>` | tropical | Objects | no category |

`morphism_from_affine<Addition>(Matrix<Rational> A, Vector<Rational> v, Int domain_chart, Int target_chart)` | tropical | Functions | Affine and projective coordinates |

`MORSE_MATCHING` | topaz | property of SimplicialComplex | Topology |

`MORSE_MATCHING()` | topaz | method of Visual::SimplicialComplex | no category |

`MORSE_MATCHING()` | topaz | method of Visual::SimplicialComplexLattice | no category |

`MorseMatching` | topaz | Objects | Topology |

`multi_associahedron_sphere(Int n, Int k)` | topaz | Functions | Producing from scratch |

`MULTIPLE_POINTS` | polytope | property of PointConfiguration | Geometry |

`MULTIPLE_VECTORS` | polytope | property of VectorConfiguration | Geometry |

`multiplex(Int d, Int n)` | polytope | Functions | Producing a polytope from scratch |

`N` | fulton | property of CyclicQuotient | Input properties |

`n1_matroid()` | matroid | Functions | Producing a matroid from scratch |

`n2_matroid()` | matroid | Functions | Producing a matroid from scratch |

`N_01POINTS` | polytope | property of Polytope | Geometry |

`n_automorphisms(Graph graph)` | graph | Functions | Comparing |

`N_AUTOMORPHISMS` | matroid | property of Matroid | Enumerative properties |

`N_BASES` | matroid | property of Matroid | Enumerative properties |

`N_BOUNDARY_LATTICE_POINTS` | polytope | property of Polytope | Lattice points in polytopes |

`N_BOUNDED_VERTICES` | polytope | property of Polytope | Unbounded polyhedra |

`n_cells()` | topaz | method of Filtration | no category |

`N_CIRCUITS` | matroid | property of Matroid | Enumerative properties |

`N_COCIRCUITS` | matroid | method of Matroid | Enumerative properties |

`N_COLOOPS` | matroid | method of Matroid | Enumerative properties |

`N_CONES` | fan | property of PolyhedralFan | Combinatorics |

`N_CONNECTED_COMPONENTS` | graph | property of Graph | no category |

`N_CONNECTED_COMPONENTS()` | topaz | method of SimplicialComplex | Topology |

`N_CONNECTED_COMPONENTS` | matroid | property of Matroid | Advanced properties |

`N_CRITICAL_FACES` | topaz | property of MorseMatching | no category |

`N_CYCLIC_FLATS` | matroid | property of Matroid | Enumerative properties |

`N_EDGES` | graph | property of Graph | no category |

`N_EDGES` | polytope | property of Cone | Combinatorics |

`N_ELEMENTS` | tropical | property of MatroidRingCycle | Matroid data |

`N_ELEMENTS` | matroid | property of Matroid | Enumerative properties |

`N_EQUATIONS` | polytope | property of Cone | Geometry |

`N_EQUATIONS_GENERATORS` | group | property of Action | Symmetry |

`N_FACET_NORMALS` | fan | property of PolyhedralFan | Geometry |

`N_FACETS` | topaz | property of SimplicialComplex | Combinatorics |

`N_FACETS` | polytope | property of Cone | Combinatorics |

`N_FACETS_GENERATORS` | group | property of Action | Symmetry |

`N_FAMILIES` | tropical | property of LinesInCubic | Counts of lines |

`n_fine_triangulations(Matrix M, Bool optimization)` | polytope | Functions | Triangulations, subdivisions and volume |

`n_fixed_points(Array<Int> p)` | common | Functions | Combinatorics |

`N_FLAGS(Int type …)` | polytope | method of Cone | Combinatorics |

`N_FLATS` | matroid | property of Matroid | Enumerative properties |

`n_frames()` | topaz | method of Filtration | no category |

`n_gon(Int n, Rational r, Rational alpha_0)` | polytope | Functions | Producing a polytope from scratch |

