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, Any O)`	group	Functions	Utilities
`action_from_generators(Array<Array<Int>> gens, Group action)`	group	Functions	Utilities
`action_inv<action_type>(Array<Int> p, Any 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 GraphAdjacency	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 GraphAdjacency	no category
`add_user_to_collection()`	common	method of PolyDB::Client	Database Administration
`ADJACENCY`	graph	property of Graph	no category
`adjacency_matrix(GraphAdjacency graph)`	common	Functions	Graph Operations
`adjacent_nodes(Int node)`	common	method of GraphAdjacency	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 Polytope	Geometry
`AFFINE_HULL`	polytope	property of PointConfiguration	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 GraphAdjacency	no category
`all_families()`	tropical	method of LinesInCubic	Lists of lines
`ALL_GROUP_ELEMENTS`	group	property of Action	Symmetry
`all_group_elements(PermutationAction a)`	group	Functions	Utilities
`all_group_elements<Scalar>(MatrixActionOnVectors<Scalar> action)`	group	Functions	Symmetry
`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(Any c)`	common	Functions	Set Operations
`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	method of PolyhedralComplex	Geometry
`AMBIENT_DIM`	fan	method of SubdivisionOfPoints	Geometry
`AMBIENT_DIM()`	polytope	method of Cone	Geometry
`AMBIENT_DIM()`	polytope	method of Polytope	Geometry
`AMBIENT_DIM()`	polytope	method of PointConfiguration	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`	common	method of Min	no category
`apply`	common	method of Max	no category
`apply(Core::BigObject o)`	core	method of Core::RuleChain	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
`arrangement_from_cones(Cone C …)`	fan	Functions	Producing a hyperplane arrangement
`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
`augmented_matroid_fan<Addition>(Matroid A)`	tropical	Functions	Matroids
`auto_group_on_coordinates(IncidenceMatrix etv, Set<Int> marked_edges)`	tropical	Functions	Symmetry
`automorphism_group(GraphAdjacency graph)`	group	Functions	Symmetry
`automorphism_group(IncidenceMatrix<NonSymmetric> m, Bool on_rows)`	group	Functions	Symmetry
`AUTOMORPHISM_GROUP`	matroid	property of Matroid	Advanced properties
`automorphisms(GraphAdjacency 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	method of Cycle	Local computations
`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`	polytope	property of PointConfiguration	Geometry
`barycenter(Matrix<Scalar> M)`	common	Functions	Linear Algebra
`barycentric_subdivision(Cone c)`	polytope	Functions	Triangulations, subdivisions and volume
`barycentric_subdivision(SimplicialComplex complex)`	topaz	Functions	Producing a new simplicial complex from others
`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`	polytope	property of AffineLattice	no category
`BASIS`	ideal	property of Groebner	Commutative algebra
`basis(Matrix A)`	common	Functions	Linear Algebra
`basis_affine(Matrix A)`	common	Functions	Linear Algebra
`basis_cols(Matrix M)`	common	Functions	Linear Algebra
`basis_rows(Matrix M)`	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
`BETTI_NUMBERS_Z2`	tropical	property of Patchwork	no category
`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`	ideal	property of Ideal	no category
`binomial(Int n, Int k)`	common	Functions	Combinatorics
`BINOMIAL_BASIS`	ideal	property of Ideal	no category
`BINOMIAL_GENERATORS`	ideal	property of Ideal	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`	polytope	property of Cone	Combinatorics
`BOUNDARY`	polytope	property of PointConfiguration	Combinatorics
`BOUNDARY`	topaz	property of SimplicialComplex	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 Polytope	Geometry
`BOUNDED`	polytope	property of PointConfiguration	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(Int chart)`	tropical	method of Cycle	Visualization
`BOUNDING_BOX`	graph	property of GeometricGraph	no category
`bounding_box(Matrix m)`	common	Functions	Utilities
`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
`braid_arrangement(Int d)`	fan	Functions	Producing a hyperplane arrangement
`broken_circuit_complex(Matroid M, Array<Int> O)`	topaz	Functions	Producing a simplicial complex from other objects
`bs2quotient_by_equivalence(Polytope P)`	topaz	Functions	Producing a new simplicial complex from others
`bs2quotient_by_equivalence(Polytope P, SimplicialComplex complex)`	topaz	Functions	Producing a new simplicial complex from others
`bs2quotient_by_group(Polytope P)`	topaz	Functions	Producing a new simplicial complex from others
`building_set(Array<Set> generators, Int n)`	fan	Functions	Other
`building_set_ycoord_2_zcoord(Map<Set<Int>,Scalar> The)`	polytope	Functions	Coordinate conversions
`CachedObjectPointer`	common	Property_types	Artificial
`CANONICAL`	polytope	property of Polytope	Lattice points in cones
`canonical_form(GraphAdjacency g)`	graph	Functions	Comparing
`canonical_hash(GraphAdjacency 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(Int i)`	fan	method of SubdivisionOfVectors	Geometry
`cell(Int i)`	fan	method of SubdivisionOfPoints	Geometry
`Cell`	topaz	Property_types	Topology
`cell_from_subdivision(Polytope P, Int cell)`	polytope	Functions	Producing a polytope from polytopes
`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 Polytope	Geometry
`CENTERED`	polytope	property of PointConfiguration	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
`CHAIN_COMPLEX_Z2`	tropical	property of Patchwork	no category
`ChainComplex<MatrixType>`	topaz	Property_types	Topology
`CHAMBER_DECOMPOSITION`	fan	property of HyperplaneArrangement	Geometry
`chamber_decomposition_brute_force`	fan	Functions	Geometry
`chamber_decomposition_rs`	fan	Functions	Producing a fan
`CHAMBER_SIGNATURES`	fan	property of HyperplaneArrangement	Combinatorics
`chamber_to_signature`	fan	method of HyperplaneArrangement	Combinatorics
`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_circuits_axiom(Array<Set> C)`	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(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(Matrix M)`	polytope	Functions	Triangulations, subdivisions and volume
`circuit_completions(Matrix L, Matrix R)`	polytope	Functions	Geometry
`CIRCUITS`	polytope	property of VectorConfiguration	Matroid properties
`CIRCUITS`	polytope	property of Polytope	Matroid properties
`CIRCUITS`	matroid	property of Matroid	Axiom systems
`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`	polytope	property of VectorConfiguration	Matroid properties
`COCIRCUITS`	polytope	property of Polytope	Matroid properties
`COCIRCUITS`	matroid	method of Matroid	Axiom systems
`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`	tropical	property of Hypersurface	no category
`COEFFICIENTS`	fulton	property of TDivisor	Combinatorics
`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 IncidenceMatrix	no category
`col(Int i)`	common	method of Matrix	no category
`col_to_row_action(Matrix M, Array<Array> p)`	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	Combinatorics
`COLORING`	topaz	property of SimplicialComplex	no category
`cols()`	common	method of IncidenceMatrix	no category
`cols()`	common	method of Matrix	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_symmetries(SimplicialComplex sigma)`	topaz	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`	fan	property of PolyhedralFan	Combinatorics
`complete(Int n)`	graph	Functions	Producing a graph
`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 M)`	common	Functions	Data Conversion
`cone(Int i)`	fan	method of PolyhedralFan	Combinatorics
`Cone<Scalar>`	polytope	Objects	no category
`cone(SimplicialComplex complex, Int k)`	topaz	Functions	Producing a new simplicial complex from others
`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_TORIC_IDEAL`	polytope	property of Cone	Lattice points in cones
`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_of_dim(Int k)`	fan	method of PolyhedralFan	Combinatorics
`CONES_ORBIT_SIZES`	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()`	polytope	method of Cone	Combinatorics
`CONNECTIVITY`	graph	property of Graph	no category
`connectivity(GraphAdjacency<Undirected> graph)`	graph	Functions	Combinatorics
`CONNECTIVITY()`	topaz	method of SimplicialComplex	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
`contained_in_ball(Vector<Scalar> c, Scalar r)`	polytope	method of Polytope	Geometry
`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`	polytope	method of Cone	Geometry
`contains(Element e)`	common	method of Set	no category
`contains_ball(Vector<Scalar> c, Scalar r)`	polytope	method of Polytope	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 GraphAdjacency	no category
`contracted_edge_incidence_matrix(IncidenceMatrix etv, Set<Int> contracted_edges)`	tropical	Functions	Symmetry
`contraction(VectorConfiguration C, Int v)`	polytope	Functions	Combinatorics
`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
`conv(Array<Polytope> P_Array)`	polytope	Functions	Producing a polytope from polytopes
`convert_to<Coord>(Cone c)`	polytope	Functions	Coordinate conversions
`convert_to<Coord>(Polytope P)`	polytope	Functions	Coordinate conversions
`convert_to<Target>(Scalar s)`	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
`CONVEX`	fan	property of SubdivisionOfVectors	Geometry
`CONVEX`	polytope	property of PointConfiguration	Geometry
`CONVEX_HULL`	polytope	property of PointConfiguration	Geometry
`conway(Polytope P, String operations)`	polytope	Functions	Producing a polytope from polytopes
`conway_ambo(Polytope P)`	polytope	Functions	Producing a polytope from polytopes
`conway_CG(Polytope P, Int k, Int l)`	polytope	Functions	Producing a polytope from polytopes
`conway_dual(Polytope P)`	polytope	Functions	Producing a polytope from polytopes
`conway_gyro(Polytope P)`	polytope	Functions	Producing a polytope from polytopes
`conway_kis(Polytope P)`	polytope	Functions	Producing a polytope from polytopes
`conway_needle(Polytope P)`	polytope	Functions	Producing a polytope from polytopes
`conway_propeller(Polytope P)`	polytope	Functions	Producing a polytope from polytopes
`conway_seed()`	polytope	Functions	Producing a polytope from polytopes
`conway_snub(Polytope P)`	polytope	Functions	Producing a polytope from polytopes
`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`	topaz	property of GeometricSimplicialComplex	no category
`coordinates`	common	method of Plucker	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<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`cramer(Matrix A, Vector b)`	common	Functions	Linear Algebra
`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<Scalar>`	tropical	Objects	no category
`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`	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`	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(Int node)`	common	method of GraphAdjacency	no category
`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 GraphAdjacency	no category
`delete_edge`	common	method of GraphAdjacency	no category
`delete_node(Int node)`	common	method of GraphAdjacency	no category
`delete_user(String user)`	common	method of PolyDB::Client	Database Administration
`deletion(VectorConfiguration C, Int v)`	polytope	Functions	Combinatorics
`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
`delocalize()`	tropical	method of Cycle	Local computations
`delpezzo(Int d, Scalar scale)`	polytope	Functions	Producing a polytope from scratch
`DENOMINATOR`	tropical	property of TropicalRationalFunction	Defining morphisms and functions
`denominator(Rational a)`	common	Functions	Arithmetic
`denominator(RationalFunction f)`	common	Functions	Arithmetic
`denominator(PuiseuxFraction f)`	common	Functions	Arithmetic
`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
`describe(Polytope P)`	polytope	Functions	Combinatorics
`description`	core	method of Core::BigObject	no category
`det(Matrix<Scalar> A)`	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()`	polytope	method of Cone	Backward compatibility
`DIAMETER`	graph	property of Graph	no category
