Available versions of this document: latest release, release 3.5, nightly master
Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2
Index
applications
Index of all things
Name  Application  Object class  Category 

_4ti2Circuits(Matrix A)  matroid  Functions  Combinatorics 
ABSTRACT_OBJECTIVE  polytope  property of LinearProgram  no category 
AccurateFloat  common  Property_types  Basic Types 
Action  group  Objects  no category 
action<action_type>(Any g, Core::Object O)  group  Functions  Utilities 
action_from_generators(Array<Array<Int>> gens, Group action)  group  Functions  Utilities 
action_inv<action_type>(Array<Int> p, Core::Object O)  group  Functions  Utilities 
action_to_cyclic_notation(PermutationAction a)  group  Functions  Utilities 
add_edge(Int tail_node, Int head_node)  common  method of Graph  no category 
add_morphisms(Morphism f, Morphism g)  tropical  Functions  Morphisms 
add_node()  common  method of Graph  no category 
ADJACENCY  graph  property of Graph  no category 
adjacency_matrix(Graph graph)  common  Functions  Graph Operations 
adjacent_nodes(Int node)  common  method of Graph  no category 
AFFINE  fulton  property of NormalToricVariety  Algebraic Geometry 
affine_chart(Int chart)  tropical  method of Cycle  Affine and projective coordinates 
affine_float_coords(Polytope P)  polytope  Functions  Coordinate conversions 
AFFINE_HULL  polytope  property of PointConfiguration  Geometry 
AFFINE_HULL  polytope  property of Polytope  Geometry 
AFFINE_HULL  fan  property of PolyhedralComplex  Geometry 
affine_linear_space<Addition>(Matrix<Rational> lineality, Vector<Rational> translate, Integer weight)  tropical  Functions  Creation functions for specific cycles 
affine_representation(Int domain_chart, Int target_chart)  tropical  method of Morphism  Affine and projective coordinates 
affine_transform(Cycle<Addition> C, Matrix<Rational> M, Vector<Rational> T)  tropical  Functions  Basic polyhedral operations 
affine_transform(Cycle<Addition> C, Morphism<Addition> M)  tropical  Functions  Basic polyhedral operations 
AffineLattice<Scalar>  polytope  Objects  Geometry 
after(Morphism g)  tropical  method of Morphism  Morphisms 
ag23_matroid()  matroid  Functions  Producing a matroid from scratch 
ag32_matroid()  matroid  Functions  Producing a matroid from scratch 
ag32_prime_matroid()  matroid  Functions  Producing a matroid from scratch 
alexander_dual(SimplicialComplex complex)  topaz  Functions  Producing a new simplicial complex from others 
all_edges(Int tail_node, Int head_node)  common  method of Graph  no category 
all_families()  tropical  method of LinesInCubic  Lists of lines 
ALL_GROUP_ELEMENTS  group  property of Action  Symmetry 
all_group_elements(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_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  polytope  property of Cone  Combinatorics 
ALTSHULER_DET  fan  property of SubdivisionOfVectors  no category 
AMBIENT_DIM()  polytope  method of Cone  Geometry 
AMBIENT_DIM()  polytope  method of PointConfiguration  Geometry 
AMBIENT_DIM()  polytope  method of Polytope  Geometry 
AMBIENT_DIM()  fan  method of PolyhedralFan  Geometry 
AMBIENT_DIM()  fan  method of PolyhedralComplex  Geometry 
AMBIENT_DIM  fan  method of SubdivisionOfPoints  Geometry 
ambient_lattice_normalization(Polytope p)  polytope  Functions  Transformations 
AMPLE  fulton  property of TDivisor  Algebraic Geometry 
anti_diag(Vector d)  common  Functions  Linear Algebra 
anti_diag(Matrix m1, Matrix m2)  common  Functions  Linear Algebra 
anti_diagonal(Int i)  common  method of Matrix  no category 
application(String name)  core  Functions  Basic 
apply(Core::Object o)  core  method of Core::RuleChain  no category 
apply  common  method of Max  no category 
apply  common  method of Min  no category 
apply_rule(String pattern)  core  method of Core::Object  no category 
ApproximateSet<Element>  common  Property_types  Set Types 
apropos(String pattern)  core  Functions  Interactive 
archimedean_solid(String s)  polytope  Functions  Producing regular polytopes and their generalizations 
are_in_same_orbit(PermutationAction a, Vector v1, Vector v2)  group  Functions  Orbits 
are_permuted(Array a, Array b)  common  Functions  Combinatorics 
Array<Element>  common  Property_types  Basic Types 
array_family_fixed_edge()  tropical  method of LinesInCubic  Lists of lines 
array_family_fixed_vertex()  tropical  method of LinesInCubic  Lists of lines 
array_family_moving_edge()  tropical  method of LinesInCubic  Lists of lines 
array_family_moving_vertex()  tropical  method of LinesInCubic  Lists of lines 
array_isolated_edge()  tropical  method of LinesInCubic  Lists of lines 
array_isolated_no_edge()  tropical  method of LinesInCubic  Lists of lines 
associahedron(Int d)  polytope  Functions  Producing a polytope from scratch 
attach(String name, Any data, String constructor_args)  core  method of Core::Object  no category 
AUTOMORPHISM_GROUP  matroid  property of Matroid  Advanced properties 
automorphism_group(Graph graph)  group  Functions  Symmetry 
automorphism_group(IncidenceMatrix<NonSymmetric> m, Bool on_rows)  group  Functions  Symmetry 
automorphisms(Graph graph)  graph  Functions  Comparing 
automorphisms(IncidenceMatrix<NonSymmetric> m)  graph  Functions  Comparing 
automorphisms(IncidenceMatrix<Symmetric> m)  graph  Functions  Comparing 
average(ARRAY array)  common  Functions  Utilities 
AVERAGE_DEGREE  graph  property of Graph  no category 
back()  common  method of Set  no category 
BALANCE  polytope  property of Polytope  Combinatorics 
BALANCED  polytope  property of Polytope  Combinatorics 
BALANCED_FACES  tropical  property of Cycle  Weights and lattices 
BALL  topaz  property of SimplicialComplex  Topology 
ball(Int d)  topaz  Functions  Producing from scratch 
ball_lifting_lp(GeometricSimplicialComplex c, Int facet_index, Rational conv_eps)  polytope  Functions  Optimization 
BARYCENTER  polytope  property of PointConfiguration  Geometry 
barycenter(Matrix A)  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 GroebnerBasis  no category 
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 A)  common  Functions  Linear Algebra 
basis_rows(Matrix A)  common  Functions  Linear Algebra 
basis_rows_integer(Matrix A)  common  Functions  Linear Algebra 
BB_VISUAL()  tropical  method of Cycle  Visualization 
before(Morphism g)  tropical  method of Morphism  Morphisms 
BETA_INVARIANT  matroid  property of Matroid  Advanced properties 
betti_number()  topaz  method of HomologyGroup  no category 
betti_numbers<Coeff>(ChainComplex C)  topaz  Functions  Topology 
betti_numbers<Coeff>(SimplicialComplex S)  topaz  Functions  Topology 
BICONNECTED_COMPONENTS  graph  property of Graph  no category 
billera_lee(Vector<Integer> H)  polytope  Functions  Producing a polytope from other objects 
BINARY  matroid  property of Matroid  Advanced properties 
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  Advanced properties 
binomial(Int n, Int k)  common  Functions  Combinatorics 
BINOMIAL_GENERATORS  fulton  property of BinomialIdeal  no category 