`N_GON_TRIANGULATION` | fulton | property of VersalComponent | Combinatorics |

`n_graph_homomorphisms(Graph G, Graph H)` | graph | Functions | Combinatorics |

`N_HILBERT_BASIS` | polytope | property of Cone | Lattice points in cones |

`N_HYPERPLANES` | fan | property of HyperplaneArrangement | Combinatorics |

`N_INEQUALITIES_GENERATORS` | group | property of Action | Symmetry |

`N_INPUT_LINEALITY` | polytope | property of Cone | Geometry |

`N_INPUT_LINEALITY_GENERATORS` | group | property of Action | Symmetry |

`N_INPUT_RAYS` | fan | property of PolyhedralFan | Geometry |

`N_INPUT_RAYS` | polytope | property of Cone | Geometry |

`N_INPUT_RAYS_GENERATORS` | group | property of Action | Symmetry |

`N_INTERIOR_LATTICE_POINTS` | polytope | property of Polytope | Lattice points in polytopes |

`N_ISOLATED` | tropical | property of LinesInCubic | Counts of lines |

`N_LATTICE_POINTS` | polytope | property of Polytope | Lattice points in polytopes |

`N_LATTICE_POINTS_IN_DILATION(Int n)` | polytope | method of Polytope | Lattice points in cones |

`N_LEAVES` | tropical | property of RationalCurve | Combinatorics |

`N_LINEALITY_SPACE_GENERATORS` | group | property of Action | Symmetry |

`N_LOOPS` | matroid | property of Matroid | Enumerative properties |

`N_MATROID_HYPERPLANES` | matroid | property of Matroid | Enumerative properties |

`N_MAX_BOUNDARY_SIMPLICES` | polytope | property of PointConfiguration | Combinatorics |

`N_MAX_INTERIOR_SIMPLICES` | polytope | property of PointConfiguration | Combinatorics |

`N_MAXIMAL_CELLS` | fan | property of SubdivisionOfVectors | Combinatorics |

`N_MAXIMAL_CONE_ORBITS` | fan | property of PolyhedralFan | Symmetry |

`N_MAXIMAL_CONES` | fan | property of PolyhedralFan | Combinatorics |

`N_MAXIMAL_CONES_GENERATORS` | group | property of Action | Symmetry |

`N_MAXIMAL_POLYTOPES` | fan | property of PolyhedralComplex | Combinatorics |

`N_MAXIMAL_POLYTOPES_ORBITS` | fan | property of PolyhedralComplex | Symmetry |

`N_MAXIMAL_TORUS_ORBITS` | fulton | property of NormalToricVariety | Basic properties |

`N_MINIMAL_NON_FACES` | topaz | property of SimplicialComplex | Combinatorics |

`N_NESTED_SUMMANDS` | tropical | property of MatroidRingCycle | Matroid data |

`N_NODES` | graph | property of Graph | no category |

`N_ORBIT_REPRESENTATIVES` | group | property of Action | Symmetry |

`N_ORBITS` | group | property of Action | Symmetry |

`N_POINTS` | fan | property of SubdivisionOfPoints | Geometry |

`N_POINTS` | fan | property of PolyhedralComplex | Geometry |

`N_POINTS` | polytope | property of PointConfiguration | Geometry |

`N_POINTS` | polytope | property of Polytope | Geometry |

`N_POINTS_GENERATORS` | fan | property of PolyhedralComplex | Symmetry |

`N_POINTS_GENERATORS` | fan | property of PolyhedralComplex | Symmetry |

`N_POINTS_GENERATORS` | polytope | property of Polytope | no category |

`N_POLYTOPES` | fan | property of PolyhedralComplex | Combinatorics |

`n_poset_homomorphisms(Graph<Directed> P, Graph<Directed> Q)` | graph | Functions | Posets |