`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`	tropical	method of CovectorLattice	Combinatorics
`dim()`	fan	method of PolyhedralFan	Combinatorics
`DIM()`	fan	method of PolyhedralFan	Geometry
`DIM()`	fan	method of PolyhedralComplex	Geometry
`DIM`	fan	method of SubdivisionOfPoints	Geometry
`DIM`	polytope	property of QuotientSpace	Combinatorics
`dim()`	polytope	method of Cone	Combinatorics
`DIM()`	polytope	method of Cone	Geometry
`DIM()`	polytope	method of Polytope	Geometry
`DIM()`	polytope	method of PointConfiguration	Geometry
`DIM`	ideal	property of Ideal	Commutative algebra
`DIM`	topaz	property of SimplicialComplex	Combinatorics
`dim`	topaz	method of SimplicialComplex	no category
`dim()`	topaz	method of ChainComplex	no category
`dim()`	topaz	method of Filtration	no category
`dim()`	common	method of Vector	no category
`dim()`	common	method of GraphAdjacency	no category
`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(LinearProgram lp)`	polytope	method of Visual::SchlegelDiagram	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`	polytope	property of LinearProgram	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
`DisjointStackyFan<Scalar>`	fan	Objects	Symmetry
`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(Scalar a, Scalar b)`	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(Cycle C, TropicalRationalFunction F)`	tropical	Functions	Divisor computation
`DIVISOR`	fulton	property of NormalToricVariety	Algebraic Geometry
`divisor_nr(Cycle C, TropicalRationalFunction F)`	tropical	Functions	Divisor computation
`dodecahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`DOMAIN`	tropical	property of TropicalRationalFunction	Defining morphisms and functions
`DOMAIN`	tropical	property of Morphism	Defining morphisms and functions
`DOMAIN_NAME`	group	property of Action	Symmetry
`DOME`	tropical	property of Polytope	Geometry
`DOME`	tropical	property of Hypersurface	no category
`dont_save`	core	method of Core::BigObject	no category
`DoublyConnectedEdgeList`	graph	Property_types	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()`	polytope	method of Cone	Combinatorics
`DUAL_CONNECTIVITY()`	topaz	method of SimplicialComplex	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`	fan	property of PolyhedralFan	Combinatorics
`DUAL_GRAPH`	polytope	property of Cone	Combinatorics
`DUAL_GRAPH`	polytope	property of Polytope	Combinatorics
`DUAL_GRAPH`	topaz	property of SimplicialComplex	Combinatorics
`DUAL_GRAPH_SIGNATURE()`	polytope	method of Cone	Topology
`DUAL_GRAPH_SIGNATURE()`	topaz	method of SimplicialComplex	Combinatorics
`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(Matrix<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 from, Int to)`	common	method of EdgeMap	no category
`edge(Int from, Int to)`	common	method of EdgeHashMap	no category
`edge(Int tail_node, Int head_node)`	common	method of GraphAdjacency	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	Geometry
`EDGE_DIRECTIONS`	polytope	property of Polytope	no category
`edge_exists(Int tail_node, Int head_node)`	common	method of GraphAdjacency	no category
`EDGE_LABELS`	topaz	property of GrassPluckerCertificate	Geometry
`EDGE_LENGTHS`	tropical	property of Curve	Weights and lattices
`EDGE_LENGTHS`	polytope	property of Polytope	no category
`edge_lengths(GraphAdjacency<Directed> G, Matrix coords)`	graph	Functions	Other
`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 GraphAdjacency	no category
`edges(GraphAdjacency graph)`	common	Functions	Graph Operations
`EDGES_THROUGH_VERTICES`	tropical	property of Curve	Weights and lattices
`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> M)`	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 IncidenceMatrix	no category
`elem(Int r, Int c)`	common	method of Matrix	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, Coefficient x, Int exp)`	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
`expand(Map<Integer,Int> factorization)`	common	Functions	Utilities
`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(Scalar a, Scalar b)`	common	Functions	Arithmetic
`extend_application(String extension, String app_name)`	core	Functions	Interactive
`ExtGCD<Scalar>`	common	Property_types	Arithmetic
`F2_VECTOR`	fan	property of PolyhedralFan	Combinatorics
`F2_VECTOR`	polytope	property of Cone	Combinatorics
`F2_VECTOR`	polytope	property of Polytope	Combinatorics
`F2_VECTOR`	topaz	property of SimplicialComplex	Combinatorics
`f8_matroid()`	matroid	Functions	Producing a matroid from scratch
`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
`F_VECTOR`	topaz	property of SimplicialComplex	Combinatorics
`F_VECTOR`	matroid	property of Matroid	Advanced properties
`fac(Int n)`	common	Functions	Arithmetic
`face(Cone P, Set S)`	polytope	Functions	Producing a polytope from polytopes
`face()`	graph	method of BasicDecoration	no category
`FACE_CLASSES`	polytope	property of QuotientSpace	Combinatorics
`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`	polytope	property of QuotientSpace	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_of_dim(Int d)`	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`	polytope	property of Cone	Geometry
`FACETS`	topaz	property of SimplicialComplex	Combinatorics
`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
`factor(Integer n)`	common	Functions	Utilities
`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(Cone P1, Cone P2)`	polytope	Functions	Comparing
`find_facet_vertex_permutations(SimplicialComplex complex1, SimplicialComplex complex2)`	topaz	Functions	Comparing
`find_lattice_permutation(Lattice L1, Lattice L2, Permutation permutation)`	graph	Functions	Combinatorics
`find_node_permutation(GraphAdjacency graph1, GraphAdjacency 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(Matrix<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>(GraphAdjacency<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<Scalar> v)`	common	Functions	Arithmetic
`gcd(UniPolynomial p, UniPolynomial q)`	common	Functions	Arithmetic
`gelfand_tsetlin<Scalar>(Vector<Scalar> lambda)`	polytope	Functions	Producing a polytope from scratch
`gelfand_tsetlin_counting<Scalar>(Vector<Scalar> lambda)`	polytope	Functions	Geometry
`gelfand_tsetlin_diagrams<Scalar>(Vector<Scalar> lambda)`	polytope	Functions	Geometry
`generalized_johnson_graph(Int n, Int k, Int i)`	graph	Functions	Producing a graph
`generalized_permutahedron<Scalar>(Int d, Map<Set<Int>,Scalar> z)`	polytope	Functions	Producing a polytope from scratch
`GENERATING_HASSE_DIAGRAM`	fan	property of DisjointStackyFan	Symmetry
`GENERATING_MAXIMAL_CONES`	fan	property of DisjointStackyFan	Symmetry
`generating_polyhedron_facets(PolyhedralFan P)`	fan	Functions	Geometry
`GENERATING_POLYTOPE`	fulton	property of NormalToricVariety	Basic properties
`GENERATING_RAYS`	fan	property of DisjointStackyFan	Symmetry
`GENERATORS`	group	property of Action	Symmetry
`GENERATORS`	ideal	property of Ideal	Input properties
`GENUS`	tropical	method of Hypersurface	Topology
`GENUS`	tropical	property of Curve	Weights and lattices
`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 Polytope	Triangulation and volume
`GKZ_VECTOR`	polytope	property of PointConfiguration	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`	tropical	property of RationalCurve	Combinatorics
`GRAPH`	fan	property of PolyhedralFan	Combinatorics
`GRAPH`	polytope	property of Cone	Combinatorics
`GRAPH`	polytope	property of Polytope	Combinatorics
`GRAPH`	polytope	property of Polytope	Combinatorics
`GRAPH`	polytope	property of PointConfiguration	Combinatorics
`Graph<Dir>`	graph	Objects	Combinatorics
`GRAPH`	topaz	property of SimplicialComplex	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()`	polytope	method of Cone	Topology
`GRAPH_SIGNATURE()`	topaz	method of SimplicialComplex	Combinatorics
`GraphAdjacency<Dir>`	common	Property_types	Graph Types
`GraphMap<Dir, Element>`	common	Property_types	Graph Types
`graphviz(Visual::Object vis_obj …)`	graph	Functions	Visualization
`grass_plucker(SimplicialComplex S)`	topaz	Functions	Other
`GRASS_PLUCKER_CERTIFICATE`	topaz	property of SimplicialComplex	Geometry
`GrassPluckerCertificate`	topaz	Objects	Geometry
`Groebner`	ideal	Objects	no category
`GROEBNER`	ideal	property of Ideal	Commutative algebra
`groebner_fan(Ideal I)`	fan	Functions	Producing a fan
`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 Polytope	Symmetry
`GROUP`	polytope	property of PointConfiguration	Symmetry
`GROUP`	topaz	property of SimplicialComplex	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_POLYNOMIAL`	polytope	property of Cone	Lattice points in cones
`H_STAR_VECTOR`	polytope	property of Cone	Lattice points in cones
`H_VECTOR`	polytope	property of Polytope	Combinatorics
`H_VECTOR`	topaz	property of SimplicialComplex	Combinatorics
`H_VECTOR`	matroid	property of Matroid	Advanced properties
`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 GraphAdjacency	no category
`HashMap<Key, Value>`	common	Property_types	Set Types
`HashSet<Element>`	common	Property_types	Set Types
`HASSE_DIAGRAM`	fan	property of PolyhedralFan	Combinatorics
`HASSE_DIAGRAM`	polytope	property of Cone	Combinatorics
`HASSE_DIAGRAM`	polytope	property of Polytope	Combinatorics
`HASSE_DIAGRAM`	topaz	property of SimplicialComplex	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`	polytope	property of Cone	Lattice points in cones
`HOMOGENEOUS`	ideal	property of Ideal	Commutative algebra
`HOMOGENEOUS_COORDINATE_ACTION`	group	property of Group	Symmetry
`HOMOLOGY`	fan	property of PolyhedralFan	Topology
`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_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_AMBIENT_DIM`	fan	property of HyperplaneArrangement	Geometry
`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 GraphAdjacency	no category
`in_degree(Int node)`	common	method of GraphAdjacency	no category
`in_edges(Int node)`	common	method of GraphAdjacency	no category
`incidence_matrix(Graph G)`	graph	Functions	Combinatorics
`incidence_matrix(GraphAdjacency 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`	group	property of Action	Symmetry
`index_of(Array<Set<Int>> array)`	common	Functions	Utilities
`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_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(GraphAdjacency graph, Set set)`	common	Functions	Graph Operations
`INEQUALITIES`	tropical	property of Polytope	Input property
`INEQUALITIES`	tropical	property of Curve	Weights and lattices
`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 Integer	no category
`inf`	common	method of Rational	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_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_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_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_array(Array objects)`	common	method of PolyDB::Collection	Database Collection Administration
`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(PolyhedralFan F, Matrix H)`	fan	Functions	Producing a fan
`intersection(Cone C …)`	polytope	Functions	Producing a polytope from polytopes
`intersection(Matroid M)`	matroid	Functions	Producing a matroid from matroids
`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 M)`	common	Functions	Linear Algebra
`invalid_node(Int node)`	common	method of GraphAdjacency	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<Int>> check_me, Set<Set<Int>> 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(Set<Set<Int>> 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 TropicalRationalFunction	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(Scalar s)`	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(Scalar s)`	common	Functions	Arithmetic
`isa(Any type)`	core	method of Core::BigObject	no category
`isfinite(Scalar a)`	common	Functions	Arithmetic
`isinf(Scalar a)`	common	Functions	Arithmetic
`isomorphic(Cone P1, Cone P2)`	polytope	Functions	Comparing
`isomorphic(IncidenceMatrix IncidenceMatrix1, IncidenceMatrix IncidenceMatrix2)`	graph	Functions	Comparing
`isomorphic(GraphAdjacency graph1, GraphAdjacency graph2)`	graph	Functions	Comparing
`isomorphic(SimplicialComplex complex1, SimplicialComplex complex2)`	topaz	Functions	Comparing