BinomialIdeal  fulton  Objects  no category 
BIPARTITE()  topaz  method of SimplicialComplex  Combinatorics 
BIPARTITE  graph  property of Graph  no category 
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  polytope  property of PointConfiguration  Geometry 
BOUNDED  polytope  property of Polytope  Geometry 
BOUNDED  fan  property of PolyhedralComplex  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(Matrix m)  common  Functions  Utilities 
bounding_box(Int chart)  tropical  method of Cycle  Visualization 
BOUNDING_BOX  graph  property of GeometricGraph  no category 
bounding_box_facets(Scalar offset, Matrix V, Scalar surplus_k, Bool fulldim, Bool make_cube)  polytope  Functions  Visualization 
bounding_box_facets(Int offset, Int chart)  tropical  method of Cycle  Visualization 
bounding_facets(Matrix H, Matrix V, Scalar offset, Scalar surplus_k, Bool transform, Bool fulldim, Bool return_nonredundant)  polytope  Functions  Visualization 
bs2quotient(Polytope P, SimplicialComplex complex)  topaz  Functions  Producing a new simplicial complex from others 
building_set(Array<Set> generators, Int n)  fan  Functions  Other 
CachedObjectPointer<>  common  Property_types  Artificial 
CANONICAL  polytope  property of Polytope  Lattice points in cones 
canonical_form(Graph g)  graph  Functions  Comparing 
canonical_hash(Graph g, Int k)  graph  Functions  Comparing 
canonical_hash(IncidenceMatrix M, Int k)  graph  Functions  Comparing 
cap_product(CycleGroup<E> cocycles, CycleGroup<E> cycles)  topaz  Functions  Topology 
cartesian_product(Cycle cycles)  tropical  Functions  Basic polyhedral operations 
CARTIER  fulton  property of TDivisor  Algebraic Geometry 
CARTIER_DATA  fulton  property of TDivisor  Combinatorics 
cast<Target>(Core::Object object)  common  Functions  Data Conversion 
catalan_solid(String s)  polytope  Functions  Producing regular polytopes and their generalizations 
CATENARY_G_INVARIANT  matroid  property of Matroid  Advanced properties 
cayley_embedding(Polytope P_0, Polytope P_1, Scalar t_0, Scalar t_1)  polytope  Functions  Producing a polytope from polytopes 
cayley_embedding(Array<Polytope> A)  polytope  Functions  Producing a polytope from polytopes 
cayley_polytope(Array<Polytope> P_Array)  polytope  Functions  Producing a polytope from polytopes 
CD_INDEX()  polytope  method of Polytope  Combinatorics 
CD_INDEX_COEFFICIENTS  polytope  property of Polytope  Combinatorics 
ceil(Rational a)  common  Functions  Arithmetic 
Cell  topaz  Property_types  Topology 
cell(Int i)  fan  method of SubdivisionOfVectors  Geometry 
cell(Int i)  fan  method of SubdivisionOfPoints  Geometry 
CELL_DECOMPOSITION  fan  property of HyperplaneArrangement  Geometry 
cell_decomposition_brute_force  fan  Functions  Geometry 
cell_from_subdivision(Polytope P, Int cell)  polytope  Functions  Producing a polytope from polytopes 
CELL_SIGNATURES  fan  property of HyperplaneArrangement  Combinatorics 
cell_to_signature  fan  method of HyperplaneArrangement  Combinatorics 
cells()  topaz  method of Filtration  no category 
cells_from_subdivision(Polytope<Scalar> P, Set<Int> cells)  polytope  Functions  Producing a polytope from polytopes 
center(Polytope P)  polytope  Functions  Transformations 
center_distance(Polytope p)  polytope  Functions  Geometry 
CENTERED  polytope  property of PointConfiguration  Geometry 
CENTERED  polytope  property of Polytope  Geometry 
CENTERED_ZONOTOPE  polytope  property of Polytope  Geometry 
CENTRALLY_SYMMETRIC  polytope  property of Polytope  Geometry 
CENTROID  polytope  property of Polytope  Geometry 
cf2rational(Vector<Integer> v)  fulton  Functions  Continued fractions 
ChainComplex<MatrixType>  topaz  Property_types  Topology 
CHARACTER  group  property of Action  Symmetry 
CHARACTER_TABLE  group  property of Group  Symmetry 
CHARACTERISTIC_POLYNOMIAL  graph  property of Graph  no category 
check_basis_exchange_axiom(Array<Set> B)  matroid  Functions  Other 
check_cycle_equality(Cycle<Addition> X, Cycle<Addition> Y, Bool check_weights)  tropical  Functions  Basic polyhedral operations 
check_fan(Matrix rays, IncidenceMatrix cones)  fan  Functions  Consistency check 
check_fan_objects<Coord>(Array<Cone> cones)  fan  Functions  Consistency check 
check_flat_axiom(Array<Set> F)  matroid  Functions  Other 
check_hyperplane_axiom(Array<Set> H)  matroid  Functions  Other 
check_inc(Matrix points, Matrix hyperplanes, String sign, Bool verbose)  polytope  Functions  Consistency check 
check_poly(IncidenceMatrix VIF)  polytope  Functions  Consistency check 
check_transversality(Matroid M)  matroid  Functions  Advanced properties 
check_valuated_basis_axioms(Array<Set<Int>> bases, Vector<TropicalNumber<Addition,Scalar>> valuation)  matroid  Functions  Other 
check_valuated_circuit_axioms(Matrix<TropicalNumber<Addition,Scalar>> M)  matroid  Functions  Other 
CHIROTOPE  polytope  property of Polytope  Matroid properties 
CHIROTOPE  polytope  property of VectorConfiguration  Matroid properties 
chirotope(Polytope P)  polytope  Functions  Triangulations, subdivisions and volume 
chirotope(VectorConfiguration P)  polytope  Functions  Triangulations, subdivisions and volume 
chirotope(Polytope P)  polytope  Functions  Triangulations, subdivisions and volume 
chirotope(VectorConfiguration P)  polytope  Functions  Triangulations, subdivisions and volume 
circuit_completions(Matrix L, Matrix R)  polytope  Functions  Geometry 
CIRCUITS  matroid  property of Matroid  Axiom systems 
CIRCUITS  polytope  property of Polytope  Matroid properties 
CIRCUITS  polytope  property of VectorConfiguration  Matroid properties 
circuits2matrix(Set<Pair<Set<Int>,Set<Int>>> co)  polytope  Functions  Combinatorics 
clear(Int r, Int c)  common  method of Matrix  no category 
clip_graph(Graph G, Matrix V, Matrix BB)  graph  Functions  Visualization 
clique_complex(Graph graph)  topaz  Functions  Producing a simplicial complex from other objects 
CLOSED_PSEUDO_MANIFOLD  topaz  property of SimplicialComplex  Topology 
coarse_covectors(Matrix<TropicalNumber<Addition,Scalar>> points, Matrix<TropicalNumber<Addition,Scalar>> generators)  tropical  Functions  Tropical covector decomposition 
coarse_covectors_of_scalar_vertices(Matrix<Scalar> points, Matrix<TropicalNumber<Addition,Scalar>> generators)  tropical  Functions  Tropical covector decomposition 
coarsen(Cycle<Addition> complex, Bool testFan)  tropical  Functions  Basic polyhedral operations 
cocircuit_equation_of_ridge(Cone C, Set rho)  polytope  Functions  Combinatorics 
COCIRCUIT_EQUATIONS  polytope  property of QuotientSpace  Combinatorics 
COCIRCUIT_EQUATIONS  polytope  property of Cone  Combinatorics 
COCIRCUIT_EQUATIONS  polytope  property of PointConfiguration  Combinatorics 
cocircuit_equations(Cone C, Array<Set> interior_ridge_simplices, Array<Set> interior_simplices)  polytope  Functions  Combinatorics 
cocircuit_equations_support_reps(Matrix<Scalar> points, Array<Array<Int>> gens, Array<SetType> rirs, Array<SetType> rmis)  polytope  Functions  Symmetry 
COCIRCUITS  matroid  method of Matroid  Axiom systems 