`N_RAY_FACET_INC` | polytope | property of Cone | Combinatorics |

`N_RAY_ORBITS` | fan | property of PolyhedralFan | Symmetry |

`N_RAYS` | fan | property of PolyhedralFan | Geometry |

`N_RAYS` | polytope | property of Cone | Combinatorics |

`N_RAYS_GENERATORS` | group | property of Action | Symmetry |

`N_REPRESENTATIVE_CERTIFIERS` | polytope | property of Polytope | no category |

`N_REPRESENTATIVE_CORE_POINTS` | polytope | property of Polytope | no category |

`N_RIDGES` | polytope | property of Cone | Combinatorics |

`N_SIMPLICES` | polytope | property of QuotientSpace | Combinatorics |

`N_SITES` | tropical | property of VoronoiDiagram | no category |

`N_SITES` | polytope | property of VoronoiPolyhedron | no category |

`N_STRONG_GENERATORS` | group | property of PermutationAction | no category |

`N_SYMMETRIES` | fan | property of PolyhedralFan | Symmetry |

`N_UNIMODULAR` | topaz | property of GeometricSimplicialComplex | no category |

`N_VARIABLES` | ideal | property of Ideal | Commutative algebra |

`n_vars` | common | method of UniPolynomial | no category |

`n_vars()` | common | method of Polynomial | no category |

`N_VECTORS` | fan | property of SubdivisionOfVectors | Geometry |

`N_VECTORS` | polytope | property of VectorConfiguration | Geometry |

`N_VERTEX_FACET_INC` | polytope | property of Polytope | Combinatorics |

`n_vertices()` | common | method of FacetList | no category |

`N_VERTICES` | topaz | property of SimplicialComplex | Combinatorics |

`N_VERTICES` | fan | property of PolyhedralComplex | Geometry |

`N_VERTICES` | polytope | property of Polytope | Combinatorics |

`N_VERTICES_GENERATORS` | fan | property of PolyhedralComplex | Symmetry |

`N_VERTICES_GENERATORS` | fan | property of PolyhedralComplex | Symmetry |

`N_VERTICES_GENERATORS` | polytope | property of Polytope | no category |

`N_VERTICES_ORBITS` | fan | property of PolyhedralComplex | Symmetry |

`name` | core | method of Core::BigObject | no category |

`nearest_point(Polytope<Addition,Scalar> C, Vector<TropicalNumber<Addition,Scalar>> x)` | tropical | Functions | Tropical operations |

`NEF` | fulton | property of TDivisor | Algebraic Geometry |

`NEF_CONE` | fulton | property of NormalToricVariety | Algebraic Geometry |

`NEIGHBOR_FACETS_CYCLIC_NORMAL` | polytope | property of Cone | Visualization |

`NEIGHBOR_RAYS_CYCLIC_NORMAL` | polytope | property of Cone | Visualization |

`NEIGHBOR_VERTICES_CYCLIC_NORMAL` | polytope | property of Polytope | Visualization |

`neighborhood_graph(Matrix<Rational> D, Rational delta)` | graph | Functions | Producing a graph |

`NEIGHBORLINESS` | polytope | property of Polytope | Combinatorics |

`NEIGHBORLY` | polytope | property of Polytope | Combinatorics |

`neighborly_cubical(Int d, Int n)` | polytope | Functions | Producing a polytope from scratch |

`NESTED` | matroid | property of Matroid | Advanced properties |

`NESTED_COEFFICIENTS` | tropical | property of MatroidRingCycle | Matroid data |

`nested_matroids` | tropical | method of MatroidRingCycle | Matroid data |

`NESTED_PRESENTATIONS` | tropical | property of MatroidRingCycle | Matroid data |

`nestedOPGraph(Vector gen_point, Matrix points, Matrix lattice_points, Group group, Bool verbose)` | polytope | Functions | Symmetry |

`newton(Polynomial p)` | polytope | Functions | Producing a polytope from scratch |

`NN_CRUST_GRAPH` | polytope | property of VoronoiPolyhedron | no category |

`NN_GRAPH` | polytope | property of VoronoiPolyhedron | no category |

`NODE_DEGREES` | graph | property of Graph | no category |

`NODE_DEGREES` | tropical | property of RationalCurve | Combinatorics |

`node_edge_incidences<Coord>(Graph graph)` | common | Functions | Graph Operations |

`node_exists(Int node)` | common | method of Graph | no category |

`NODE_IN_DEGREES` | graph | property of Graph | no category |

`NODE_LABELS` | graph | property of Graph | no category |

`NODE_OUT_DEGREES` | graph | property of Graph | no category |

`node_out_of_range(Int node)` | common | method of Graph | no category |

`NodeHashMap<Dir, Element>` | common | Property_types | Graph Types |

`NodeMap<Dir, Element>` | common | Property_types | Graph Types |

`nodes()` | common | method of Graph | no category |

`nodes(Graph graph)` | common | Functions | Graph Operations |

`NODES_BY_LEAVES` | tropical | property of RationalCurve | Combinatorics |

`NODES_BY_SETS` | tropical | property of RationalCurve | Combinatorics |

`nodes_of_dim` | tropical | method of CovectorLattice | Combinatorics |

`nodes_of_dim` | topaz | method of SimplicialComplex | no category |

`nodes_of_dim(Int d)` | fan | method of PolyhedralFan | Combinatorics |

`nodes_of_dim(Int d)` | polytope | method of Cone | Combinatorics |

`nodes_of_dim_range` | tropical | method of CovectorLattice | Combinatorics |

`nodes_of_dim_range` | topaz | method of SimplicialComplex | no category |

`nodes_of_dim_range(Int d1, Int d1)` | fan | method of PolyhedralFan | Combinatorics |