`isomorphic_curves(IncidenceMatrix etv, Array<Int> vertex_weights, Vector<Scalar> v, Vector<Scalar> w)`	tropical	Functions	Symmetry
`isomorphic_curves(Curve<Scalar> G, Curve<Scalar> H)`	tropical	Functions	Symmetry
`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(Cone c, Int n)`	polytope	Functions	Triangulations, subdivisions and volume
`iterated_barycentric_subdivision(SimplicialComplex complex, Int k)`	topaz	Functions	Producing a new simplicial complex from others
`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
`jockusch_3_ball(Int n)`	topaz	Functions	Producing from scratch
`jockusch_3_sphere(Int n)`	topaz	Functions	Producing from scratch
`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<Coord>(PolyhedralFan F, Int k)`	fan	Functions	Producing a fan
`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
`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_FACETS`	polytope	property of Cone	Visualization
`LABELED_FACETS`	topaz	property of SimplicialComplex	Topology
`LABELED_ORIENTATION`	topaz	property of SimplicialComplex	Topology
`labeled_vertices(String label …)`	polytope	method of Polytope	Geometry
`labeled_vertices(String label …)`	topaz	method of SimplicialComplex	Combinatorics
`LABELS`	fan	property of SubdivisionOfVectors	Visualization
`LABELS`	polytope	property of VectorConfiguration	Visualization
`LABELS`	matroid	property of Matroid	Other
`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()`	polytope	method of Visual::Polytope	no category
`LATTICE`	polytope	property of Polytope	Geometry
`Lattice<Decoration, SeqType>`	graph	Objects	Combinatorics
`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`	polytope	property of Polytope	Lattice points in cones
`lattice_basis(Matrix<Integer> A)`	common	Functions	Linear Algebra
`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<Scalar> v)`	common	Functions	Arithmetic
`lecture_hall_simplex(Int d)`	polytope	Functions	Producing a polytope from scratch
`LEDA_graph(GraphAdjacency 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`	fan	property of PolyhedralFan	Geometry
`LINEALITY_SPACE`	fan	property of HyperplaneArrangement	Geometry
`LINEALITY_SPACE`	polytope	property of Cone	Geometry
`lineality_space(Matrix M)`	common	Functions	Linear Algebra
`LINEALITY_SPACE_GENERATORS`	group	property of Action	Symmetry
`LINEALITY_VALUES`	tropical	property of TropicalRationalFunction	Defining morphisms and functions
`LINEALITY_VALUES`	tropical	property of Morphism	Defining morphisms and functions
`LINEAR_OBJECTIVE`	polytope	property of LinearProgram	no category
`LINEAR_OBJECTIVE`	polytope	property of MixedIntegerLinearProgram	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(Matrix M)`	polytope	Functions	Symmetry
`linear_symmetries(Cone C)`	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_subcomplex(SimplicialComplex complex, Set<Int> face)`	topaz	Functions	Producing a new simplicial complex from others
`List<Element>`	common	Property_types	Basic Types
`list`	core	method of Core::RuleChain	no category
`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
`MARKED_EDGES`	tropical	property of Curve	Weights and lattices
`MASSIVE_GKZ_VECTOR`	polytope	property of PointConfiguration	Triangulation and volume
`MATCHING`	topaz	property of SimplicialComplex	no category
`MATRIX`	tropical	property of Morphism	Defining morphisms and functions
`Matrix<Element, Sym>`	common	Property_types	Algebraic Types
`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 Polytope	Symmetry
`MATRIX_ACTION`	polytope	property of PointConfiguration	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_ball(Polytope<Rational> P)`	polytope	Functions	Geometry
`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_INCIDENCES`	fan	property of PolyhedralFan	Combinatorics
`MAXIMAL_CONES_LINEAR_SPAN_NORMALS`	fan	property of PolyhedralFan	Geometry
`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_INCIDENCES`	fan	property of PolyhedralComplex	Combinatorics
`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 LinearProgram	no category
`MAXIMAL_VALUE`	polytope	property of MixedIntegerLinearProgram	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::SchlegelDiagram	no category
`MIN_MAX_FACE(LinearProgram lp)`	polytope	method of Visual::PolytopeLattice	no category
`MIN_MAX_FACE(LinearProgram lp)`	polytope	method of Visual::Polytope	no category
`MIN_MAX_FACE(LinearProgram lp)`	polytope	method of Visual::PolytopeGraph	no category
`min_metric(Int n)`	fan	Functions	Finite metric spaces
`MIN_WEIGHTS`	fan	property of SubdivisionOfVectors	Geometry
`MINIMAL_BALL`	polytope	property of Polytope	Geometry
`minimal_base(Matroid matroid, Vector weights)`	matroid	Functions	Other
`MINIMAL_FACE`	polytope	property of LinearProgram	no category
`MINIMAL_NON_FACES`	polytope	property of Polytope	Combinatorics
`MINIMAL_NON_FACES`	topaz	property of SimplicialComplex	Combinatorics
`MINIMAL_SOLUTION`	polytope	property of MixedIntegerLinearProgram	no category
`MINIMAL_VALUE`	polytope	property of LinearProgram	no category
`MINIMAL_VALUE`	polytope	property of MixedIntegerLinearProgram	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(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(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_fukuda(Array<Polytope> summands)`	polytope	Functions	Producing a polytope from polytopes
`minor(Set r, Set c)`	common	method of IncidenceMatrix	no category
`minor(Set r, Set c)`	common	method of Matrix	no category
`minus_inf`	common	method of Float	no category
`minus_inf`	common	method of Integer	no category
`minus_inf`	common	method of Rational	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
`MODULI_CELL`	tropical	property of Curve	Weights and lattices
`moduli_cell(Curve G)`	tropical	Functions	Weights and lattices
`moduli_cell_of_curve`	tropical	Functions	Symmetry
`moduli_space(Curve<Scalar> G1, Curve<Scalar> G2, Curve<Scalar> Gn)`	tropical	Functions	Symmetry
`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`	ideal	property of Ideal	Commutative algebra
`monomial`	common	method of UniPolynomial	no category
`monomial(Int var_index, Int n_vars)`	common	method of Polynomial	no category
`monomial_cone_lattice(Matrix M)`	tropical	Functions	Tropical operations
`monomial_dual_description(Matrix monomial_generators)`	tropical	Functions	Tropical operations
`MONOMIALS`	tropical	property of Hypersurface	no category
`monomials<Coefficient, Exponent>(Int n)`	common	Functions	Arithmetic
`monomials_as_matrix()`	common	method of Polynomial	no category
`monomials_as_vector()`	common	method of UniPolynomial	no category
`moore_penrose_inverse(Matrix<Float> 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	method of Visual::SimplicialComplex	no category
`MORSE_MATCHING()`	topaz	method of Visual::SimplicialComplexLattice	no category
`MORSE_MATCHING`	topaz	property of SimplicialComplex	Topology
`MorseMatching`	topaz	Objects	Topology
`mps2poly<Scalar>(String file, String prefix, Bool use_lazy)`	polytope	Functions	Optimization
`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(GraphAdjacency 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`	tropical	property of Curve	Combinatorics
`N_EDGES`	polytope	property of Cone	Combinatorics
`N_EDGES`	graph	property of Graph	no category
`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`	polytope	property of Cone	Combinatorics
`N_FACETS`	topaz	property of SimplicialComplex	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_GENERATING_RAYS`	fan	property of DisjointStackyFan	Symmetry
`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_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_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 PolyhedralComplex	Geometry
`N_POINTS`	fan	property of SubdivisionOfPoints	Geometry
`N_POINTS`	polytope	property of Polytope	Geometry
`N_POINTS`	polytope	property of PointConfiguration	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_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_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`	tropical	property of Curve	Combinatorics
`N_VERTICES`	fan	property of PolyhedralComplex	Geometry
`N_VERTICES`	polytope	property of Polytope	Combinatorics
`N_VERTICES`	topaz	property of SimplicialComplex	Combinatorics
`n_vertices()`	common	method of FacetList	no category
`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
`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`	tropical	property of RationalCurve	Combinatorics
`NODE_DEGREES`	graph	property of Graph	no category
`node_edge_incidences<Coord>(GraphAdjacency graph)`	common	Functions	Graph Operations
`node_exists(Int node)`	common	method of GraphAdjacency	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 GraphAdjacency	no category
`NodeHashMap<Dir, Element>`	common	Property_types	Graph Types
`NodeMap<Dir, Element>`	common	Property_types	Graph Types
`nodes()`	common	method of GraphAdjacency	no category
`nodes(GraphAdjacency 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(Int d)`	fan	method of PolyhedralFan	Combinatorics
`nodes_of_dim(Int d)`	polytope	method of Cone	Combinatorics
`nodes_of_dim`	topaz	method of SimplicialComplex	no category
`nodes_of_dim_range`	tropical	method of CovectorLattice	Combinatorics
`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_dim_range`	topaz	method of SimplicialComplex	no category
`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_REALIZABLE`	topaz	property of SimplicialComplex	Geometry
`NON_SATURATED`	ideal	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> M)`	common	Functions	Linear Algebra
`NormalToricVariety`	fulton	Objects	no category
`null_space(Matrix M)`	common	Functions	Linear Algebra
`null_space(Vector v)`	common	Functions	Linear Algebra
`null_space_integer(Matrix A)`	common	Functions	Linear Algebra
`numbered(Vector data)`	common	Functions	Formatting
`NUMERATOR`	tropical	property of TropicalRationalFunction	Defining morphisms and functions
`numerator(Rational a)`	common	Functions	Arithmetic
`numerator(RationalFunction f)`	common	Functions	Arithmetic
`numerator(PuiseuxFraction f)`	common	Functions	Arithmetic
`nz_4_ball(Int n)`	topaz	Functions	Producing from scratch
`nz_4_sphere(Int n)`	topaz	Functions	Producing from scratch
`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_contains(Polytope P_in, Polytope P_out)`	polytope	Functions	Geometry
`optimal_permutations(Matrix<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`ORBIFOLD`	fulton	property of NormalToricVariety	Basic properties
`orbit<action_type>(Array G, Any O)`	group	Functions	Orbits
`orbit<action_type>(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(PolyhedralComplex input_complex, 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(PermutationAction G, Set S)`	group	Functions	Orbits
`orbit_permlib(PermutationAction 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`	topaz	property of SimplicialComplex	Topology
`orientation()`	common	method of TropicalNumber	no category
`orientation`	common	method of Min	no category
`orientation`	common	method of Max	no category
`ORIENTED_PSEUDO_MANIFOLD`	topaz	property of SimplicialComplex	Topology
`ORIGIN`	polytope	property of AffineLattice	no category
`ORIGINAL_RAYS_ACTION_GENERATORS`	fan	property of DisjointStackyFan	Symmetry
`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 GraphAdjacency	no category
`out_degree(Int node)`	common	method of GraphAdjacency	no category
`out_edges(Int node)`	common	method of GraphAdjacency	no category
`OUTER_DESCRIPTION()`	polytope	method of Polytope	Geometry
`outitudePolynomials(Matrix<Int> dcel_data)`	topaz	Functions	Other
`outitudes(Matrix<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 GraphAdjacency	no category
`permute_nodes`	common	method of GraphAdjacency	no category
`permuted`	common	method of Plucker	no category
`persistent_homology(Filtration<Matrix<Scalar>> F, Int i, Int p, Int k)`	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
`pitman_stanley<Scalar>(Vector<Scalar> y)`	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
`PLUCKER_RELATIONS`	topaz	property of GrassPluckerCertificate	Geometry
`pluecker(Matrix M)`	common	Functions	Linear Algebra
`pluecker_ideal(Int d, Int n)`	ideal	Functions	Producing an ideal from scratch