COCIRCUITS  polytope  property of Polytope  Matroid properties 
COCIRCUITS  polytope  property of VectorConfiguration  Matroid properties 
COCUBICAL  polytope  property of Polytope  Combinatorics 
COCUBICALITY  polytope  property of Polytope  Combinatorics 
COCYCLES  topaz  property of SimplicialComplex  Topology 
codegree<Scalar>(Cone P)  polytope  Functions  Combinatorics 
codegree<Scalar>(PointConfiguration P)  polytope  Functions  Combinatorics 
CODIMENSION_ONE_POLYTOPES  tropical  property of Cycle  Combinatorics 
coeff()  topaz  method of CycleGroup  no category 
COEFFICIENTS  fulton  property of TDivisor  Combinatorics 
COEFFICIENTS  tropical  property of Hypersurface  no category 
coefficients_as_vector()  common  method of Polynomial  no category 
coefficients_as_vector()  common  method of UniPolynomial  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 of)  group  Functions  Symmetry 
collect(Element e)  common  method of Set  no category 
COLOOPS  matroid  method of Matroid  Axiom systems 
Color  common  Property_types  Visualization 
colored_ball_from_colored_sphere(SimplicialComplex complex)  topaz  Functions  Producing a new simplicial complex from others 
COLORING  topaz  property of SimplicialComplex  no category 
COLORING  topaz  property of SimplicialComplex  Combinatorics 
cols()  common  method of IncidenceMatrix  no category 
cols()  common  method of Matrix  no category 
cols  common  Functions  Data Conversion 
cols(Matrix A)  common  Functions  Data Conversion 
COMBINATORIAL_DIM  polytope  property of Cone  Combinatorics 
COMBINATORIAL_DIM  fan  property of PolyhedralFan  Combinatorics 
combinatorial_symmetries(Polytope p)  polytope  Functions  Symmetry 
combinatorial_symmetries(PolyhedralFan f)  fan  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 
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 
common_refinement(PolyhedralFan f1, PolyhedralFan f2)  fan  Functions  Producing a fan 
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 A)  common  Functions  Data Conversion 
Cone<Scalar>  polytope  Objects  no category 
cone(SimplicialComplex complex, Int k)  topaz  Functions  Producing a new simplicial complex from others 
cone(Int i)  fan  method of PolyhedralFan  Combinatorics 
CONE_AMBIENT_DIM  polytope  property of Cone  Geometry 
CONE_AMBIENT_DIM  polytope  property of Polytope  Geometry 
CONE_DIM  polytope  property of Cone  Geometry 
CONE_DIM  polytope  property of Polytope  Geometry 
cone_of_tubing(Graph G, Graph T)  fan  Functions  Other 
cone_representative(Int i)  fan  method of PolyhedralFan  Symmetry 
CONES  fan  property of PolyhedralFan  Combinatorics 
cones_action(PolyhedralFan f, Int k)  fan  Functions  Symmetry 
CONES_COMBINATORIAL_DIMS  fan  property of PolyhedralFan  Combinatorics 
CONES_DIMS()  fan  method of PolyhedralFan  Combinatorics 
CONES_ORBIT_SIZES  fan  property of PolyhedralFan  Symmetry 
CONES_REPS  fan  property of PolyhedralFan  Symmetry 
congruent(Polytope P1, Polytope P2)  polytope  Functions  Comparing 
conjugacy_class<Element>(Action action, Element e)  group  Functions  Symmetry 
conjugacy_class<Scalar>(MatrixActionOnVectors<Scalar> action, Matrix<Scalar> e)  group  Functions  Symmetry 
CONJUGACY_CLASS_REPRESENTATIVES  group  property of Action  Symmetry 
CONJUGACY_CLASS_SIZES  group  property of Group  Symmetry 
CONJUGACY_CLASSES  group  property of Action  Symmetry 
CONNECTED  matroid  property of Matroid  Advanced properties 
CONNECTED()  topaz  method of SimplicialComplex  Topology 
CONNECTED  graph  property of Graph  no category 
CONNECTED_COMPONENTS  matroid  property of Matroid  Advanced properties 
CONNECTED_COMPONENTS()  topaz  method of SimplicialComplex  Combinatorics 
CONNECTED_COMPONENTS  graph  property of Graph  no category 
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()  topaz  method of SimplicialComplex  Combinatorics 
CONNECTIVITY  graph  property of Graph  no category 
connectivity(Graph<Undirected> graph)  graph  Functions  Combinatorics 
constant_coefficient()  common  method of Polynomial  no category 
constant_coefficient()  common  method of UniPolynomial  no category 
CONSTRUCTION()  polytope  method of Visual::SchlegelDiagram  no category 
Container  common  Property_types  Artificial 
containing_normal_cone(Cone P, Vector q)  polytope  Functions  Geometry 
containing_outer_cone(Polytope P, Vector q)  polytope  Functions  Geometry 
contains(Vector<Scalar> v)  polytope  method of Cone  Geometry 
contains(Element e)  common  method of Set  no category 
contains_in_interior(Vector<Scalar> v)  polytope  method of Cone  Geometry 
contains_monomial(String s)  ideal  method of Ideal  no category 
contains_point(Cycle A, Vector<Rational> point)  tropical  Functions  Basic polyhedral operations 
CONTINUED_FRACTION  fulton  property of CyclicQuotient  Input properties 
CONTINUED_FRACTION  fulton  property of VersalComponent  Combinatorics 
contract_edge(Int node1, Int node2)  common  method of Graph  no category 
contraction(Matroid m, Set<Int> S)  matroid  Functions  Producing a matroid from matroids 
contraction(Matroid m, Int x)  matroid  Functions  Producing a matroid from matroids 
contraction(VectorConfiguration C, Int v)  polytope  Functions  Combinatorics 
conv(Array<Polytope> P_Array)  polytope  Functions  Producing a polytope from polytopes 
convert_to<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  polytope  property of PointConfiguration  Geometry 
CONVEX  fan  property of SubdivisionOfVectors  Geometry 
CONVEX_HULL  polytope  property of PointConfiguration  Geometry 
COORDINATE_ACTION  polytope  property of Polytope  Symmetry 
COORDINATE_ACTION  fan  property of PolyhedralComplex  Symmetry 
COORDINATE_LABELS  polytope  property of Cone  Visualization 
COORDINATES  topaz  property of GeometricSimplicialComplex  no category 
coordinates  common  method of Plucker  no category 
COORDINATES  graph  property of GeometricGraph  no category 
Core::Object  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_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)  topaz  Functions  Producing a new simplicial complex from others 
coxeter_group(String type)  polytope  Functions  Producing other objects 
CP_INDICES  polytope  property of Polytope  no category 
CQS_MATRIX  fulton  property of VersalComponent  Combinatorics 
cramer(Matrix A, Vector b)  common  Functions  Linear Algebra 
cramer(Matrix<TropicalNumber> matrix)  tropical  Functions  Tropical operations 
CRITICAL_FACE_VECTOR  topaz  property of MorseMatching  no category 
CRITICAL_FACES  topaz  property of MorseMatching  no category 
cross<Scalar>(Int d, Scalar scale)  polytope  Functions  Producing regular polytopes and their generalizations 
cross_variety<Addition>(Int n, Int k, Rational h, Integer weight)  tropical  Functions  Creation functions for specific cycles 
crosscut_complex(Polytope p)  polytope  Functions  Producing other objects 
CRUST_GRAPH  polytope  property of VoronoiPolyhedron  no category 
CS_PERMUTATION  polytope  property of Polytope  Geometry 