`nodes_of_dim_range(Int d1, Int d2)` | polytope | method of Cone | Combinatorics |

`nodes_of_rank(Int r)` | graph | method of Lattice | Combinatorics |

`nodes_of_rank(Int r)` | graph | method of InverseRankMap | Combinatorics |

`nodes_of_rank_range(Int r1, Int r2)` | graph | method of Lattice | Combinatorics |

`nodes_of_rank_range(Int r1, Int r2)` | graph | method of InverseRankMap | Combinatorics |

`NON_BASES` | matroid | property of Matroid | Axiom systems |

`non_fano_matroid()` | matroid | Functions | Producing a matroid from scratch |

`non_p8_matroid()` | matroid | Functions | Producing a matroid from scratch |

`non_pappus_matroid()` | matroid | Functions | Producing a matroid from scratch |

`NON_SATURATED` | polytope | property of SlackIdeal | no category |

`non_vamos_matroid()` | matroid | Functions | Producing a matroid from scratch |

`NON_VERTICES` | polytope | property of PointConfiguration | Geometry |

`Nonsequential` | graph | Property_types | Artificial |

`NonSymmetric` | common | Property_types | Artificial |

`NOP_GRAPH` | polytope | property of Polytope | no category |

`norm(Vector<TropicalNumber<Addition,Scalar>> v)` | tropical | Functions | Tropical operations |

`NORMAL` | polytope | property of Polytope | Lattice points in cones |

`normal_cone(PointConfiguration p, Set<Int> F)` | polytope | Functions | Producing a cone |

`normal_cone(Cone p, Set<Int> F)` | polytope | Functions | Producing a cone |

`normal_fan<Coord>(Polytope p)` | fan | Functions | Producing a fan |

`normaliz_compute(Cone C)` | polytope | Functions | Geometry |

`normalized(Matrix<Float> A)` | common | Functions | Linear Algebra |

`NormalToricVariety` | fulton | Objects | no category |

`null_space(Matrix A)` | common | Functions | Linear Algebra |

`null_space(Vector b)` | common | Functions | Linear Algebra |

`null_space_integer(Matrix A)` | common | Functions | Linear Algebra |

`numbered(Vector data)` | common | Functions | Formatting |

`numerator(Rational a)` | common | Functions | Arithmetic |

`numerator(RationalFunction f)` | common | Functions | Arithmetic |

`numerator(PuiseuxFraction f)` | common | Functions | Arithmetic |

`NUMERATOR` | tropical | property of RationalFunction | Defining morphisms and functions |

`o7_matroid()` | matroid | Functions | Producing a matroid from scratch |

`obliterate_extension(String extension)` | core | Functions | Interactive |

`occluding_cone(Cone P, Set F)` | polytope | Functions | Geometry |

`octahedron()` | polytope | Functions | Producing regular polytopes and their generalizations |

`ODD_SUBCOMPLEX` | topaz | property of SimplicialComplex | Combinatorics |

`on_cols` | group | Property_types | no category |

`on_container` | group | Property_types | no category |

`on_elements` | group | Property_types | no category |

`on_nonhomog_cols` | group | Property_types | no category |

`on_nonhomog_container` | group | Property_types | no category |

`on_rows` | group | Property_types | no category |

`ONE_RAY` | polytope | property of Cone | Geometry |

`ONE_VERTEX` | polytope | property of Polytope | Geometry |

`ones_matrix<Element>(Int m, Int n)` | common | Functions | Linear Algebra |

`ones_vector<Element>(Int d)` | common | Functions | Linear Algebra |

`optimal_permutations(Matrix<TropicalNumber> matrix)` | tropical | Functions | Tropical operations |

`ORBIFOLD` | fulton | property of NormalToricVariety | Basic properties |

`orbit<action_type>(Array G, Core::BigObject O)` | group | Functions | Orbits |

`orbit(Group G, Any C)` | group | Functions | Orbits |

`orbit<Scalar>(Array<Matrix<Scalar>> G, Vector<Scalar> V)` | group | Functions | Orbits |