`poincare_sphere()`	topaz	Functions	Producing 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 PolyhedralComplex	Visualization
`POINT_LABELS`	fan	property of SubdivisionOfPoints	Visualization
`POINT_LABELS`	polytope	property of Polytope	Visualization
`POINT_LABELS`	polytope	property of PointConfiguration	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 PolyhedralComplex	Input property
`POINTS`	fan	property of SubdivisionOfPoints	Geometry
`POINTS`	polytope	property of Polytope	Input property
`POINTS`	polytope	property of PointConfiguration	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 Polytope	Symmetry
`POINTS_ACTION`	polytope	property of PointConfiguration	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
`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
`poly2mps(Polytope P, LinearProgram LP, Set<Int> br, String file)`	polytope	Functions	Optimization
`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`	tropical	property of LinesInCubic	Defining properties
`POLYNOMIAL`	tropical	property of Hypersurface	no category
`Polynomial<Coefficient, Exponent>`	common	Property_types	Algebraic Types
`polynomial_support<Addition, Scalar>(Polynomial<TropicalNumber<Addition,Scalar>> p, Vector<TropicalNumber<Addition,Scalar>> pt)`	tropical	Functions	Tropical operations
`polynomial_vanishes<Addition, Scalar>(Polynomial<TropicalNumber<Addition,Scalar>> p, Vector<TropicalNumber<Addition,Scalar>> pt)`	tropical	Functions	Tropical operations
`POLYTOPAL_SUBDIVISION(Int index)`	polytope	method of Visual::PointConfiguration	no category
`POLYTOPAL_SUBDIVISION`	polytope	property of Polytope	Triangulation and volume
`POLYTOPAL_SUBDIVISION`	polytope	property of PointConfiguration	Triangulation and volume
`Polytope<Addition, Scalar>`	tropical	Objects	no category
`polytope(Int i)`	fan	method of PolyhedralComplex	Geometry
`POLYTOPE`	fan	property of PlanarNet	Geometry
`Polytope<Scalar>`	polytope	Objects	no category
`POLYTOPE`	matroid	property of Matroid	Advanced properties
`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
`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
`POSITIVE_VALUATION`	matroid	property of ValuatedMatroid	Valuation
`POSITROID`	matroid	property of Matroid	Advanced properties
`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 TropicalRationalFunction	Defining morphisms and functions
`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(Cone<Scalar> C)`	polytope	Functions	Optimization
`print_constraints(Matrix<Scalar> M)`	common	Functions	Formatting
`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
`project_out<Scalar>(VectorConfiguration V, Matrix B)`	polytope	Functions	Producing a vector configuration
`project_out<Scalar>(Cone C, Matrix B)`	polytope	Functions	Producing a vector configuration
`project_to<Scalar>(VectorConfiguration V, Matrix B)`	polytope	Functions	Producing a vector configuration
`project_to<Scalar>(Cone C, Matrix B)`	polytope	Functions	Producing a vector configuration
`project_to_orthogonal_complement(Matrix M, Matrix N)`	common	Functions	Linear Algebra
`PROJECTED_EQUATIONS`	polytope	property of SymmetrizedCocircuitEquations	no category
`projection(Cone P, Array<Int> indices)`	polytope	Functions	Producing a polytope from polytopes
`projection<Scalar>(VectorConfiguration P, Array<Int> indices)`	polytope	Functions	Producing a vector configuration
`PROJECTION`	fulton	property of RationalDivisorClassGroup	Algebraic Geometry
`projection_map<Addition>(Int n, Set<Int> s)`	tropical	Functions	Creation function for specific morphisms and functions
`projection_map(Int n, Int m)`	tropical	Functions	Creation function for specific morphisms and functions
`projection_preimage(Array<Cone> P_Array)`	polytope	Functions	Producing a polytope from polytopes
`projection_preimage<Scalar>(Array<VectorConfiguration> P_Array)`	polytope	Functions	Producing a vector configuration
`PROJECTIVE`	fulton	property of NormalToricVariety	Algebraic Geometry
`PROJECTIVE_AMBIENT_DIM`	tropical	property of Polytope	Geometry
`PROJECTIVE_AMBIENT_DIM`	tropical	property of Cycle	Affine and projective coordinates
`PROJECTIVE_CODIMENSION`	tropical	property of Cycle	Affine and projective coordinates
`PROJECTIVE_DIM`	tropical	property of Cycle	Affine and projective coordinates
`projective_plane(Integer p)`	matroid	Functions	Producing a matroid from scratch
`projective_potato(Matrix<Int> DCEL_data, Vector<Rational> A_coords, Matrix<Rational> first_two_vertices, Int depth)`	topaz	Functions	Producing other objects
`projective_space(Int d)`	fulton	Functions	Producing a normal toric variety
`projective_symmetries(Cone C)`	polytope	Functions	Symmetry
`projective_torus<Addition>(Int n, Integer w)`	tropical	Functions	Creation functions for specific cycles
`PROJECTIVE_VERTICES`	tropical	property of Cycle	Input property
`PropagatedPolytope<Scalar>`	polytope	Objects	no category
`properties()`	core	method of Core::BigObject	no category
`provide(String property_name)`	core	method of Core::BigObject	no category
`pseudo_delpezzo(Int d, Scalar scale)`	polytope	Functions	Producing a polytope from scratch
`PSEUDO_MANIFOLD`	topaz	property of SimplicialComplex	Topology
`PSEUDO_REGULAR`	fan	property of PolyhedralFan	Geometry
`pseudopower(Integer l, Int i)`	polytope	Functions	Other
`PSEUDOVERTEX_COARSE_COVECTORS`	tropical	property of Polytope	Combinatorics
`PSEUDOVERTEX_COVECTORS`	tropical	property of Polytope	Combinatorics
`PSEUDOVERTICES`	tropical	property of Polytope	Geometry
`psi_class<Addition>(Int n, Int i)`	tropical	Functions	Moduli of rational curves
`psi_product<Addition>(Int n, Vector<Int> exponents)`	tropical	Functions	Moduli of rational curves
`PuiseuxFraction<MinMax, Coefficient, Exponent>`	common	Property_types	Algebraic Types
`pullback(Morphism m, TropicalRationalFunction r)`	tropical	Functions	Intersection theory
`PURE`	fan	property of PolyhedralFan	Combinatorics
`PURE`	topaz	property of SimplicialComplex	Combinatorics
`pyramid(Polytope P, Scalar z)`	polytope	Functions	Producing a polytope from polytopes
`PYRAMID_LATTICE`	fulton	property of VersalComponent	Combinatorics
`q()`	common	method of ExtGCD	no category
`Q`	fulton	property of CyclicQuotient	Input properties
`q3_gf3_star_matroid()`	matroid	Functions	Producing a matroid from scratch
`q8_matroid()`	matroid	Functions	Producing a matroid from scratch
`Q_CARTIER`	fulton	property of TDivisor	Algebraic Geometry
`Q_GORENSTEIN`	fan	property of PolyhedralFan	Toric Varieties
`Q_GORENSTEIN_CONE`	polytope	property of Cone	Lattice points in cones
`Q_GORENSTEIN_CONE_INDEX`	polytope	property of Cone	Lattice points in cones
`Q_GORENSTEIN_INDEX`	fan	property of PolyhedralFan	Toric Varieties
`qr_decomp(Matrix<Float> M)`	common	Functions	Linear Algebra
`QuadraticExtension<Field>`	common	Property_types	Basic Types
`quarter_turn_manifold()`	polytope	Functions	Quotient spaces
`quot()`	common	method of Div	no category
`QUOTIENT_SPACE`	polytope	property of Polytope	Geometry
`quotient_space_simplexity_ilp(Int d, Matrix V, Scalar volume, SparseMatrix cocircuit_equations)`	polytope	Functions	Triangulations, subdivisions and volume
`quotient_space_simplexity_lower_bound(Int d, Matrix V, Scalar volume, SparseMatrix cocircuit_equations)`	polytope	Functions	Triangulations, subdivisions and volume
`QuotientSpace`	polytope	Objects	Symmetry
`r10_matroid()`	matroid	Functions	Producing a matroid from scratch
`r8_matroid()`	matroid	Functions	Producing a matroid from scratch
`r9a_matroid()`	matroid	Functions	Producing a matroid from scratch
`r9b_matroid()`	matroid	Functions	Producing a matroid from scratch
`RADICAL`	ideal	property of Ideal	Commutative algebra
`ragsdale_counterexample()`	tropical	Functions	no category
`rand01(Int d, Int n)`	polytope	Functions	Producing a polytope from scratch
`rand_aof(Polytope P, Int start)`	polytope	Functions	Optimization
`rand_box(Int d, Int n, Int b)`	polytope	Functions	Producing a polytope from scratch
`rand_cyclic(Int d, Int n)`	polytope	Functions	Producing a polytope from scratch
`rand_inner_points(Polytope P, Int n)`	polytope	Functions	Producing a polytope from polytopes
`rand_knot(Int n_edges)`	topaz	Functions	Producing from scratch
`rand_metric<Scalar>(Int n)`	polytope	Functions	Producing a polytope from scratch
`rand_metric_int<Scalar>(Int n)`	polytope	Functions	Producing a polytope from scratch
`rand_normal(Int d, Int n)`	polytope	Functions	Producing a polytope from scratch
`rand_perm(Int n)`	common	Functions	Utilities
`rand_sphere<Num>(Int d, Int n)`	polytope	Functions	Producing a polytope from scratch
`rand_vert(Matrix V, Int n)`	polytope	Functions	Producing a polytope from polytopes
`random_discrete_morse(SimplicialComplex complex)`	topaz	Functions	Other
`RANDOM_EDGE_EPL`	polytope	property of LinearProgram	no category
`random_edge_epl(Graph<Directed> G)`	polytope	Functions	Optimization
`random_graph(Int n)`	graph	Functions	Producing a graph
`random_spanningtree(Graph G)`	graph	Functions	Combinatorics
`randomInteger(Int max_arg, Int n)`	tropical	Functions	Lattices
`range(Int a, Int b)`	common	Functions	Set Operations
`range_from(Int a)`	common	Functions	Set Operations
`RANK`	tropical	property of MatroidRingCycle	Matroid data
`rank()`	graph	method of Lattice	Combinatorics
`rank()`	graph	method of BasicDecoration	no category
`RANK`	matroid	property of Matroid	Enumerative properties
`rank()`	matroid	method of Matroid	Axiom systems
`rank()`	common	method of SmithNormalForm	no category
`rank()`	common	method of HermiteNormalForm	no category
`rank(Matrix A)`	common	Functions	Linear Algebra
`rank_mod_p(Matrix M, Integer p)`	common	Functions	Linear Algebra
`Rational`	common	Property_types	Basic Types
`rational2cf(Rational r)`	fulton	Functions	Continued fractions
`rational_curve_from_cone(Cycle<Addition> X, Int n_leaves, Int coneIndex)`	tropical	Functions	Abstract rational curves
`rational_curve_from_matroid_coordinates<Addition>(Vector<Rational> v)`	tropical	Functions	Abstract rational curves
`rational_curve_from_metric(Vector<Rational> v)`	tropical	Functions	Abstract rational curves
`rational_curve_from_rays<Addition>(Matrix<Rational> rays)`	tropical	Functions	Abstract rational curves
`rational_curve_immersion<Addition>(Matrix<Rational> delta, RationalCurve type)`	tropical	Functions	Abstract rational curves
`rational_curve_list_from_matroid_coordinates<Addition>(Matrix<Rational> m)`	tropical	Functions	Abstract rational curves
`rational_curve_list_from_metric(Matrix<Rational> m)`	tropical	Functions	Abstract rational curves
`RATIONAL_DIVISOR_CLASS_GROUP`	fulton	property of NormalToricVariety	Algebraic Geometry
`rational_fct_from_affine_denominator(Polynomial<TropicalNumber<Addition>> p, Int chart)`	tropical	Functions	Affine and projective coordinates
`rational_fct_from_affine_denominator(String p, Int chart)`	tropical	Functions	Affine and projective coordinates
`rational_fct_from_affine_numerator(Polynomial<TropicalNumber<Addition>> p, Int chart)`	tropical	Functions	Affine and projective coordinates
`rational_fct_from_affine_numerator(String p, Int chart)`	tropical	Functions	Affine and projective coordinates
`RationalCurve`	tropical	Objects	no category
`RationalDivisorClassGroup`	fulton	Objects	no category
`RationalFunction<Coefficient, Exponent>`	common	Property_types	Algebraic Types
`RAY_LABELS`	fan	property of PolyhedralFan	Visualization
`RAY_LABELS`	polytope	property of Cone	Visualization
`RAY_SEPARATORS`	polytope	property of Cone	Geometry
`RAY_SIZES`	polytope	property of Cone	Combinatorics
`RAYS`	fan	property of PolyhedralFan	Geometry
`RAYS`	polytope	property of Cone	Geometry
`RAYS_ACTION`	group	property of Group	Symmetry
`RAYS_GENERATORS`	group	property of Action	Symmetry
`RAYS_IN_FACETS`	polytope	property of Cone	Combinatorics
`RAYS_IN_HYPERPLANES`	fan	property of HyperplaneArrangement	Combinatorics
`RAYS_IN_INEQUALITIES`	polytope	property of Cone	Geometry
`RAYS_IN_RIDGES`	polytope	property of Cone	Combinatorics
`RAYS_ORBITS`	polytope	property of Cone	Symmetry
`REAL_FACETS`	tropical	property of Patchwork	no category
`REAL_PHASE`	tropical	property of Patchwork	no category
`real_projective_plane()`	topaz	Functions	Producing from scratch