cs_quotient(Polytope P)  polytope  Functions  Quotient spaces 
cube<Scalar>(Int d, Scalar x_up, Scalar x_low)  polytope  Functions  Producing regular polytopes and their generalizations 
cube_complex(Array<Int> x)  topaz  Functions  Producing from scratch 
cube_group(Int d)  group  Functions  Producing a group 
CUBIC  tropical  property of LinesInCubic  Defining properties 
CUBICAL  polytope  property of Polytope  Combinatorics 
CUBICAL_H_VECTOR  polytope  property of Polytope  Combinatorics 
CUBICALITY  polytope  property of Polytope  Combinatorics 
cuboctahedron()  polytope  Functions  Producing regular polytopes and their generalizations 
CURVE_EDGE_LENGTHS()  tropical  method of Cycle  Weights and lattices 
cutting_functions(Cycle<Addition> F, Vector<Integer> weight_aim)  tropical  Functions  Inverse problems 
Cycle<Addition>  tropical  Objects  no category 
cycle_graph(Int n)  graph  Functions  Producing a graph 
CycleGroup<Scalar>  topaz  Property_types  Topology 
CYCLES  topaz  property of SimplicialComplex  Topology 
cyclic(Int d, Int n)  polytope  Functions  Producing a polytope from scratch 
cyclic<Addition>(Int d, Int n)  tropical  Functions  Producing a tropical polytope 
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 
db_aggregate  common  Functions  no category 
db_count(HASH query)  common  Functions  Database 
db_cursor(HASH query)  common  Functions  Database 
db_get_list_col_for_db()  common  Functions  Database 
db_get_list_db()  common  Functions  Database 
db_get_list_db_col()  common  Functions  Database 
db_get_type_information  common  Functions  no category 
db_ids(HASH query)  common  Functions  Database 
db_info()  common  Functions  Database 
db_insert(Core::Object obj)  common  Functions  Database Write Access 
db_metadata(Core::Object p)  common  Functions  Database 
db_print_metadata(Core::Object p)  common  Functions  Database 
db_print_searchable_fields  common  Functions  no category 
db_query(HASH query)  common  Functions  Database 
db_remove(String id)  common  Functions  Database Write Access 
db_searchable_fields(String db, String collection)  common  Functions  Database 
db_set_type_information()  common  Functions  Database Admin 
db_write_collection_info()  common  Functions  Database 
db_write_db_info(String db)  common  Functions  Database 
DBCursor  common  Property_types  Database 
DCEL_DATA  topaz  property of HyperbolicSurface  no category 
decomposition_polytope(Cycle A)  tropical  Functions  Weight space 
DECORATION  graph  property of Lattice  Combinatorics 
deg()  common  method of Polynomial  no category 
deg()  common  method of UniPolynomial  no category 
DEGENERATE  fulton  property of NormalToricVariety  Algebraic Geometry 
DEGREE  group  property of Action  Symmetry 
degree<Scalar>(PointConfiguration P)  polytope  Functions  Combinatorics 
degree(Int node)  common  method of Graph  no category 
DEGREE  tropical  property of Cycle  Intersection theory 
degree(Cycle A)  tropical  Functions  Intersection theory 
DEGREE_ONE_GENERATORS  polytope  property of Cone  Lattice points in cones 
DEGREE_SEQUENCE  graph  property of Graph  no category 
DELAUNAY_DIAGRAM  polytope  property of VoronoiPolyhedron  no category 
DELAUNAY_GRAPH  polytope  property of VoronoiPolyhedron  no category 
DELAUNAY_TRIANGULATION  polytope  property of VoronoiPolyhedron  no category 
delaunay_triangulation(VoronoiPolyhedron V)  polytope  Functions  Triangulations, subdivisions and volume 
delete_all_edges(Int tail_node, Int head_node)  common  method of Graph  no category 
delete_edge  common  method of Graph  no category 
delete_node(Int node)  common  method of Graph  no category 
deletion(Matroid m, Set<Int> S)  matroid  Functions  Producing a matroid from matroids 
deletion(Matroid m, Int x)  matroid  Functions  Producing a matroid from matroids 
deletion(VectorConfiguration C, Int v)  polytope  Functions  Combinatorics 
deletion(SimplicialComplex complex, Set<Int> face)  topaz  Functions  Producing a new simplicial complex from others 
delocalize()  tropical  method of Cycle  Local computations 
delpezzo(Int d, Scalar scale)  polytope  Functions  Producing a polytope from scratch 
denominator(Rational a)  common  Functions  Arithmetic 
denominator(RationalFunction f)  common  Functions  Arithmetic 
denominator(PuiseuxFraction f)  common  Functions  Arithmetic 
DENOMINATOR  tropical  property of RationalFunction  Defining morphisms and functions 
dense(Vector v)  common  Functions  Data Conversion 
dense(Matrix m)  common  Functions  Data Conversion 
dense<Element>(SparseVector<Element> v)  common  Functions  Data Conversion 
dense<Element>(SparseMatrix<Element> m)  common  Functions  Data Conversion 
dense(IncidenceMatrix m)  common  Functions  Data Conversion 
dense(Set s, Int dim)  common  Functions  Data Conversion 
DEPTH  ideal  property of Ideal  Commutative algebra 
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  polytope  property of QuotientSpace  Combinatorics 
dim()  polytope  method of Cone  Combinatorics 
DIM()  polytope  method of Cone  Geometry 
DIM()  polytope  method of PointConfiguration  Geometry 
DIM()  polytope  method of Polytope  Geometry 
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  ideal  property of Ideal  Commutative algebra 
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()  common  method of Graph  no category 
dim()  common  method of Vector  no category 
dim  tropical  method of CovectorLattice  Combinatorics 
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::Object  no category 
disable_rules(String pattern)  core  Functions  Basic 
disjoint_union(SimplicialComplex complex1, SimplicialComplex complex2)  topaz  Functions  Producing a new simplicial complex from others 
distance_matrix(Matrix S, CODE d)  common  Functions  Utilities 
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  fulton  property of NormalToricVariety  Algebraic Geometry 
divisor(Cycle C, RationalFunction F)  tropical  Functions  Divisor computation 
divisor_nr(Cycle C, RationalFunction F)  tropical  Functions  Divisor computation 
dodecahedron()  polytope  Functions  Producing regular polytopes and their generalizations 
DOMAIN  tropical  property of Morphism  Defining morphisms and functions 
DOMAIN  tropical  property of RationalFunction  Defining morphisms and functions 
DOMAIN_NAME  group  property of Action  Symmetry 
DOME  tropical  property of Hypersurface  no category 
DOME  tropical  property of Polytope  Geometry 
dont_save  core  method of Core::Object  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_description(Matrix monomial_generators)  tropical  Functions  Tropical operations 
DUAL_DIAMETER()  polytope  method of Cone  Backward compatibility 
DUAL_EVEN()  polytope  method of Cone  Combinatorics 
dual_faces()  graph  method of Lattice  Combinatorics 
DUAL_GRAPH  polytope  property of Cone  Combinatorics 
DUAL_GRAPH  polytope  property of Polytope  Combinatorics 
DUAL_GRAPH  topaz  property of SimplicialComplex  Combinatorics 
DUAL_GRAPH  fan  property of PolyhedralFan  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 