`orbit_complex(PolyhedralComplex input_complex, Array<Array<Int>> gens)` | fan | Functions | Symmetry |

`orbit_complex(PolyhedralFan input_fan, PermutationAction a)` | fan | Functions | Symmetry |

`orbit_fan(PolyhedralFan input_fan, Array<Array<Int>> gens)` | fan | Functions | Symmetry |

`orbit_fan<Scalar>(PolyhedralFan input_fan, Array<Matrix<Scalar>> gens)` | fan | Functions | Symmetry |

`orbit_permlib(Group G, Set S)` | group | Functions | Orbits |

`orbit_permlib(Group G, Set<Set> S)` | group | Functions | Orbits |

`orbit_polytope(Vector input_point, PermutationAction a)` | polytope | Functions | Symmetry |

`orbit_polytope(Matrix input_points, PermutationAction a)` | polytope | Functions | Symmetry |

`orbit_polytope(Vector input_point, Group g)` | polytope | Functions | Symmetry |

`orbit_polytope(Matrix input_points, Group g)` | polytope | Functions | Symmetry |

`orbit_polytope(Matrix input_points, Array<Array<Int>> gens)` | polytope | Functions | Symmetry |

`orbit_polytope<Scalar>(Vector input_point, MatrixActionOnVectors a)` | polytope | Functions | Symmetry |

`orbit_polytope<Scalar>(Matrix<Scalar> input_points, MatrixActionOnVectors<Scalar> a)` | polytope | Functions | Symmetry |

`ORBIT_REPRESENTATIVE_LABELS` | group | property of Action | Symmetry |

`ORBIT_REPRESENTATIVES` | group | property of Action | Symmetry |

`orbit_representatives(Array<GeneratorType> G)` | group | Functions | Orbits |

`orbit_reps_and_sizes<Container>(Array<Array<Int>> generators, Container S)` | group | Functions | Symmetry |

`ORBIT_SIZES` | group | property of Action | Symmetry |

`ORBITS` | group | property of Action | Symmetry |

`ORBITS_F_VECTOR` | fan | property of PolyhedralFan | Symmetry |

`orbits_in_orbit_order(PermutationAction a, Matrix M)` | group | Functions | Orbits |

`orbits_of_action(PermutationAction a)` | group | Functions | Orbits |

`orbits_of_coordinate_action(PermutationAction a, Matrix<Scalar> M)` | group | Functions | Orbits |

`orbits_of_induced_action(PermutationAction a, IncidenceMatrix I)` | group | Functions | Orbits |

`ORDER` | group | property of Group | Symmetry |

`ORDER_MATRIX` | ideal | property of Groebner | Input properties |

`ORDER_NAME` | ideal | property of Groebner | Input properties |

`ORDER_VECTOR` | ideal | property of Groebner | Input properties |

`orientation()` | common | method of TropicalNumber | no category |

`orientation` | common | method of Min | no category |

`orientation` | common | method of Max | no category |

`ORIENTATION` | topaz | property of SimplicialComplex | Topology |

`ORIENTED_PSEUDO_MANIFOLD` | topaz | property of SimplicialComplex | Topology |

`ORIGIN` | polytope | property of AffineLattice | no category |

`ORTH_LINEALITY_SPACE` | fan | property of PolyhedralFan | Geometry |

`orthant_subdivision<Addition>(Vector<Rational> point, Int chart, Integer weight)` | tropical | Functions | Creation functions for specific cycles |

`orthantify(Polytope P, Int v)` | polytope | Functions | Transformations |

`ortho_project(Polytope p)` | polytope | Functions | Symmetry |

`orthonormal_col_basis(Matrix M)` | polytope | Functions | Transformations |

`orthonormal_row_basis(Matrix M)` | polytope | Functions | Transformations |

`out_adjacent_nodes(Int node)` | common | method of Graph | no category |

`out_degree(Int node)` | common | method of Graph | no category |

`out_edges(Int node)` | common | method of Graph | no category |

`OUTER_DESCRIPTION()` | polytope | method of Polytope | Geometry |

`outitudePolynomials(Array<Array<Int>> dcel_data)` | topaz | Functions | Other |

`outitudes(Array<Array<Int>> DCEL_data, Vector<Rational> A_coords)` | topaz | Functions | Producing other objects |