`realize(String method)`	tropical	method of Patchwork	no category
`recession_cone(Polytope<Scalar> P)`	polytope	Functions	Producing a cone
`recession_fan(Cycle complex)`	tropical	Functions	Basic polyhedral operations
`reconfigure(String rulename)`	core	Functions	Interactive
`reconfigure_extension(String extension, String options)`	core	Functions	Interactive
`reduce`	ideal	method of Groebner	no category
`reduce(Matrix A, Vector b)`	common	Functions	Linear Algebra
`reduced(Rational t, Rational x, Rational s, Rational h, Rational r)`	polytope	Functions	Producing regular polytopes and their generalizations
`REDUNDANT_MONOMIALS`	tropical	property of Hypersurface	no category
`REFINED_SPLITS`	polytope	property of Cone	Combinatorics
`REFINED_SPLITS`	polytope	property of Polytope	Combinatorics
`REFINED_SPLITS`	polytope	property of PointConfiguration	Triangulation and volume
`REFINED_SPLITS`	polytope	property of PointConfiguration	Combinatorics
`REFLEXIVE`	polytope	property of Polytope	Lattice points in cones
`REGIONS`	tropical	property of Hypersurface	no category
`REGULAR`	fan	property of PolyhedralFan	Geometry
`REGULAR`	fan	property of SubdivisionOfPoints	Geometry
`REGULAR`	matroid	property of Matroid	Realizability
`regular_120_cell()`	polytope	Functions	Producing regular polytopes and their generalizations
`regular_24_cell()`	polytope	Functions	Producing regular polytopes and their generalizations
`regular_600_cell()`	polytope	Functions	Producing regular polytopes and their generalizations
`REGULAR_REPRESENTATION`	group	property of Group	Symmetry
`regular_representation(PermutationAction a)`	group	Functions	Symmetry
`regular_simplex(Int d)`	polytope	Functions	Producing regular polytopes and their generalizations
`regular_subdivision(Matrix points, Vector weights)`	polytope	Functions	Triangulations, subdivisions and volume
`regularity_lp(Matrix points, Array<Set<Int>> subdiv)`	polytope	Functions	Triangulations, subdivisions and volume
`REL_INT_POINT`	polytope	property of Cone	Geometry
`RELATIVE_VOLUME`	polytope	property of Polytope	Triangulation and volume
`rem()`	common	method of Div	no category
`remove(String id)`	common	method of PolyDB::Collection	Database Collection Administration
`remove(String property_name)`	core	method of Core::BigObject	no category
`remove_all`	common	method of PolyDB::Collection	Database Collection Administration
`remove_attachment(String name)`	core	method of Core::BigObject	no category
`remove_collection()`	common	method of PolyDB::Client	Database Administration
`remove_section()`	common	method of PolyDB::Client	Database Administration
`remove_user_from_collection()`	common	method of PolyDB::Client	Database Administration
`remove_zero_rows(Matrix M)`	common	Functions	Linear Algebra
`repeat_col(Vector v, Int i)`	common	Functions	Data Conversion
`repeat_row(Vector v, Int i)`	common	Functions	Data Conversion
`replay_history`	core	Functions	Interactive
`representation_conversion_up_to_symmetry(Cone c)`	polytope	Functions	Symmetry
`representative`	tropical	method of LinesInCubic	Lists of lines
`representative`	tropical	method of LinesInCubic	Lists of lines
`representative`	tropical	method of LinesInCubic	Lists of lines
`representative`	tropical	method of LinesInCubic	Lists of lines
`REPRESENTATIVE_BOUNDARY_RIDGE_SIMPLICES`	polytope	property of Cone	Symmetry
`REPRESENTATIVE_BOUNDARY_RIDGE_SIMPLICES`	polytope	property of PointConfiguration	Symmetry
`REPRESENTATIVE_CERTIFIERS`	polytope	property of Polytope	no category
`REPRESENTATIVE_COMBINATORIAL_DIMS`	fan	property of PolyhedralFan	Symmetry
`REPRESENTATIVE_CONES`	fan	property of PolyhedralFan	Symmetry
`REPRESENTATIVE_CORE_POINTS`	polytope	property of Polytope	no category
`REPRESENTATIVE_F_VECTOR`	fan	property of PolyhedralFan	Symmetry
`REPRESENTATIVE_FACETS`	polytope	property of Cone	Symmetry
`REPRESENTATIVE_INEQUALITIES()`	polytope	method of Cone	Symmetry
`REPRESENTATIVE_INEQUALITIES`	polytope	method of Polytope	no category
`REPRESENTATIVE_INPUT_CONES`	fan	method of PolyhedralFan	Symmetry
`REPRESENTATIVE_INPUT_RAYS`	fan	method of PolyhedralFan	Symmetry
`REPRESENTATIVE_INPUT_RAYS()`	polytope	method of Cone	Symmetry
`REPRESENTATIVE_INTERIOR_RIDGE_SIMPLICES`	polytope	property of QuotientSpace	Combinatorics
`REPRESENTATIVE_INTERIOR_RIDGE_SIMPLICES`	polytope	property of Cone	Symmetry
`REPRESENTATIVE_INTERIOR_RIDGE_SIMPLICES`	polytope	property of PointConfiguration	Symmetry
`REPRESENTATIVE_MAX_BOUNDARY_SIMPLICES`	polytope	property of QuotientSpace	Combinatorics
`REPRESENTATIVE_MAX_BOUNDARY_SIMPLICES`	polytope	property of Cone	Symmetry
`REPRESENTATIVE_MAX_BOUNDARY_SIMPLICES`	polytope	property of PointConfiguration	Symmetry
`REPRESENTATIVE_MAX_INTERIOR_SIMPLICES`	polytope	property of QuotientSpace	Combinatorics
`REPRESENTATIVE_MAX_INTERIOR_SIMPLICES`	polytope	property of Cone	Symmetry
`REPRESENTATIVE_MAX_INTERIOR_SIMPLICES`	polytope	property of PointConfiguration	Symmetry
`REPRESENTATIVE_MAXIMAL_CONES`	fan	property of PolyhedralFan	Symmetry
`REPRESENTATIVE_MAXIMAL_POLYTOPES`	fan	property of PolyhedralComplex	Symmetry
`REPRESENTATIVE_RAYS`	fan	property of PolyhedralFan	Symmetry
`REPRESENTATIVE_RAYS`	polytope	property of Cone	Symmetry
`REPRESENTATIVE_VERTICES`	fan	property of PolyhedralComplex	Symmetry
`REPRESENTATIVE_VERTICES`	polytope	property of Polytope	Symmetry
`reset_custom(Any variable)`	core	Functions	Basic
`reset_preference(String label_expression)`	core	Functions	Basic
`reset_var_names`	common	method of UniPolynomial	no category
`reset_var_names`	common	method of Polynomial	no category
`resize(Int r, Int c)`	common	method of SparseMatrix	no category
`resize(Int r, Int c)`	common	method of Matrix	no category
`restrict(Cycle<Addition> C)`	tropical	method of TropicalRationalFunction	Defining morphisms and functions
`restrict(Cycle Some)`	tropical	method of Morphism	Morphisms
`revert(Polytope P)`	polytope	Functions	Transformations
`REVLEX_BASIS_ENCODING`	matroid	property of Matroid	Advanced properties
`RGB`	common	Property_types	Visualization
`rhombicosidodecahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`rhombicuboctahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`RIDGES`	polytope	property of SymmetrizedCocircuitEquations	no category
`RIF_CYCLIC_NORMAL`	polytope	property of Cone	Visualization
`right_companion()`	common	method of SmithNormalForm	no category
`right_companion()`	common	method of SingularValueDecomposition	no category
`root_system(String type)`	polytope	Functions	Producing regular polytopes and their generalizations
`ROTATION`	polytope	property of SchlegelDiagram	no category
`row(Int i)`	common	method of IncidenceMatrix	no category
`row(Int i)`	common	method of Matrix	no category
`row_support_sizes(SparseMatrix M)`	group	Functions	Symmetry
`rows()`	common	method of IncidenceMatrix	no category
`rows()`	common	method of Matrix	no category
`rows`	common	Functions	Data Conversion
`rows(Matrix A)`	common	Functions	Data Conversion
`rows_labeled(Matrix data, Array<String> row_labels, Array<String> elem_labels)`	common	Functions	Formatting
`rows_labeled(GraphAdjacency graph, Array<String> elem_labels)`	common	Functions	Formatting
`rows_numbered(Matrix data)`	common	Functions	Formatting
`rss_associahedron(Int l)`	polytope	Functions	Producing a polytope from scratch
`SATURATION`	ideal	method of Ideal	no category
`save(Core::BigObject object, String filename)`	core	Functions	Basic
`save_data(Any data, String filename)`	core	Functions	Basic
`save_history(String filename)`	core	Functions	Interactive
`save_schema(Schema schema, String filename)`	core	Functions	Schemas
`scalar2set(Scalar s)`	common	Functions	Set Operations
`scale(Polytope P, Scalar factor, Bool store)`	polytope	Functions	Transformations
`Schema`	core	Objects	no category
`SCHLEGEL()`	polytope	method of Polytope	Visualization
`SCHLEGEL_DIAGRAM`	polytope	property of Polytope	Visualization
`SchlegelDiagram<Scalar>`	polytope	Objects	no category
`script(String filename, Any Arguments)`	core	Functions	Basic
`second_barycentric_subdivision(Lattice L)`	topaz	Functions	Other
`second_barycentric_subdivision(Polytope P)`	topaz	Functions	Other
`second_tdet_and_perm(Matrix<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`secondary_cone()`	fan	method of SubdivisionOfVectors	Geometry
`secondary_configuration(PointConfiguration pc)`	polytope	Functions	Triangulations, subdivisions and volume
`secondary_configuration(Polytope pc)`	polytope	Functions	Triangulations, subdivisions and volume
`secondary_fan(VectorConfiguration V)`	fan	Functions	Triangulations, subdivisions and volume
`secondary_fan`	fan	Functions	Triangulations, subdivisions and volume
`SECONDARY_FAN`	topaz	property of HyperbolicSurface	no category
`secondary_polyhedron(HyperbolicSurface s, Int depth)`	topaz	Functions	Producing other objects
`secondary_polytope(PointConfiguration pc)`	polytope	Functions	Triangulations, subdivisions and volume
`secondary_polytope(Polytope pc)`	polytope	Functions	Triangulations, subdivisions and volume
`SECTION_POLYTOPE`	fulton	property of TDivisor	Combinatorics
`SedentarityDecoration`	fan	Property_types	no category
`select_subset(Set s, Set<Int> indices)`	common	Functions	Set Operations
`SELF_DUAL`	polytope	property of Cone	Combinatorics
`SELF_DUAL`	polytope	property of Polytope	Combinatorics
`SELF_DUAL`	matroid	property of Matroid	Advanced properties
`SEMIAMPLE`	fulton	property of TDivisor	Algebraic Geometry
`separable(Vector q, Cone P)`	polytope	Functions	Geometry
`SEPARATED_CODIMENSION_ONE_POLYTOPES`	tropical	property of Cycle	Defining morphisms and functions
`SEPARATED_CONVERSION_VECTOR`	tropical	property of Cycle	Defining morphisms and functions
`SEPARATED_MAXIMAL_POLYTOPES`	tropical	property of Cycle	Defining morphisms and functions
`SEPARATED_VERTICES`	tropical	property of Cycle	Defining morphisms and functions
`separating_hyperplane(Vector q, Matrix points)`	polytope	Functions	Optimization
`separating_hyperplane(Polytope p1, Polytope p2)`	polytope	Functions	Optimization
`sequence(Int a, Int c)`	common	Functions	Set Operations
`Sequential`	graph	Property_types	Artificial
`Serialized<X>`	common	Property_types	Artificial
`series_extension(Matroid m_1, Int e_1, Matroid m_2, Int e_2)`	matroid	Functions	Producing a matroid from matroids
`series_extension(Matroid m, Int e)`	matroid	Functions	Producing a matroid from matroids
`SERIES_PARALLEL`	matroid	property of Matroid	Advanced properties
`Set<Element>`	common	Property_types	Set Types
`SET_ACTION`	group	property of Group	Symmetry
`set_as_default`	core	method of Core::BigObject	no category
`set_as_default_now`	core	method of Core::BigObject	no category
`set_collection_doc(HASH doc)`	common	method of PolyDB::Collection	Database Collection Administration
`set_custom(Any assignment)`	core	Functions	Basic
`set_info(HASH info)`	common	method of PolyDB::Collection	Database Collection Administration
`set_preference(String label_expression)`	core	Functions	Basic
`set_rank(Int r, Int n)`	graph	method of InverseRankMap	Combinatorics
`set_schema(HASH schema)`	common	method of PolyDB::Collection	Database Collection Administration
`set_section_doc(HASH doc)`	common	method of PolyDB::Client	Database Administration
`set_theoretic_intersection(Cycle A, Cycle B)`	tropical	Functions	Basic polyhedral operations
`set_var_names`	common	method of UniPolynomial	no category
`set_var_names`	common	method of Polynomial	no category
`set_var_names(String names …)`	common	Functions	Arithmetic
`SETS`	tropical	property of RationalCurve	Combinatorics
`SHELLABLE`	topaz	property of SimplicialComplex	Combinatorics
`SHELLING`	topaz	property of SimplicialComplex	Combinatorics
`shift_cycle(Cycle<Addition> C, Vector<Rational> T)`	tropical	Functions	Basic polyhedral operations
`shortest_path_dijkstra(Graph G, EdgeMap weights, Int source, Int target, Bool if)`	graph	Functions	no category
`show_credits`	core	Functions	Interactive
`show_extensions`	core	Functions	Interactive
`show_preferences`	core	Functions	Interactive
`show_unconfigured`	core	Functions	Interactive
`sigma()`	common	method of SingularValueDecomposition	no category
`SIGNATURE`	graph	property of Graph	no category