dualOutitudes(Array<Array<Int>> dcel_data)  topaz  Functions  Other 
dwarfed_cube(Int d)  polytope  Functions  Producing a polytope from scratch 
dwarfed_product_polygons(Int d, Int s)  polytope  Functions  Producing a polytope from scratch 
edge(Int from, Int to)  common  method of EdgeMap  no category 
edge(Int tail_node, Int head_node)  common  method of Graph  no category 
edge(Int from, Int to)  common  method of EdgeHashMap  no category 
EDGE_COLORS()  polytope  method of Visual::PolytopeGraph  no category 
EDGE_COLORS  polytope  property of Polytope  no category 
edge_contraction(SimplicialComplex complex)  topaz  Functions  Producing a new simplicial complex from others 
EDGE_DIRECTIONS  polytope  property of Polytope  no category 
EDGE_DIRECTIONS  polytope  property of Polytope  Geometry 
edge_exists(Int tail_node, Int head_node)  common  method of Graph  no category 
EDGE_LENGTHS  polytope  property of Polytope  no category 
edge_lengths(Graph<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()  common  method of Graph  no category 
edges(Graph graph)  common  Functions  Graph Operations 
EDGES()  graph  method of Graph  Combinatorics 
EFFECTIVE  fulton  property of TDivisor  Algebraic Geometry 
EFFECTIVE_CONE  fulton  property of NormalToricVariety  Algebraic Geometry 
EHRHART_POLYNOMIAL  polytope  property of Polytope  Lattice points in cones 
EHRHART_POLYNOMIAL_COEFF()  polytope  method of Polytope  Lattice points in cones 
EHRHART_QUASI_POLYNOMIAL  polytope  property of Polytope  Lattice points in cones 
eigenvalues(Matrix<Float> A)  common  Functions  Linear Algebra 
EIGENVALUES_LAPLACIAN  graph  property of Graph  no category 
eigenvalues_laplacian(Graph G)  graph  Functions  Combinatorics 
eigenvalues_laplacian(Graph G)  graph  Functions  Combinatorics 
elem(Int r, Int c)  common  method of 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(Int from, Int to)  common  method of EdgeHashMap  no category 
erase(Set f)  common  method of FacetList  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  common  method of PuiseuxFraction  no category 
evaluate(Coefficient x, Exponent exp)  common  method of UniPolynomial  no category 
evaluate_float  common  method of PuiseuxFraction  no category 
evaluate_float(Float x)  common  method of UniPolynomial  no category 
evaluation_map<Addition>(Int n, Matrix<Rational> Delta, Int i)  tropical  Functions  Moduli of rational curves 
evaluation_map<Addition>(Int n, Int r, Int d, Int i)  tropical  Functions  Moduli of rational curves 
EVEN()  polytope  method of Cone  Combinatorics 
EXCESS_FACET_DEGREE  polytope  property of Cone  Combinatorics 
EXCESS_RAY_DEGREE  polytope  property of Cone  Combinatorics 
EXCESS_VERTEX_DEGREE  polytope  property of Polytope  Combinatorics 
exit  core  Functions  Interactive 
EXPLICIT_ORBIT_REPRESENTATIVE_MATRIX  group  property of Action  Symmetry 
EXPLICIT_ORBIT_REPRESENTATIVES  group  property of Action  Symmetry 
explicit_zonotope(Matrix zones)  polytope  Functions  Producing a polytope from scratch 
export_configured(String filename)  core  Functions  Interactive 
ext_gcd(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  polytope  property of Cone  Combinatorics 
F2_VECTOR  polytope  property of Polytope  Combinatorics 
F2_VECTOR  topaz  property of SimplicialComplex  Combinatorics 
F2_VECTOR  fan  property of PolyhedralFan  Combinatorics 
f8_matroid()  matroid  Functions  Producing a matroid from scratch 
F_VECTOR  matroid  property of Matroid  Advanced properties 
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  fan  property of PolyhedralFan  Combinatorics 
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_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(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  graph  property of Lattice  Combinatorics 
faces_of_dim(Cone c)  polytope  method of Cone  Combinatorics 
faces_of_dim(PointConfiguration p)  polytope  method of PointConfiguration  Combinatorics 
FACET  polytope  property of SchlegelDiagram  no category 
facet(Cone P, Int facet)  polytope  Functions  Producing a polytope from polytopes 
FACET_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_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 
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  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 m)  common  Functions  Utilities 
Filtration<MatrixType>  topaz  Property_types  Topology 
find(Int from, Int to)  common  method of EdgeHashMap  no category 
find(Set f)  common  method of FacetList  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(Graph graph1, Graph graph2)  graph  Functions  Comparing 
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  method of Visual::PlanarNet  no category 
FLAPS  fan  property of PlanarNet  Combinatorics 
Flexible  common  Property_types  Visualization 
flip_tube(Graph G, Graph T, Int t)  fan  Functions  Other 
FLIP_WORDS  topaz  property of HyperbolicSurface  no category 
Float  common  Property_types  Basic Types 
floor(Rational a)  common  Functions  Arithmetic 
flow_polytope<Scalar>(Graph<Directed> G, EdgeMap<Directed,Scalar> Arc_Bounds, Int source, Int sink)  polytope  Functions  Producing a polytope from graphs 
flow_polytope<Scalar>(Graph<Directed> G, Array<Scalar> Arc_Bounds, Int source, Int sink)  polytope  Functions  Producing a polytope from graphs 
FOLDABLE  topaz  property of SimplicialComplex  Combinatorics 
FOLDABLE_COCIRCUIT_EQUATIONS  polytope  property of Cone  Combinatorics 
foldable_max_signature_ilp(Int d, Matrix points, Rational volume, SparseMatrix cocircuit_equations)  polytope  Functions  Triangulations, subdivisions and volume 
FOLDABLE_MAX_SIGNATURE_UPPER_BOUND  polytope  property of Polytope  Combinatorics 
foldable_max_signature_upper_bound(Int d, Matrix points, Rational volume, SparseMatrix cocircuit_equations)  polytope  Functions  Triangulations, subdivisions and volume 
foldable_prism(GeometricSimplicialComplex complex)  topaz  Functions  Producing a new simplicial complex from others 
forgetful_map<Addition>(Int n, Set<Int> S)  tropical  Functions  Moduli of rational curves 
form()  common  method of SmithNormalForm  no category 
found_application(String extension, String app_name)  core  Functions  Interactive 
found_extension(String path)  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(VectorConfiguration P1, VectorConfiguration P2)  polytope  Functions  Producing a vector configuration 
free_sum(Polytope P1, Polytope P2)  polytope  Functions  Producing a polytope from polytopes 
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  polytope  property of Cone  Geometry 
FULL_DIM  polytope  property of VectorConfiguration  Geometry 
FULL_DIM  fan  property of PolyhedralFan  Geometry 
FULL_DIM  fan  property of SubdivisionOfVectors  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 Polytope  Geometry 
GALE_TRANSFORM  polytope  property of VectorConfiguration  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 
generalized_johnson_graph(Int n, Int k, Int i)  graph  Functions  Producing a graph 