`p()` | common | method of ExtGCD | no category |

`p7_matroid()` | matroid | Functions | Producing a matroid from scratch |

`p8_matroid()` | matroid | Functions | Producing a matroid from scratch |

`P_RESOLUTION` | fulton | property of VersalComponent | Combinatorics |

`Pair<First, Second>` | common | Property_types | Basic Types |

`pappus_matroid()` | matroid | Functions | Producing a matroid from scratch |

`parallel_extension(Matroid m_1, Int e_1, Matroid m_2, Int e_2)` | matroid | Functions | Producing a matroid from matroids |

`parallel_extension(Matroid m, Int e)` | matroid | Functions | Producing a matroid from matroids |

`partition_representatives(Array<Array<Int>> gens, Set<Int> S)` | group | Functions | Symmetry |

`PATCHWORK` | tropical | property of Hypersurface | Combinatorics |

`Patchwork` | tropical | Objects | no category |

`path_graph(Int n)` | graph | Functions | Producing a graph |

`PAVING` | matroid | property of Matroid | Advanced properties |

`PENNER_COORDINATES` | topaz | property of HyperbolicSurface | no category |

`perles_irrational_8_polytope()` | polytope | Functions | Producing a polytope from scratch |

`PermBase` | common | Objects | Combinatorics |

`permutahedron(Int d)` | polytope | Functions | Producing a polytope from scratch |

`PERMUTATION` | common | property of PermBase | no category |

`PERMUTATION_ACTION` | group | property of Group | Symmetry |

`permutation_cycle_lengths(Array<Int> p)` | common | Functions | Combinatorics |

`permutation_cycles(Array<Int> p)` | common | Functions | Combinatorics |

`permutation_matrix<Scalar>(Array<Int> p)` | common | Functions | Combinatorics |

`permutation_order(Array<Int> p)` | common | Functions | Combinatorics |

`permutation_sign(Array<Int> p)` | common | Functions | Combinatorics |

`PERMUTATION_TO_ORBIT_ORDER` | group | property of Action | Symmetry |

`PermutationAction` | group | Objects | no category |

`PermutationActionOnSets` | group | Objects | no category |

`permute_inv_nodes` | common | method of Graph | no category |

`permute_nodes` | common | method of Graph | no category |

`permuted` | common | method of Plucker | no category |

`persistent_homology(Filtration<Matrix<` | topaz | Functions | Other |

`persistent_homology(Filtration F)` | topaz | Functions | Other |

`perturb_matrix(Matrix M, Float eps, Bool not_hom)` | common | Functions | Utilities |

`perturbed_long_and_winding(Int r)` | polytope | Functions | Producing a polytope from scratch |

`petersen()` | graph | Functions | Producing a graph |

`pg23_matroid()` | matroid | Functions | Producing a matroid from scratch |

`piecewise_divisor(Cycle<Addition> F, IncidenceMatrix cones, Vector<Integer> coefficients)` | tropical | Functions | Divisor computation |

`PIF_CYCLIC_NORMAL` | polytope | property of PointConfiguration | Visualization |

`pile(Vector<Int> sizes)` | polytope | Functions | Producing a polytope from scratch |

`pl_homeomorphic(SimplicialComplex complex1, SimplicialComplex complex2)` | topaz | Functions | Comparing |

`placing_triangulation(Matrix Points)` | polytope | Functions | Triangulations, subdivisions and volume |

`planar_net(Polytope p)` | fan | Functions | Producing a fan |

`PlanarNet<Scalar>` | fan | Objects | Geometry |

`platonic_solid(String s)` | polytope | Functions | Producing regular polytopes and their generalizations |

`Plucker<Scalar>` | common | Property_types | Algebraic Types |

`pluecker(Matrix V)` | common | Functions | Linear Algebra |

`pluecker_ideal(Int d, Int n)` | ideal | Functions | Producing an ideal from scratch |

`point_collection<Addition>(Matrix<Rational> points, Vector<Integer> weights)` | tropical | Functions | Creation functions for specific cycles |

`point_functions<Addition>(Vector<Rational> A)` | tropical | Functions | Intersection theory |