`SIGNATURE`	topaz	property of GeometricSimplicialComplex	no category
`signature_to_chamber`	fan	method of HyperplaneArrangement	Combinatorics
`SIGNED_INCIDENCE_MATRIX`	graph	property of Graph	no category
`signed_incidence_matrix(Graph G)`	graph	Functions	Combinatorics
`signed_incidence_matrix(GraphAdjacency G)`	graph	Functions	Combinatorics
`signed_permutahedron(Int d)`	polytope	Functions	Producing a polytope from scratch
`SIGNS`	tropical	property of Patchwork	no category
`SIM_body<Scalar>(Vector<Scalar> alpha)`	polytope	Functions	Producing a polytope from scratch
`SIMPLE`	polytope	property of Cone	Combinatorics
`SIMPLE`	polytope	property of Polytope	Combinatorics
`SIMPLE`	matroid	property of Matroid	Advanced properties
`SIMPLE_POLYHEDRON`	polytope	property of Polytope	Unbounded polyhedra
`simple_polytope_vertices_rs(Polytope<Scalar> P, Vector<Scalar> min_vertex)`	polytope	Functions	Geometry
`simple_roots_type_A(Int index)`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_B(Int index)`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_C(Int index)`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_D(Int index)`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_E6()`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_E7()`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_E8()`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_F4()`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_G2()`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_H3()`	polytope	Functions	Producing regular polytopes and their generalizations
`simple_roots_type_H4()`	polytope	Functions	Producing regular polytopes and their generalizations
`simplex(Int d, Scalar scale)`	polytope	Functions	Producing a polytope from scratch
`simplex(Int d)`	topaz	Functions	Producing from scratch
`simplexity_ilp(Int d, Matrix points, Array<Set> MIS, Scalar volume, SparseMatrix cocircuit_equations)`	polytope	Functions	Triangulations, subdivisions and volume
`simplexity_ilp_with_angles(Int d, Matrix V, Matrix F, IncidenceMatrix VIF, IncidenceMatrix VIR, Array<Array<Int>> gens, Array<Set> MIS, Scalar volume, SparseMatrix cocircuit_equations)`	polytope	Functions	Triangulations, subdivisions and volume
`SIMPLEXITY_LOWER_BOUND`	group	property of Group	Symmetry
`SIMPLEXITY_LOWER_BOUND`	polytope	property of QuotientSpace	Combinatorics
`SIMPLEXITY_LOWER_BOUND`	polytope	property of Polytope	Combinatorics
`SIMPLEXITY_LOWER_BOUND`	polytope	property of PointConfiguration	Combinatorics
`simplexity_lower_bound(Int d, Matrix points, Scalar volume, SparseMatrix cocircuit_equations)`	polytope	Functions	Triangulations, subdivisions and volume
`SIMPLICES`	polytope	property of QuotientSpace	Combinatorics
`SIMPLICIAL`	fan	property of PolyhedralFan	Combinatorics
`SIMPLICIAL`	polytope	property of Cone	Combinatorics
`SIMPLICIAL`	polytope	property of Polytope	Combinatorics
`SIMPLICIAL_COMPLEX`	polytope	property of QuotientSpace	Combinatorics
`SIMPLICIAL_CONE`	polytope	property of Cone	Combinatorics
`simplicial_diagonal_system(Cycle<Addition> fan)`	tropical	Functions	Inverse problems
`simplicial_piecewise_system(Cycle<Addition> F)`	tropical	Functions	Inverse problems
`simplicial_product(SimplicialComplex complex1, SimplicialComplex complex2)`	topaz	Functions	Producing a new simplicial complex from others
`simplicial_product<Scalar>(GeometricSimplicialComplex complex1, GeometricSimplicialComplex complex2)`	topaz	Functions	Producing a new simplicial complex from others
`simplicial_with_diagonal(Cycle<Addition> F)`	tropical	Functions	Inverse problems
`SimplicialComplex`	topaz	Objects	no category
`SIMPLICIALITY`	polytope	property of Polytope	Combinatorics
`SIMPLICITY`	polytope	property of Polytope	Combinatorics
`singular_eval(String s)`	ideal	Functions	Singular interface
`singular_get_var(String s)`	ideal	Functions	Singular interface
`SINGULAR_IDEAL`	ideal	property of Groebner	Singular interface
`singular_value_decomposition(Matrix<Float> M)`	common	Functions	Linear Algebra
`SingularIdeal`	ideal	Property_types	Singular interface
`SingularValueDecomposition`	common	Property_types	Linear Algebra
`SITE_LABELS`	polytope	property of VoronoiPolyhedron	no category
`SITES`	tropical	property of VoronoiDiagram	no category
`SITES`	polytope	property of VoronoiPolyhedron	no category
`SIZE`	topaz	property of MorseMatching	no category
`size()`	common	method of FacetList	no category
`size()`	common	method of HashSet	no category
`size()`	common	method of HashMap	no category
`size()`	common	method of Set	no category
`size()`	common	method of SparseVector	no category
`size()`	common	method of Array	no category
`skeleton_complex(Cycle<Addition> C, Int k, Bool preserveRays)`	tropical	Functions	Basic polyhedral operations
`sketch(Visual::Object vis_obj …)`	common	Functions	Visualization
`SLACK_IDEAL`	polytope	property of Polytope	Geometry
`slack_ideal_non_saturated`	ideal	Functions	Singular interface
`SLACK_MATRIX`	polytope	property of Polytope	Geometry
`SlackIdeal`	ideal	Objects	no category
`slice(Set s)`	common	method of Vector	no category
`smith_normal_form(Matrix M, Bool inv)`	common	Functions	Linear Algebra
`smith_normal_form_flint(Matrix M)`	common	Functions	Linear Algebra
`SmithNormalForm<Scalar>`	common	Property_types	Linear Algebra
`SMOOTH`	polytope	property of Polytope	Lattice points in cones
`SMOOTH`	fulton	property of NormalToricVariety	Algebraic Geometry
`SMOOTH_CONE`	polytope	property of Cone	Lattice points in cones
`SMOOTH_FAN`	fan	property of PolyhedralFan	Toric Varieties
`SOLID()`	polytope	method of Visual::SchlegelDiagram	no category
`SOLIDS`	topaz	property of GrassPluckerCertificate	Geometry
`SOLVE`	ideal	method of Ideal	no category
`solve_left(Matrix A, Matrix B)`	common	Functions	Linear Algebra
`solve_right(Matrix A, Matrix B)`	common	Functions	Linear Algebra
`source()`	core	method of Schema	no category
`space_of_stable_maps<Addition>(Int n, Int d, Int r)`	tropical	Functions	Moduli of rational curves
`span_same_subspace(Array<HashMap<SetType,Rational>> S1, Array<HashMap<SetType,Rational>> S2)`	group	Functions	Symmetry
`SPANNING`	polytope	property of Polytope	Lattice points in cones
`spans_invariant_subspace(ImplicitActionOnSets a, Array<HashMap<Bitset,Rational>> S)`	group	Functions	Symmetry
`sparse_isotypic_basis(PermutationActionOnSets rep, Int i)`	group	Functions	Symmetry
`sparse_isotypic_spanning_set(PermutationActionOnSets rep, Int i)`	group	Functions	Symmetry
`sparse_isotypic_support(PermutationActionOnSets rep, Int i)`	group	Functions	Symmetry
`SPARSE_PAVING`	matroid	property of Matroid	Advanced properties
`SparseMatrix<Element, Sym>`	common	Property_types	Algebraic Types
`SparseVector<Element>`	common	Property_types	Algebraic Types
`SPECIAL_FACETS`	polytope	property of Polytope	Geometry
`special_matroid(String s)`	matroid	Functions	Producing a matroid from scratch
`SPECIAL_POINT`	topaz	property of HyperbolicSurface	no category
`SPHERE`	topaz	property of SimplicialComplex	Topology
`sphere(Int d)`	topaz	Functions	Producing from scratch
`spherize(Polytope P)`	polytope	Functions	Producing a polytope from polytopes
`SPLIT`	matroid	property of Matroid	Advanced properties
`SPLIT_COMPATIBILITY_GRAPH`	polytope	property of Polytope	Geometry
`SPLIT_COMPATIBILITY_GRAPH`	polytope	property of PointConfiguration	Combinatorics
`split_compatibility_graph(Matrix splits, Polytope P)`	polytope	Functions	Triangulations, subdivisions and volume
`SPLIT_FLACETS`	matroid	property of Matroid	Advanced properties
`split_polyhedron(Polytope P)`	polytope	Functions	Triangulations, subdivisions and volume
`SPLITS`	polytope	property of Polytope	Geometry
`SPLITS`	polytope	property of PointConfiguration	Combinatorics
`splits(Matrix V, Graph G, Matrix F, Int dimension)`	polytope	Functions	Triangulations, subdivisions and volume
`splits_in_subdivision(Matrix vertices, Array<Set<Int>> subdivision, Matrix splits)`	polytope	Functions	Triangulations, subdivisions and volume
`splitstree(Visual::Object vis_obj …)`	fan	Functions	Visualization
`spring_embedder(GraphAdjacency<Undirected> graph)`	graph	Functions	Visualization
`sqr(Vector<Scalar> v)`	common	Functions	Linear Algebra
`SQUARED_DETERMINANT`	polytope	property of AffineLattice	no category
`SQUARED_EDGE_LENGTHS`	polytope	property of Polytope	Geometry
`SQUARED_RELATIVE_VOLUMES`	polytope	property of Polytope	Triangulation and volume
`squeeze`	common	method of IncidenceMatrix	no category
`squeeze`	common	method of SparseMatrix	no category
`squeeze`	common	method of GraphAdjacency	no category
`squeeze_cols`	common	method of IncidenceMatrix	no category
`squeeze_cols`	common	method of SparseMatrix	no category
`squeeze_isolated`	common	method of GraphAdjacency	no category
`squeeze_rows`	common	method of IncidenceMatrix	no category
`squeeze_rows`	common	method of SparseMatrix	no category
`stabbing_order(GeometricSimplicialComplex P)`	topaz	Functions	Other
`stabilizer_of_set(PermutationAction a, Set S)`	group	Functions	Producing a group
`stabilizer_of_vector(PermutationAction a, Vector v)`	group	Functions	Producing a group
`stable_set(Graph G)`	polytope	Functions	Producing a polytope from scratch
`stack(Polytope P, Set<Int> stack_facets)`	polytope	Functions	Producing a polytope from polytopes
`STACKY_F_VECTOR`	fan	property of DisjointStackyFan	Symmetry
`STACKY_FACES`	fan	property of DisjointStackyFan	Symmetry
`stacky_fan(Curve G)`	tropical	Functions	Weights and lattices
`stacky_fan(Cone C)`	fan	Functions	Symmetry
`stacky_fundamental_domain(DisjointStackyFan F)`	fan	Functions	Symmetry
`staircase_weight(Int k, Int l)`	polytope	Functions	Triangulations, subdivisions and volume
`stanley_reisner(SimplicialComplex complex)`	topaz	Functions	Other
`star_at_point(Cycle<Addition> C, Vector<Rational> v)`	tropical	Functions	Local computations
`star_at_vertex(Cycle<Addition> C, Int i)`	tropical	Functions	Local computations
`star_deletion(SimplicialComplex complex, Set<Int> face)`	topaz	Functions	Producing a new simplicial complex from others
`star_of_zero(GeometricSimplicialComplex C)`	topaz	Functions	Other
`star_shaped_balls(GeometricSimplicialComplex P)`	topaz	Functions	Other
`star_subcomplex(SimplicialComplex complex, Set<Int> face)`	topaz	Functions	Producing a new simplicial complex from others
`static(Visual::Object vis_obj)`	common	Functions	Visualization
`STEINER()`	polytope	method of Visual::SchlegelDiagram	no category
`STEINER()`	polytope	method of Visual::Polytope	no category
`STEINER_POINT`	polytope	property of Polytope	Geometry
`steiner_point(Polytope P)`	polytope	Functions	Geometry
`STEINER_POINTS`	polytope	property of Polytope	Geometry
`stellar_all_faces(Polytope P, Int d)`	polytope	Functions	Producing a polytope from polytopes
`stellar_indep_faces(Polytope P, Array<Set<Int>> in_faces)`	polytope	Functions	Producing a polytope from polytopes
`stellar_subdivision(SimplicialComplex complex, Array<Set<Int>> faces)`	topaz	Functions	Producing a new simplicial complex from others
`stellar_subdivision(SimplicialComplex complex, Set<Int> face)`	topaz	Functions	Producing a new simplicial complex from others
`STIEFEL_WHITNEY`	topaz	property of SimplicialComplex	Topology
`stiefel_whitney(Array<Set<Int>> facets)`	topaz	Functions	Other
`stregular(Matrix<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`STRICT_GAMMOID`	matroid	method of Matroid	Advanced properties
`String`	common	Property_types	Basic Types
`STRONG_COMPONENTS`	graph	property of Graph	no category
`STRONG_GENERATORS`	group	property of PermutationAction	no category
`STRONGLY_CONNECTED`	graph	property of Graph	no category
`SUBCOMPLEX(String PROPERTY_NAME)`	topaz	method of Visual::SimplicialComplex	no category
`SUBCOMPLEX(String property)`	topaz	method of Visual::SimplicialComplexLattice	no category
`subcone(Cone C)`	polytope	Functions	Producing a cone
`subcramer(Matrix<TropicalNumber<Addition,Scalar>> m, Set<Int> J, Set<Int> I)`	tropical	Functions	Tropical operations
`SUBDIVISION`	matroid	property of ValuatedMatroid	Combinatorics
`SubdivisionOfPoints<Scalar>`	fan	Objects	Geometry
`SubdivisionOfVectors<Scalar>`	fan	Objects	Geometry
`SUBRIDGE_SIZES`	polytope	property of Polytope	Combinatorics
`substitute`	common	method of UniPolynomial	no category