generating_polyhedron_facets(PolyhedralFan P)  fan  Functions  Geometry 
GENERATING_POLYTOPE  fulton  property of NormalToricVariety  Basic properties 
GENERATORS  group  property of Action  Symmetry 
GENERATORS  ideal  property of Ideal  Input properties 
GENUS  topaz  property of SimplicialComplex  Topology 
GENUS  tropical  method of Hypersurface  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::Object  no category 
get_map()  graph  method of InverseRankMap  Combinatorics 
get_schedule(String request)  core  method of Core::Object  no category 
get_var_names  common  method of Polynomial  no category 
get_var_names  common  method of UniPolynomial  no category 
get_var_names()  common  Functions  Arithmetic 
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 
gkz_dome(Int k, Int depth)  topaz  method of HyperbolicSurface  Other 
GKZ_VECTOR  polytope  property of PointConfiguration  Triangulation and volume 
GKZ_VECTOR  polytope  property of Polytope  Triangulation and volume 
GKZ_VECTORS(Int depth)  topaz  method of HyperbolicSurface  Other 
goldfarb(Int d, Scalar e, Scalar g)  polytope  Functions  Producing a polytope from scratch 
goldfarb_sit(Int d, Scalar eps, Scalar delta)  polytope  Functions  Producing a polytope from scratch 
GORENSTEIN  polytope  property of Polytope  Lattice points in cones 
GORENSTEIN  fan  property of PolyhedralFan  Toric Varieties 
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  polytope  property of Cone  Combinatorics 
GRAPH  polytope  property of PointConfiguration  Combinatorics 
GRAPH  polytope  property of Polytope  Combinatorics 
GRAPH  polytope  property of Polytope  Combinatorics 
GRAPH  topaz  property of SimplicialComplex  Combinatorics 
GRAPH  fan  property of PolyhedralFan  Combinatorics 
Graph<Dir>  common  Property_types  Graph Types 
GRAPH  tropical  property of RationalCurve  Combinatorics 
Graph<Dir>  graph  Objects  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 
GraphMap<Dir, Element>  common  Property_types  Graph Types 
graphviz(Visual::Object vis_obj …)  graph  Functions  Visualization 
GROEBNER  ideal  property of Ideal  Commutative algebra 
Groebner  ideal  Objects  no category 
GROEBNER_BASIS  polytope  property of Polytope  Lattice points in cones 
groebner_fan(Ideal I)  fan  Functions  Producing a fan 
GroebnerBasis  polytope  Objects  Lattice points in cones 
Group  group  Objects  no category 
GROUP  polytope  property of Cone  Symmetry 
GROUP  polytope  property of PointConfiguration  Symmetry 
GROUP  polytope  property of Polytope  Symmetry 
GROUP  polytope  property of VectorConfiguration  Symmetry 
GROUP  topaz  property of SimplicialComplex  Symmetry 
GROUP  fan  property of PolyhedralFan  Symmetry 
GROUP  fan  property of PolyhedralComplex  Symmetry 
group_from_cyclic_notation0(String generators)  group  Functions  Producing a group 
group_from_cyclic_notation1(String generators)  group  Functions  Producing a group 
group_from_permlib_cyclic_notation(Array<String> gens, Int degree)  group  Functions  Producing a group 
group_left_multiplication_table(Group G)  group  Functions  Symmetry 
group_right_multiplication_table(Group G)  group  Functions  Symmetry 
gudkov_curve()  tropical  Functions  no category 
h_induced_quotient(SimplicialComplex C, Set<Int> vertices)  topaz  Functions  Producing a new simplicial complex from others 
H_STAR_VECTOR  polytope  property of Cone  Lattice points in cones 
H_VECTOR  matroid  property of Matroid  Advanced properties 
H_VECTOR  polytope  property of Polytope  Combinatorics 
H_VECTOR  topaz  property of SimplicialComplex  Combinatorics 
hadamard_product(Matrix M1, Matrix M2)  common  Functions  Linear Algebra 
halfspace_subdivision<Addition>(Rational a, Vector<Rational> g, Integer w)  tropical  Functions  Creation functions for specific cycles 
harnack_curve(Int d)  tropical  Functions  no category 
has_gaps()  common  method of Graph  no category 
HashMap<Key, Value>  common  Property_types  Set Types 
HashSet<Element>  common  Property_types  Set Types 
HASSE_DIAGRAM  polytope  property of Cone  Combinatorics 
HASSE_DIAGRAM  polytope  property of Polytope  Combinatorics 
HASSE_DIAGRAM  topaz  property of SimplicialComplex  Combinatorics 
HASSE_DIAGRAM  fan  property of PolyhedralFan  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)  topaz  Functions  Producing a new simplicial complex from others 
hom_poset(Array<Array<Int>> homs, Graph<Directed> Q)  topaz  Functions  Producing a new simplicial complex from others 
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  topaz  property of SimplicialComplex  Topology 
homology(Array<Set<Int>> complex, Bool co)  topaz  Functions  Topology 
homology(ChainComplex CC, Bool co)  topaz  Functions  Topology 
HOMOLOGY  fan  property of PolyhedralFan  Topology 
homology_and_cycles(Array<Set<Int>> complex, Bool co)  topaz  Functions  Topology 
homology_and_cycles(ChainComplex<SparseMatrix<Integer>> CC, Bool co)  topaz  Functions  Topology 
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_arrangement(Matrix H)  fan  Functions  Producing a fan 
HyperplaneArrangement<Scalar>  fan  Objects  Geometry 
HYPERPLANES  fan  property of HyperplaneArrangement  Geometry 
hypersimplex(Int k, Int d)  polytope  Functions  Producing a polytope from scratch 
hypersimplex<Addition>(Int d, Int k)  tropical  Functions  Producing a tropical polytope 
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 path, List options)  core  Functions  Interactive 
in_adjacent_nodes(Int node)  common  method of Graph  no category 
in_degree(Int node)  common  method of Graph  no category 
in_edges(Int node)  common  method of Graph  no category 
incidence_matrix(Graph G)  graph  Functions  Combinatorics 
incidence_matrix(Graph G)  graph  Functions  Combinatorics 
IncidenceMatrix<Sym>  common  Property_types  Set Types 
incl(Set s1, Set s2)  common  Functions  Set Operations 
include(String rulefile)  core  Functions  Basic 
included_polyhedra(Polytope P1, Polytope P2)  polytope  Functions  Comparing 
independence_complex(Matroid matroid)  topaz  Functions  Producing a simplicial complex from other objects 
index_matrix(SparseMatrix m)  common  Functions  Data Conversion 
INDEX_OF  group  property of Action  Symmetry 
index_of(Array<Set<Int>> array)  common  Functions  Utilities 
indices(SparseVector v)  common  Functions  Data Conversion 
induce_implicit_action(PermutationAction original_action, String property)  group  Functions  Symmetry 
induce_set_action(Cone c, PermutationAction a, String domain)  group  Functions  Symmetry 
induced_action(PermutationAction a, Array<Set<Int>> domain)  group  Functions  Symmetry 
INDUCED_FROM  group  property of Action  Symmetry 
induced_lattice_basis(Polytope p)  polytope  Functions  Geometry 
induced_permutations(Array<Array<Int>> gens, Matrix M)  group  Functions  Symmetry 
induced_permutations(Array<Matrix<Scalar>> gens, Matrix M)  group  Functions  Symmetry 
induced_permutations(Array<Array<Int>> gens, Array<DomainType> S)  group  Functions  Symmetry 