`POINT_LABELS` | fan | property of SubdivisionOfPoints | Visualization |

`POINT_LABELS` | fan | property of PolyhedralComplex | Visualization |

`POINT_LABELS` | polytope | property of PointConfiguration | Visualization |

`POINT_LABELS` | polytope | property of Polytope | Visualization |

`PointConfiguration<Scalar>` | polytope | Objects | no category |

`POINTED` | fan | property of PolyhedralFan | Geometry |

`POINTED` | polytope | property of Cone | Geometry |

`POINTED` | polytope | property of Polytope | Geometry |

`pointed_part(Polytope P)` | polytope | Functions | Producing a polytope from polytopes |

`POINTS` | tropical | property of Polytope | Geometry |

`POINTS` | fan | property of SubdivisionOfPoints | Geometry |

`POINTS` | fan | property of PolyhedralComplex | Input property |

`POINTS` | polytope | property of PointConfiguration | Input property |

`POINTS` | polytope | property of Polytope | Input property |

`points2hypersurface(Matrix<TropicalNumber<Addition>> points)` | tropical | Functions | Producing a tropical hypersurface |

`points2metric(Matrix points)` | polytope | Functions | Triangulations, subdivisions and volume |

`POINTS_ACTION` | fan | property of PolyhedralComplex | Symmetry |

`POINTS_ACTION` | polytope | property of PointConfiguration | Symmetry |

`POINTS_ACTION` | polytope | property of Polytope | Symmetry |

`POINTS_GENERATORS` | fan | property of PolyhedralComplex | Symmetry |

`POINTS_GENERATORS` | fan | property of PolyhedralComplex | Symmetry |

`POINTS_GENERATORS` | polytope | property of Polytope | no category |

`POINTS_IN_FACETS` | polytope | property of Polytope | Geometry |

`points_in_pseudovertices(Matrix<TropicalNumber<Addition,Scalar>> points, Matrix<Scalar> pseudovertices)` | tropical | Functions | Other |

`POINTS_ORBITS` | polytope | property of PointConfiguration | Symmetry |

`POINTS_REPS` | fan | property of PolyhedralComplex | Symmetry |

`POLAR_SMOOTH` | polytope | property of Polytope | Lattice points in cones |

`polarize(Cone C)` | polytope | Functions | Transformations |

`polarized_toric_variety(Polytope<Rational> P, String name)` | fulton | Functions | Producing a normal toric variety |

`poly2lp(Polytope P, LinearProgram LP, Bool maximize, String file)` | polytope | Functions | Optimization |

`poly2metric(Polytope P)` | polytope | Functions | Triangulations, subdivisions and volume |

`poly2porta(Polytope<Rational> p, String file)` | polytope | Functions | Optimization |

`polyDB(String host)` | common | Functions | Database Access |

`PolyDB::Client` | common | Objects | Database Access |

`PolyDB::Collection` | common | Objects | Database Access |

`PolyDB::Cursor` | common | Objects | Database Query Operations |

`POLYHEDRAL_COMPLEX` | fan | property of SubdivisionOfPoints | Geometry |

`PolyhedralComplex<Scalar>` | fan | Objects | Geometry |

`PolyhedralFan<Scalar>` | fan | Objects | Geometry |

`Polynomial<Coefficient, Exponent>` | common | Property_types | Algebraic Types |

`POLYNOMIAL` | tropical | property of Hypersurface | no category |

`POLYNOMIAL` | tropical | property of LinesInCubic | Defining properties |

`POLYTOPAL_SUBDIVISION(Int index)` | polytope | method of Visual::PointConfiguration | no category |

`POLYTOPAL_SUBDIVISION` | polytope | property of PointConfiguration | Triangulation and volume |

`POLYTOPAL_SUBDIVISION` | polytope | property of Polytope | Triangulation and volume |

`Polytope<Addition, Scalar>` | tropical | Objects | no category |

`POLYTOPE` | matroid | property of Matroid | Advanced properties |

`polytope(Int i)` | fan | method of PolyhedralComplex | Geometry |

`POLYTOPE` | fan | property of PlanarNet | Geometry |

`Polytope<Scalar>` | polytope | Objects | no category |

`POLYTOPE_COVECTOR_DECOMPOSITION` | tropical | property of Polytope | Combinatorics |

`POLYTOPE_IN_STD_BASIS(Polytope<Rational> P)` | polytope | method of Polytope | Lattice points in cones |

`POLYTOPE_MAXIMAL_COVECTOR_CELLS` | tropical | property of Polytope | Combinatorics |