`substitute`	common	method of Polynomial	no category
`sum(ARRAY array)`	common	Functions	Utilities
`sum_curves(RationalCurve An, Vector<Rational> v)`	tropical	Functions	Abstract rational curves
`sum_of_square_roots_naive(Array<Rational> input_array)`	common	Functions	Arithmetic
`SUM_PRODUCT_GRAPH`	polytope	property of PropagatedPolytope	no category
`sum_triangulation(GeometricSimplicialComplex P, GeometricSimplicialComplex Q, IncidenceMatrix WebOfStars)`	topaz	Functions	Producing a new simplicial complex from others
`SUPPORT`	fan	property of HyperplaneArrangement	Input property
`support(Vector v)`	common	Functions	Data Conversion
`SURFACE`	topaz	property of SimplicialComplex	Topology
`surface(Int g)`	topaz	Functions	Producing from scratch
`suspension(SimplicialComplex complex, Int k)`	topaz	Functions	Producing a new simplicial complex from others
`svg(Visual::Object vis_obj …)`	common	Functions	Visualization
`SWITCH_TABLE`	group	property of PermutationAction	Orbits
`SwitchTable`	group	Property_types	no category
`Symmetric`	common	Property_types	Artificial
`SYMMETRIC_FACETS`	polytope	property of Polytope	Symmetry
`symmetric_group(Int d)`	group	Functions	Producing a group
`SYMMETRIC_RAYS`	polytope	property of Polytope	Symmetry
`SYMMETRIZED_COCIRCUIT_EQUATIONS`	polytope	property of Polytope	Symmetry
`SYMMETRIZED_COCIRCUIT_EQUATIONS`	polytope	property of PointConfiguration	Symmetry
`symmetrized_cocircuit_equations<Scalar>(Cone P, Set<Int> comps)`	polytope	Functions	Symmetry
`symmetrized_foldable_max_signature_ilp(Int d, Matrix points, Rational volume, Array<Array<Int>> generators, SparseMatrix symmetrized_foldable_cocircuit_equations)`	polytope	Functions	Triangulations, subdivisions and volume
`symmetrized_foldable_max_signature_upper_bound(Int d, Matrix points, Rational volume, SparseMatrix cocircuit_equations)`	polytope	Functions	Triangulations, subdivisions and volume
`SymmetrizedCocircuitEquations`	polytope	Objects	Symmetry
`SYMMETRY_GROUP`	polytope	property of QuotientSpace	Combinatorics
`t8_matroid()`	matroid	Functions	Producing a matroid from scratch
`take(String property_name, Any value, Int temp)`	core	method of Core::BigObject	no category
`tdehomog(Matrix<Rational> A, Int chart, Bool has_leading_coordinate)`	tropical	Functions	Affine and projective coordinates
`tdet(Matrix<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`tdet_and_perm(Matrix<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`tdet_and_perms(Matrix<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`tdiam(Matrix<TropicalNumber<Addition,Scalar>> matrix)`	tropical	Functions	Tropical operations
`tdist(Vector<TropicalNumber<Addition,Scalar>> v, Vector<TropicalNumber<Addition,Scalar>> w)`	tropical	Functions	Tropical operations
`TDivisor`	fulton	Objects	no category
`tensor(Polytope P1, Polytope P2)`	polytope	Functions	Producing a polytope from polytopes
`TERMINAL`	polytope	property of Polytope	Lattice points in cones
`TERNARY`	matroid	property of Matroid	Realizability
`TERNARY_VECTORS`	matroid	property of Matroid	Realizability
`testFourPointCondition(Vector<Rational> v)`	tropical	Functions	Abstract rational curves
`tetrahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`Text`	common	Property_types	Basic Types
`thomog(Matrix<Rational> A, Int chart, Bool has_leading_coordinate)`	tropical	Functions	Affine and projective coordinates
`thrackle_metric(Int n)`	fan	Functions	Finite metric spaces
`threejs(Visual::Object vis_obj)`	common	Functions	Visualization
`TIGHT_SPAN`	fan	property of SubdivisionOfPoints	Geometry
`tight_span_envelope(SubdivisionOfPoints sd)`	polytope	Functions	Finite metric spaces
`tight_span_max_metric(Int n)`	fan	Functions	Finite metric spaces
`tight_span_min_metric(Int n)`	fan	Functions	Finite metric spaces
`tight_span_thrackle_metric(Int n)`	fan	Functions	Finite metric spaces
`tikz(Visual::Object vis_obj)`	common	Functions	Visualization
`TILING_LATTICE`	polytope	property of Polytope	Geometry
`tiling_quotient<Coord>(Polytope P, Polytope Q)`	fan	Functions	Producing a polyhedral complex
`toMatrix<Scalar>(IncidenceMatrix M)`	common	Functions	Data Conversion
`TOP_NODE`	graph	property of Lattice	Combinatorics
`topcom_all_triangulations(PointConfiguration pc)`	polytope	Functions	Triangulations, subdivisions and volume
`topcom_fine_and_connected_triangulations(PointConfiguration pc)`	polytope	Functions	Triangulations, subdivisions and volume
`topcom_input_format(Cone P)`	polytope	Functions	Triangulations, subdivisions and volume
`topcom_regular_and_connected_triangulations(PointConfiguration pc)`	polytope	Functions	Triangulations, subdivisions and volume
`topcom_regular_triangulations(PointConfiguration pc)`	polytope	Functions	Triangulations, subdivisions and volume
`TORIC_IDEAL`	polytope	property of Polytope	Lattice points in cones
`TORIC_IDEAL`	fulton	property of NormalToricVariety	no category
`torsion()`	topaz	method of HomologyGroup	no category
`torsion()`	common	method of SmithNormalForm	no category
`torus()`	topaz	Functions	Producing from scratch
`TORUS_COVECTOR_DECOMPOSITION`	tropical	property of Polytope	Combinatorics
`torus_subdivision_as_complex(Int chart)`	tropical	method of Polytope	Geometry
`TOTAL_LENGTH`	polytope	property of Polytope	no category
`TOTAL_SPACE`	fulton	property of VersalComponent	Algebraic Geometry
`totally_dual_integral(Matrix inequalities)`	polytope	Functions	Optimization
`totally_unimodular(Matrix M)`	common	Functions	Linear Algebra
`toTropicalPolynomial(String s, String vars)`	common	Functions	Data Conversion
`toVector<Scalar>(Set S, Int d)`	common	Functions	Data Conversion
`TOWARDS_FAR_FACE`	polytope	property of Polytope	Unbounded polyhedra
`tpluecker(Matrix<TropicalNumber<Addition>> M)`	tropical	Functions	Other
`trace(Matrix<Scalar> M)`	common	Functions	Linear Algebra
`TRANSFORM`	polytope	property of SchlegelDiagram	no category
`transform(Polytope P, Matrix trans, Bool store)`	polytope	Functions	Transformations
`TRANSLATE`	tropical	property of Morphism	Defining morphisms and functions
`translate(Polytope P, Vector trans, Bool store)`	polytope	Functions	Transformations
`TRANSLATIONS`	polytope	property of PropagatedPolytope	no category
`transportation(Vector r, Vector c)`	polytope	Functions	Producing a polytope from scratch
`transpose(IncidenceMatrix A)`	common	Functions	Linear Algebra
`transpose(Matrix M)`	common	Functions	Linear Algebra
`TRANSVERSAL`	matroid	property of Matroid	Advanced properties
`TRANSVERSAL_PRESENTATION`	matroid	property of Matroid	Input properties
`TRANSVERSAL_SIZES`	group	property of PermutationAction	no category
`TRANSVERSAL_VALUATED_MATROID`	matroid	property of ValuatedMatroid	Valuation
`TRANSVERSALS`	group	property of PermutationAction	no category
`tregular(Matrix<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`triang_neighborhood(SimplicialComplex complex, Rational width)`	topaz	Functions	Producing a new simplicial complex from others
`TRIANGLE_FREE()`	polytope	method of Cone	Backward compatibility
`TRIANGLE_FREE`	graph	property of Graph	no category
`TRIANGLES`	fulton	property of VersalComponent	Combinatorics
`triangulate_cycle(Cycle<Addition> F)`	tropical	Functions	Basic polyhedral operations
`TRIANGULATION(Array<Set<Int>> t)`	polytope	method of Visual::PointConfiguration	no category
`TRIANGULATION(Array<Set<Int>> t)`	polytope	method of Visual::Polytope	no category
`TRIANGULATION`	polytope	property of Cone	Triangulation and volume
`TRIANGULATION`	polytope	property of Polytope	Triangulation and volume
`TRIANGULATION`	polytope	property of PointConfiguration	Triangulation and volume
`TRIANGULATION_BOUNDARY()`	polytope	method of Visual::SchlegelDiagram	no category
`TRIANGULATION_BOUNDARY()`	polytope	method of Visual::Polytope	no category
`TRIANGULATION_BOUNDARY_SOLID()`	polytope	method of Visual::SchlegelDiagram	no category
`TRIANGULATION_INT`	polytope	property of Cone	Triangulation and volume
`TRIANGULATION_INT_SIGNS()`	polytope	method of Polytope	Triangulation and volume
`TRIVIAL`	polytope	property of Cone	Geometry
`trivial()`	common	method of Polynomial	no category
`trivial_valuation<Addition, Scalar>(Matroid M)`	matroid	Functions	Producing a matroid from matroids
`trop_witness<Addition, Scalar>(Matrix<TropicalNumber<Addition,Scalar>> m, Array<Int > t, Int start)`	tropical	Functions	Tropical operations
`trop_witness<Addition, Scalar>(Matrix<TropicalNumber<Addition,Scalar>> m, Array<Int > t, Int start)`	tropical	Functions	Tropical operations
`TropicalNumber<Addition, Scalar>`	common	Property_types	Arithmetic
`TropicalRationalFunction<Addition>`	tropical	Objects	no category
`truncated_cube()`	polytope	Functions	Producing regular polytopes and their generalizations
`truncated_cuboctahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`truncated_dodecahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`truncated_icosahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`truncated_icosidodecahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`truncated_octahedron()`	polytope	Functions	Producing regular polytopes and their generalizations
`truncated_orbit_polytope(Polytope P, Scalar eps)`	polytope	Functions	Symmetry
`truncation(Polytope P, Set<Int> trunc_vertices)`	polytope	Functions	Producing a polytope from polytopes
`truncation(Matroid M)`	matroid	Functions	Producing a matroid from matroids
`tsgn(Matrix<TropicalNumber> matrix)`	tropical	Functions	Tropical operations
`tubes_of_graph(Graph G)`	fan	Functions	Other
`tubes_of_tubing(Graph G, Graph T)`	fan	Functions	Other
`tubing_of_graph(Graph G)`	fan	Functions	Other
`tutte_lifting(Graph G)`	polytope	Functions	Producing a polytope from graphs
`TUTTE_POLYNOMIAL`	matroid	property of Matroid	Advanced properties
`TWO_FACE_SIZES`	polytope	property of Polytope	Combinatorics
`two_sum(Matroid m_1, Int e_1, Matroid m_2, Int e_2)`	matroid	Functions	Producing a matroid from matroids
`type`	core	method of Core::BigObject	no category
`UNBALANCED_FACES`	tropical	property of Cycle	Weights and lattices
`UNBOUNDED_FACETS`	polytope	property of Polytope	Unbounded polyhedra
`unconfigure(String rulename)`	core	Functions	Interactive
`UNDETERMINED_SOLIDS`	topaz	property of GrassPluckerCertificate	Geometry
`Undirected`	common	Property_types	Artificial
`UndirectedMulti`	common	Property_types	Artificial
`UNIFORM`	matroid	property of Matroid	Advanced properties
`uniform_linear_space<Addition>(Int n, Int k, Integer weight)`	tropical	Functions	Creation functions for specific cycles
`uniform_matroid(Int r, Int n)`	matroid	Functions	Producing a matroid from scratch
`UNIMODULAR`	fan	property of SubdivisionOfPoints	Geometry
`UNIMODULAR`	topaz	property of GeometricSimplicialComplex	no category
`union(SimplicialComplex complex1, SimplicialComplex complex2)`	topaz	Functions	Producing a new simplicial complex from others
`union(Matroid M)`	matroid	Functions	Producing a matroid from matroids
`union_of_cones(Cone C …)`	fan	Functions	Producing a fan
`UniPolynomial<Coefficient, Exponent>`	common	Property_types	Algebraic Types
`unirand(Polytope P, Int n)`	polytope	Functions	Producing a polytope from polytopes
`unit_matrix<Element>(Int d)`	common	Functions	Linear Algebra
`unit_vector<Element>(Int d, Int pos)`	common	Functions	Linear Algebra
`universal_polytope<Scalar>(PointConfiguration<Scalar> PC)`	polytope	Functions	Triangulations, subdivisions and volume
`universal_polytope(Polytope P)`	polytope	Functions	Triangulations, subdivisions and volume
`universal_polytope(Polytope P, Array<Set> reps, SparseMatrix cocircuit_equations)`	polytope	Functions	Triangulations, subdivisions and volume
`unknot(Int m, Int n)`	topaz	Functions	Producing from scratch
`upper_bound_theorem(Int d, Int n)`	polytope	Functions	Producing a polytope from scratch
`val()`	common	method of PuiseuxFraction	no category
`VALID_POINT`	tropical	property of Polytope	Geometry
`VALID_POINT`	polytope	property of Polytope	Geometry
`validate(Any primitive)`	core	method of Schema	no category
`validate_moebius_strip(Polytope P)`	polytope	Functions	Consistency check
`validate_moebius_strip_quads(Polytope P)`	polytope	Functions	Consistency check
`validate_self()`	core	method of Schema	no category