induced_permutations(Array<Array<Int>> a, IncidenceMatrix M)  group  Functions  Symmetry 
induced_permutations_set_set(Array<Array<Int>> gens, Array<Set<Set>> domain)  group  Functions  Symmetry 
induced_rep(Cone C, PermutationActionOnSets A, Array<Int> g)  group  Functions  Symmetry 
induced_subcomplex(SimplicialComplex complex, Set<Int> vertices)  topaz  Functions  Producing a new simplicial complex from others 
induced_subdivision<Scalar>(VectorConfiguration<Scalar> pc, Matrix<Scalar> R, Set I)  fan  Functions  Geometry 
induced_subdivision  fan  Functions  Geometry 
induced_subgraph(Graph graph, Set set)  common  Functions  Graph Operations 
INEQUALITIES  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 Rational  no category 
inf  common  method of Integer  no category 
inf  common  method of Float  no category 
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 
inner_cone(Cone p, Set<Int> F)  polytope  Functions  Producing a cone 
INNER_DESCRIPTION()  polytope  method of Polytope  Geometry 
INNER_POINT  polytope  property of SchlegelDiagram  no category 
inner_point(Matrix points)  polytope  Functions  Optimization 
INPUT_COEFFS  tropical  property of RationalCurve  Input property 
INPUT_CONES  fan  property of PolyhedralFan  Input property 
INPUT_CONES_ACTION  group  property of Group  Symmetry 
INPUT_CONES_REPS  fan  property of PolyhedralFan  Input property 
INPUT_FACES  topaz  property of SimplicialComplex  Input property 
INPUT_HYPERPLANES  fan  property of HyperplaneArrangement  Input property 
INPUT_LINEALITY  polytope  property of Cone  Input property 
INPUT_LINEALITY  fan  property of PolyhedralFan  Input property 
INPUT_LINEALITY_GENERATORS  group  property of Action  Symmetry 
INPUT_POLYTOPES  fan  property of PolyhedralComplex  Input property 
INPUT_POLYTOPES_ACTION  fan  property of PolyhedralComplex  Symmetry 
INPUT_POLYTOPES_REPS  fan  property of PolyhedralComplex  Symmetry 
INPUT_RAY_LABELS  polytope  property of Cone  Visualization 
INPUT_RAY_LABELS  fan  property of PolyhedralFan  Visualization 
INPUT_RAYS  polytope  property of Cone  Input property 
INPUT_RAYS  fan  property of PolyhedralFan  Input property 
INPUT_RAYS_ACTION  group  property of Group  Symmetry 
INPUT_RAYS_GENERATORS  group  property of Action  Symmetry 
INPUT_RAYS_IN_FACETS  polytope  property of Cone  Geometry 
INPUT_RAYS_REPS  fan  property of PolyhedralFan  Input property 
INPUT_SETS  tropical  property of RationalCurve  Input property 
INPUT_STRING  tropical  property of RationalCurve  Input property 
insert(Set f)  common  method of FacetList  no category 
insert_leaves(RationalCurve curve, Vector<Int> nodes)  tropical  Functions  Abstract rational curves 
insert_rays(Cycle<Addition> F, Matrix<Rational> R)  tropical  Functions  Basic polyhedral operations 
insertMax(Set f)  common  method of FacetList  no category 
insertMin(Set f)  common  method of FacetList  no category 
Int  common  Property_types  Basic Types 
Integer  common  Property_types  Basic Types 
integer_hull(Polytope P)  polytope  Functions  Producing a polytope from polytopes 
integer_points_bbox(Polytope<Scalar> P)  polytope  Functions  Geometry 
INTEGER_VARIABLES  polytope  property of MixedIntegerLinearProgram  no category 
INTEGRAL  fulton  property of TDivisor  Algebraic Geometry 
interior_and_boundary_ridges(Polytope P)  polytope  Functions  Triangulations, subdivisions and volume 
INTERIOR_LATTICE_POINTS  polytope  property of Polytope  Lattice points in polytopes 
INTERIOR_RIDGE_SIMPLICES  polytope  property of Cone  Combinatorics 
INTERIOR_RIDGE_SIMPLICES  polytope  property of PointConfiguration  Combinatorics 
internal_activity()  matroid  Functions  Other 
intersect(Cycle X, Cycle Y)  tropical  Functions  Intersection theory 
intersect_check_transversality(Cycle X, Cycle Y, Bool ensure_transversality)  tropical  Functions  Intersection theory 
intersect_container(Cycle cycle, Cycle container, Bool forceLatticeComputation)  tropical  Functions  Basic polyhedral operations 
intersect_in_smooth_surface(Cycle<Addition> surface, Cycle<Addition> A, Cycle<Addition> B)  tropical  Functions  Intersection theory 
intersection(Matroid M)  matroid  Functions  Producing a matroid from matroids 
intersection(Cone C …)  polytope  Functions  Producing a polytope from polytopes 
intersection(PolyhedralFan F, Matrix H)  fan  Functions  Producing a fan 
INTERSECTION_COMPLEX  fan  property of PolyhedralFan  Topology 
intersection_extremals(Matrix<TropicalNumber> G, Vector<TropicalNumber> a, Vector<TropicalNumber> b)  tropical  Functions  Tropical operations 
INTERSECTION_FORM  topaz  property of SimplicialComplex  Topology 
IntersectionForm  topaz  Property_types  Topology 
inv(Matrix A)  common  Functions  Linear Algebra 
invalid_node(Int node)  common  method of Graph  no category 
invariant_polynomials(MatrixActionOnVectors a, Int d)  group  Functions  Symmetry 
INVERSE_RANK_MAP  graph  property of Lattice  Combinatorics 
InverseRankMap<SeqType>  graph  Property_types  Combinatorics 
IRREDUCIBLE_DECOMPOSITION  group  property of Action  Symmetry 
irreducible_decomposition<Scalar>(Vector<Scalar> character, Group G)  group  Functions  Symmetry 
is_B_nested(Set<Set> check_me, PowerSet B)  fan  Functions  Other 
IS_BALANCED  tropical  property of Cycle  Weights and lattices 
is_balanced(Cycle C)  tropical  Functions  Weights and lattices 
is_building_set(PowerSet check_me, Int n)  fan  Functions  Other 
is_contained(Matrix<TropicalNumber> apices, Array<Set<Int>> sectors)  tropical  Functions  Tropical operations 
is_empty  tropical  Functions  Degeneracy tests 
is_fan(Bool allow_translations)  tropical  method of Cycle  Basic polyhedral operations 
is_generalized_shelling(Array<Set> FaceList)  topaz  Functions  Other 
IS_GLOBALLY_AFFINE_LINEAR  tropical  property of Morphism  Defining morphisms and functions 
IS_GLOBALLY_DEFINED  tropical  property of RationalFunction  Defining morphisms and functions 
is_integral(Vector v)  common  Functions  Lattice Tools 
is_integral(Matrix m)  common  Functions  Lattice Tools 
IS_IRREDUCIBLE  tropical  property of Cycle  Weights and lattices 
is_isomorphic_to(Matroid M)  matroid  method of Matroid  Advanced properties 
is_modular_cut(Matroid M, Array<Set> C)  matroid  Functions  Other 
is_nested_matroid(Matroid M)  matroid  Functions  Advanced properties 
is_nonnegative(ARRAY data)  common  Functions  Utilities 
is_one(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 
isfinite(Scalar a)  common  Functions  Arithmetic 
isinf(Scalar a)  common  Functions  Arithmetic 
isomorphic(Cone P1, Cone P2)  polytope  Functions  Comparing 
isomorphic(SimplicialComplex complex1, SimplicialComplex complex2)  topaz  Functions  Comparing 
isomorphic(IncidenceMatrix IncidenceMatrix1, IncidenceMatrix IncidenceMatrix2)  graph  Functions  Comparing 
isomorphic(Graph graph1, Graph graph2)  graph  Functions  Comparing 
isotypic_basis(Group G, PermutationActionOnSets A, Int i)  group  Functions  Symmetry 
isotypic_basis(Group G, PermutationAction A, Int i)  group  Functions  Symmetry 