`POLYTOPE_MAXIMAL_COVECTORS` | tropical | property of Polytope | Combinatorics |

`polytope_of_divisor_class` | fulton | Functions | Combinatorics |

`polytope_subdivision_as_complex(Int chart)` | tropical | method of Polytope | Geometry |

`POLYTOPES` | fan | property of PolyhedralComplex | Combinatorics |

`POLYTOPES_ORBIT_SIZES` | fan | property of PolyhedralComplex | Symmetry |

`POLYTOPES_REPS` | fan | property of PolyhedralComplex | Symmetry |

`POLYTROPE_PARTITION` | tropical | property of VoronoiDiagram | no category |

`porta2poly(String file)` | polytope | Functions | Optimization |

`porta_dual` | polytope | Functions | Transformations |

`porta_primal` | polytope | Functions | Transformations |

`poset_by_inclusion(Array<T> P)` | graph | Functions | Posets |

`poset_homomorphisms(Graph<Directed> P, Graph<Directed> Q)` | graph | Functions | Posets |

`POSITIVE` | polytope | property of VectorConfiguration | Geometry |

`POSITIVE` | polytope | property of Cone | Geometry |

`positive_circuits(Polytope or, Set<Int> S)` | polytope | Functions | Triangulations, subdivisions and volume |

`positroid_from_decorated_permutation(Array<Int> perm, Set<Int> loops)` | matroid | Functions | Producing a matroid from other objects |

`postscript(Visual::Object vis_obj …)` | common | Functions | Visualization |

`povray(Visual::Object vis_obj …)` | common | Functions | Visualization |

`POWER` | tropical | property of RationalFunction | Defining morphisms and functions |

`PowerSet<Element>` | common | Property_types | Set Types |

`prefer(String label_expression)` | core | Functions | Basic |

`prefer_now(String label_expression)` | core | Functions | Basic |

`prescribe_property_types(Any properties)` | core | method of Schema | no category |

`PRIMARY` | ideal | property of Ideal | Commutative algebra |

`PRIMARY_DECOMPOSITION` | ideal | property of Ideal | Commutative algebra |

`PRIME` | ideal | property of Ideal | Commutative algebra |

`primitive(Vector v)` | common | Functions | Lattice Tools |

`primitive(Matrix M)` | common | Functions | Lattice Tools |

`primitive_affine(Vector v)` | common | Functions | Lattice Tools |

`primitive_affine(Matrix M)` | common | Functions | Lattice Tools |

`PRINCIPAL` | fulton | property of TDivisor | Algebraic Geometry |

`principal_extension(Matroid M, Set<Int> F)` | matroid | Functions | Producing a matroid from matroids |

`principal_lift(Matroid M, Set<Int> F)` | matroid | Functions | Producing a matroid from matroids |

`principal_solution(Matrix<TropicalNumber> A, Vector<TropicalNumber> b)` | tropical | Functions | Tropical operations |

`principal_truncation(Matroid M, Set<Int> F)` | matroid | Functions | Producing a matroid from matroids |

`print_constraints(Matrix<Scalar> M)` | common | Functions | Formatting |

`print_constraints(Cone<Scalar> C)` | polytope | Functions | Optimization |

`print_face_lattice(IncidenceMatrix VIF, Bool dual)` | polytope | Functions | Geometry |

`print_ordered(Exponent x)` | common | method of UniPolynomial | no category |

`print_ordered(Matrix m)` | common | method of Polynomial | no category |

`prism(Polytope P, Scalar z1, Scalar z2)` | polytope | Functions | Producing a polytope from polytopes |

`product(PolyhedralFan F1, PolyhedralFan F2)` | fan | Functions | Producing a fan |

`product(Polytope P1, Polytope P2)` | polytope | Functions | Producing a polytope from polytopes |

`PROJ_DICTIONARY` | topaz | property of SimplicialComplex | Combinatorics |

`PROJ_ORBITS` | topaz | property of SimplicialComplex | Combinatorics |

`project()` | common | method of Polynomial | no category |

`project_full(PolyhedralFan P)` | fan | Functions | Producing a fan |

`project_full(Cone P)` | polytope | Functions | Producing a polytope from polytopes |

`project_full<Scalar>(VectorConfiguration P)` | polytope | Functions | Producing a vector configuration |