`ValuatedMatroid<Addition, Scalar>`	matroid	Objects	no category
`valuation(Rational x, Integer p)`	common	Functions	Utilities
`VALUATION_ON_BASES`	matroid	property of ValuatedMatroid	Valuation
`VALUATION_ON_CIRCUITS`	matroid	property of ValuatedMatroid	Valuation
`vamos_matroid()`	matroid	Functions	Producing a matroid from scratch
`Vector<Element>`	common	Property_types	Algebraic Types
`vector2col(Vector v)`	common	Functions	Data Conversion
`vector2row(Vector v)`	common	Functions	Data Conversion
`VECTOR_ACTION`	group	property of Group	Symmetry
`VECTOR_AMBIENT_DIM`	fan	property of SubdivisionOfVectors	Geometry
`VECTOR_AMBIENT_DIM`	polytope	property of VectorConfiguration	Geometry
`VECTOR_DIM`	fan	property of SubdivisionOfVectors	Geometry
`VECTOR_DIM`	polytope	property of VectorConfiguration	Geometry
`VectorConfiguration<Scalar>`	polytope	Objects	Geometry
`VECTORS`	fan	property of SubdivisionOfVectors	Geometry
`VECTORS`	polytope	property of VectorConfiguration	Input property
`VECTORS`	matroid	property of Matroid	Realizability
`VECTORS_ORBITS`	group	property of MatrixActionOnVectors	Symmetry
`VERSAL_COMPONENT`	fulton	property of CyclicQuotient	Algebraic Geometry
`VERSAL_COMPONENTS`	fulton	property of CyclicQuotient	Algebraic Geometry
`VersalComponent`	fulton	Objects	no category
`VERTEX_BARYCENTER`	polytope	property of Polytope	Geometry
`VERTEX_COLORS(LinearProgram lp)`	polytope	method of Visual::SchlegelDiagram	no category
`VERTEX_COLORS(LinearProgram lp)`	polytope	method of Visual::Polytope	no category
`VERTEX_COLORS(LinearProgram lp)`	polytope	method of Visual::PolytopeGraph	no category
`vertex_colors(Polytope P, LinearProgram LP)`	polytope	Functions	Optimization
`VERTEX_DEGREES()`	polytope	method of Cone	Combinatorics
`VERTEX_DEGREES()`	topaz	method of SimplicialComplex	Combinatorics
`vertex_figure(Polytope p, Int n)`	polytope	Functions	Producing a polytope from polytopes
`VERTEX_IN_DEGREES()`	polytope	method of LinearProgram	no category
`VERTEX_INDICES`	topaz	property of SimplicialComplex	Combinatorics
`VERTEX_LABELS`	fan	property of PolyhedralComplex	Visualization
`VERTEX_LABELS`	fan	property of DisjointStackyFan	Symmetry
`VERTEX_LABELS`	polytope	property of Polytope	Visualization
`VERTEX_LABELS`	topaz	property of SimplicialComplex	Visualization
`vertex_lattice_normalization(Polytope p)`	polytope	Functions	Transformations
`VERTEX_MAP`	polytope	property of Polytope	Unbounded polyhedra
`VERTEX_MAP`	topaz	property of SimplicialComplex	Combinatorics
`VERTEX_NORMALS`	polytope	property of Polytope	Geometry
`VERTEX_OUT_DEGREES()`	polytope	method of LinearProgram	no category
`VERTEX_POINT_MAP`	polytope	property of PointConfiguration	Geometry
`VERTEX_POINT_MAP`	polytope	property of PointConfiguration	no category
`VERTEX_SIZES`	polytope	property of Polytope	Combinatorics
`VERTEX_VALUES`	tropical	property of TropicalRationalFunction	Defining morphisms and functions
`VERTEX_VALUES`	tropical	property of Morphism	Defining morphisms and functions
`VERTEX_WEIGHTS`	tropical	property of Curve	Weights and lattices
`VERTICES`	tropical	property of Polytope	Geometry
`VERTICES`	fan	property of PolyhedralComplex	Geometry
`VERTICES`	polytope	property of Polytope	Geometry
`VERTICES`	polytope	property of SchlegelDiagram	no category
`VERTICES_ACTION`	fan	property of PolyhedralComplex	Symmetry
`VERTICES_ACTION`	polytope	property of Polytope	Symmetry
`VERTICES_GENERATORS`	fan	property of PolyhedralComplex	Symmetry
`VERTICES_GENERATORS`	fan	property of PolyhedralComplex	Symmetry
`VERTICES_GENERATORS`	fan	property of PolyhedralComplex	Symmetry
`VERTICES_GENERATORS`	polytope	property of Polytope	no category
`VERTICES_IN_FACETS`	polytope	property of Polytope	Combinatorics
`VERTICES_IN_INEQUALITIES`	polytope	property of Polytope	Geometry
`VERTICES_IN_POINTS`	tropical	property of Polytope	Geometry
`VERTICES_IN_RIDGES`	polytope	property of Polytope	Geometry
`VERTICES_ORBITS`	polytope	property of Polytope	no category
`VERY_AMPLE`	polytope	property of Polytope	Lattice points in cones
`VERY_AMPLE`	fulton	property of TDivisor	Algebraic Geometry
`VF_MAP`	fan	property of PlanarNet	Combinatorics
`VF_MAP_INV`	fan	property of PlanarNet	Combinatorics
`vietoris_rips_complex(Matrix D, Rational delta)`	topaz	Functions	Producing a simplicial complex from other objects
`vietoris_rips_filtration<Coeff>(Matrix D, Array<Int> deg, Float step_size, Int k)`	topaz	Functions	Other
`VIEWPOINT`	polytope	property of SchlegelDiagram	no category
`VIF_CYCLIC_NORMAL`	fan	property of PlanarNet	Combinatorics
`VIF_CYCLIC_NORMAL`	polytope	property of Polytope	Visualization
`violations(Cone P, Vector q)`	polytope	Functions	Geometry
`visible_face_indices(Cone P, Vector q)`	polytope	Functions	Geometry
`visible_facet_indices(Cone P, Vector q)`	polytope	Functions	Geometry
`VISUAL()`	tropical	method of TropicalRationalFunction	Visualization
`VISUAL()`	tropical	method of Polytope	Visualization
`VISUAL()`	tropical	method of Morphism	Visualization
`VISUAL()`	tropical	method of RationalCurve	Visualization
`VISUAL()`	tropical	method of Cycle	Visualization
`VISUAL`	tropical	method of VoronoiDiagram	no category
`VISUAL`	tropical	method of CovectorLattice	Visualization
`VISUAL()`	fan	method of PolyhedralFan	Visualization
`VISUAL()`	fan	method of PolyhedralComplex	no category
`VISUAL()`	fan	method of HyperplaneArrangement	Visualization
`VISUAL()`	fan	method of PlanarNet	Visualization
`VISUAL()`	fan	method of SubdivisionOfPoints	Visualization
`VISUAL()`	polytope	method of VectorConfiguration	Visualization
`VISUAL()`	polytope	method of Cone	Visualization
`VISUAL()`	polytope	method of Polytope	Visualization
`VISUAL()`	polytope	method of PointConfiguration	Visualization
`VISUAL()`	polytope	method of SchlegelDiagram	no category
`VISUAL()`	graph	method of Graph	Visualization
`VISUAL()`	graph	method of Lattice	Visualization
`VISUAL()`	topaz	method of GeometricSimplicialComplex	no category
`VISUAL()`	topaz	method of SimplicialComplex	Visualization
`Visual::Cone`	polytope	Objects	Visualization
`Visual::Container`	common	Objects	Visualization
`Visual::Gale`	polytope	Objects	Visualization
`Visual::Graph`	graph	Objects	Visualization
`Visual::Lattice`	graph	Objects	Visualization
`Visual::Object`	common	Objects	Visualization
`Visual::PlanarNet`	fan	Objects	Visualization
`Visual::PointConfiguration`	polytope	Objects	Visualization
`Visual::PolyhedralFan`	fan	Objects	Visualization
`Visual::Polytope`	polytope	Objects	Visualization
`Visual::PolytopeGraph`	polytope	Objects	Visualization
`Visual::PolytopeLattice`	polytope	Objects	Visualization
`Visual::SchlegelDiagram`	polytope	Objects	Visualization
`Visual::SimplicialComplex`	topaz	Objects	no category
`Visual::SimplicialComplexLattice`	topaz	Objects	no category
`VISUAL_BOUNDED_GRAPH()`	polytope	method of Polytope	Visualization
`VISUAL_CRUST()`	polytope	method of VoronoiPolyhedron	Visualization
`VISUAL_DUAL()`	polytope	method of Polytope	Visualization
`VISUAL_DUAL()`	graph	method of Lattice	Visualization
`VISUAL_DUAL_FACE_LATTICE()`	polytope	method of Cone	Visualization
`VISUAL_DUAL_FACE_LATTICE()`	polytope	method of Polytope	Visualization
`VISUAL_DUAL_GRAPH()`	polytope	method of Polytope	Visualization
`VISUAL_DUAL_GRAPH()`	topaz	method of SimplicialComplex	Visualization
`VISUAL_FACE_LATTICE()`	polytope	method of Cone	Visualization
`VISUAL_FACE_LATTICE()`	polytope	method of Polytope	Visualization
`VISUAL_FACE_LATTICE()`	topaz	method of SimplicialComplex	Visualization
`VISUAL_GRAPH()`	polytope	method of Polytope	Visualization
`VISUAL_GRAPH()`	topaz	method of SimplicialComplex	Visualization
`VISUAL_HYPERPLANE_ARRANGEMENT()`	tropical	method of Polytope	Visualization
`VISUAL_METRIC_TIGHT_SPAN()`	fan	method of PolyhedralComplex	no category
`VISUAL_MIXED_GRAPH()`	topaz	method of SimplicialComplex	Visualization
`VISUAL_NN_CRUST()`	polytope	method of VoronoiPolyhedron	Visualization
`VISUAL_NOP(ARRAY colors_ref, ARRAY trans_ref)`	polytope	method of Polytope	Symmetry
`VISUAL_NOP_GRAPH(String filename)`	polytope	method of Polytope	Symmetry
`VISUAL_ORBIT_COLORED_GRAPH()`	fan	method of PolyhedralComplex	Visualization
`VISUAL_ORBIT_COLORED_GRAPH()`	polytope	method of Polytope	Visualization
`VISUAL_POINTS()`	polytope	method of PointConfiguration	Visualization
`visual_splitstree(Matrix<Rational> M)`	fan	Functions	Visualization
`VISUAL_SUBDIVISION()`	tropical	method of Polytope	Visualization
`VISUAL_VORONOI()`	polytope	method of VoronoiPolyhedron	Visualization
`visualize_in_surface`	tropical	Functions	Visualization
`vlabels(Matrix vertices, Bool wo_zero)`	polytope	Functions	Visualization
`VOLUME`	polytope	property of Polytope	Triangulation and volume
`VOLUME`	topaz	property of GeometricSimplicialComplex	no category
`VORONOI_DIAGRAM`	polytope	property of VoronoiPolyhedron	no category
`VORONOI_GRAPH`	polytope	property of VoronoiPolyhedron	no category
`VORONOI_VERTICES`	polytope	property of VoronoiPolyhedron	no category
`VoronoiDiagram`	tropical	Objects	no category
`VoronoiPolyhedron<Scalar>`	polytope	Objects	no category
`WEAKLY_CENTERED`	polytope	property of Polytope	Geometry
`WEAKLY_CONNECTED`	graph	property of Graph	no category
`WEAKLY_CONNECTED_COMPONENTS`	graph	property of Graph	no category
`web_of_stars(Array<Int> poset_hom, Array<Set<Set<Int>>> star_shaped_balls, Array<Set<Int>> triang)`	topaz	Functions	Producing a new simplicial complex from others
`wedge(Polytope P, Int facet, Rational z, Rational z_prime)`	polytope	Functions	Producing a polytope from polytopes
`WEIGHT_CONE`	tropical	property of Cycle	Weights and lattices
`weight_cone(Cycle X, Set<Int> negative)`	tropical	Functions	Weight space
`WEIGHT_CONE`	fulton	property of NormalToricVariety	Combinatorics
`WEIGHT_SPACE`	tropical	property of Cycle	Weights and lattices
`WEIGHT_SYSTEM`	tropical	property of Cycle	Weights and lattices
`weighted_digraph_polyhedron(Matrix encoding)`	polytope	Functions	Producing a polytope from graphs
`weighted_projective_space(Vector<Int> a)`	fulton	Functions	Producing a normal toric variety
`WEIGHTS`	tropical	property of Cycle	Weights and lattices
`WEIGHTS`	fan	property of SubdivisionOfPoints	Geometry
`WEIGHTS`	polytope	property of Cone	Geometry
`WEIGHTS`	polytope	property of PointConfiguration	Triangulation and volume
`wheel4_matroid()`	matroid	Functions	Producing a matroid from scratch
`wheel_graph(Int n)`	graph	Functions	Producing a graph
`wreath(Polytope P1, Polytope P2)`	polytope	Functions	Producing a polytope from polytopes
`write_foldable_max_signature_ilp(Polytope P, String outfile_name)`	polytope	Functions	Optimization
`write_quotient_space_simplexity_ilp`	polytope	Functions	Quotient spaces
`write_simplexity_ilp(Polytope P)`	polytope	Functions	Optimization
`write_simplexity_ilp_with_angles(Polytope P, String outfile_name)`	polytope	Functions	Optimization
`write_stl(String filename)`	polytope	method of Polytope	Visualization
`write_symmetrized_simplexity_ilp(Polytope P, Set<Int> isotypic_components, String outfile_name)`	polytope	Functions	Optimization
`wronski_center_ideal(Matrix<Int> L, Vector<Int> lambda)`	polytope	Functions	Other
`wronski_polynomial(Matrix<Int> M, Vector<Int> lambda, Array<Rational> coeff, Rational s)`	polytope	Functions	Other
`wronski_system(Matrix<Int> M, Vector<Int> lambda, Array<Array<Rational>> coeff_array, Rational s)`	polytope	Functions	Other
`wythoff(String type, Set rings)`	polytope	Functions	Producing regular polytopes and their generalizations
`x3d(Visual::Object vis_obj …)`	common	Functions	Visualization
`ZERO`	ideal	property of Ideal	Commutative algebra
`zero()`	common	method of TropicalNumber	no category
`zero_in_matroid_ring<Addition>(Int n)`	tropical	Functions	Matroid ring cycle arithmetics
`zero_matrix<Element>(Int i, Int j)`	common	Functions	Linear Algebra
`zero_vector<Element>(Int d)`	common	Functions	Linear Algebra
`zonotope(Matrix<Scalar> M)`	polytope	Functions	Producing a polytope from scratch
`ZONOTOPE_INPUT_POINTS`	polytope	property of Polytope	Geometry
`zonotope_tiling_lattice(Polytope P)`	polytope	Functions	Geometry
`zonotope_vertices_fukuda(Matrix M)`	polytope	Functions	Producing a polytope from scratch
`ZOOM`	polytope	property of SchlegelDiagram	no category