isotypic_basis<Scalar>(Group G, MatrixActionOnVectors<Scalar> A, Int i)  group  Functions  Symmetry 
ISOTYPIC_COMPONENTS  polytope  property of SymmetrizedCocircuitEquations  no category 
isotypic_configuration(Polytope P, Int i)  polytope  Functions  Symmetry 
isotypic_projector(Group G, PermutationAction A, Int i)  group  Functions  Symmetry 
isotypic_projector<Scalar>(Group G, MatrixActionOnVectors<Scalar> A, Int i)  group  Functions  Symmetry 
isotypic_supports(PermutationActionOnSets a, Array<Set> A)  group  Functions  Symmetry 
isotypic_supports(PermutationActionOnSets a, SparseMatrix M)  group  Functions  Symmetry 
iterated_barycentric_subdivision(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 
johnson_graph(Int n, Int k)  graph  Functions  Producing a graph 
johnson_solid(Int n)  polytope  Functions  Producing regular polytopes and their generalizations 
johnson_solid(String s)  polytope  Functions  Producing regular polytopes and their generalizations 
join_complexes(SimplicialComplex complex1, SimplicialComplex complex2)  topaz  Functions  Producing a new simplicial complex from others 
join_polytopes(Polytope P1, Polytope P2)  polytope  Functions  Producing a polytope from polytopes 
jreality(Visual::Object vis_obj …)  common  Functions  Visualization 
k1()  common  method of ExtGCD  no category 
k2()  common  method of ExtGCD  no category 
k_cyclic(Int n, Vector s)  polytope  Functions  Producing a polytope from scratch 
k_skeleton(SimplicialComplex complex, Int k)  topaz  Functions  Producing a new simplicial complex from others 
k_skeleton(GeometricSimplicialComplex complex, Int k)  topaz  Functions  Producing a new simplicial complex from others 
k_skeleton<Coord>(PolyhedralFan F, Int k)  fan  Functions  Producing a fan 
klee_minty_cube(Int d, Scalar e)  polytope  Functions  Producing a polytope from scratch 
klein_bottle()  topaz  Functions  Producing from scratch 
kneser_graph(Int n, Int k)  graph  Functions  Producing a graph 
KNOT  topaz  property of SimplicialComplex  Topology 
l8_matroid()  matroid  Functions  Producing a matroid from scratch 
labeled(Vector data, Array<String> elem_labels)  common  Functions  Formatting 
labeled_vertices(String label …)  polytope  method of Polytope  Geometry 
labeled_vertices(String label …)  topaz  method of SimplicialComplex  Combinatorics 
LABELS  matroid  property of Matroid  Other 
LABELS  polytope  property of VectorConfiguration  Visualization 
LABELS  fan  property of SubdivisionOfVectors  Visualization 
LAMINAR  matroid  property of Matroid  Advanced properties 
laplacian(Graph G)  graph  Functions  Combinatorics 
laplacian(Graph G)  graph  Functions  Combinatorics 
latex(Matrix data, Array<String> elem_labels)  common  Functions  Formatting 
LATTICE()  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_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 Polynomial  no category 
lc()  common  method of UniPolynomial  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(Graph G)  graph  Functions  Visualization 
left_companion()  common  method of SmithNormalForm  no category 
left_companion()  common  method of SingularValueDecomposition  no category 
lex_extension(Matroid M, Array<Set> C)  matroid  Functions  Producing a matroid from matroids 
lex_maximal  group  method of PermutationAction  Orbits 
lex_min_representative(Group G, Set S)  group  Functions  Symmetry 
lex_minimal  group  method of PermutationAction  Orbits 
lex_ordered(FacetList f)  common  Functions  Data Conversion 
lifted_pluecker(Matrix<TropicalNumber<Addition>> V)  tropical  Functions  Other 
LIFTING  fulton  property of RationalDivisorClassGroup  Algebraic Geometry 
lin_solve(Matrix A, Vector b)  common  Functions  Linear Algebra 
line_graph(Graph G)  graph  Functions  Combinatorics 
LINEALITY_DIM  polytope  property of Cone  Geometry 
LINEALITY_DIM  fan  property of PolyhedralFan  Geometry 
LINEALITY_SPACE  polytope  property of Cone  Geometry 
LINEALITY_SPACE  fan  property of PolyhedralFan  Geometry 
lineality_space(Matrix A)  common  Functions  Linear Algebra 
LINEALITY_SPACE_GENERATORS  group  property of Action  Symmetry 
LINEALITY_VALUES  tropical  property of Morphism  Defining morphisms and functions 
LINEALITY_VALUES  tropical  property of RationalFunction  Defining morphisms and functions 
LINEAR_OBJECTIVE  polytope  property of MixedIntegerLinearProgram  no category 
LINEAR_OBJECTIVE  polytope  property of LinearProgram  no category 
linear_space(ValuatedMatroid<Addition,Rational> A)  tropical  Functions  Tropical linear spaces 
LINEAR_SPAN  polytope  property of Cone  Geometry 
LINEAR_SPAN  polytope  property of VectorConfiguration  Geometry 
LINEAR_SPAN  fan  property of SubdivisionOfVectors  Geometry 
LINEAR_SPAN_NORMALS  fan  property of PolyhedralFan  Geometry 
linear_symmetries  polytope  Functions  Symmetry 
linear_symmetries(Matrix m)  polytope  Functions  Symmetry 
LinearProgram<Scalar>  polytope  Objects  Optimization 
lines_in_cubic(Polynomial<TropicalNumber<Addition>> p)  tropical  Functions  Lines in surfaces 
LinesInCubic<Addition>  tropical  Objects  no category 
link_complex(SimplicialComplex complex, Set<Int> face)  topaz  Functions  Producing a new simplicial complex from others 
list  core  method of Core::RuleChain  no category 
List<Element>  common  Property_types  Basic Types 
list_attachments  core  method of Core::Object  no category 
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::Object  no category 
list_new_properties  core  method of Core::RuleChain  no category 
list_properties(Bool deep)  core  method of Core::Object  no category 
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_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  common  Property_types  Basic Types 
long_and_winding(Int r)  polytope  Functions  Producing a polytope from scratch 
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_totally_dual_integral(Polytope P)  polytope  Functions  Producing a polytope from polytopes 
MANIFOLD  topaz  property of SimplicialComplex  Topology 
Map<Key, Value>  common  Property_types  Set Types 
mapping_polytope(Polytope P1, Polytope P2)  polytope  Functions  Producing a polytope from polytopes 
mapvars(Array<Int> indices, Int nvars)  common  method of Polynomial  no category 
MASSIVE_GKZ_VECTOR  polytope  property of PointConfiguration  Triangulation and volume 
MATCHING  topaz  property of SimplicialComplex  no category 
Matrix<Element, Sym>  common  Property_types  Algebraic Types 
MATRIX  tropical  property of Morphism  Defining morphisms and functions 
MATRIX_ACTION  polytope  property of Cone  Symmetry 
MATRIX_ACTION  polytope  property of PointConfiguration  Symmetry 
MATRIX_ACTION  polytope  property of Polytope  Symmetry 
MATRIX_ACTION  polytope  property of VectorConfiguration  Symmetry 
MATRIX_ACTION  fan  property of PolyhedralFan  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_BOUNDARY_SIMPLICES  polytope  property of Cone  Combinatorics 
MAX_BOUNDARY_SIMPLICES  polytope  property of PointConfiguration  Combinatorics 
MAX_CLIQUES()  topaz  method of SimplicialComplex  Combinatorics 
MAX_CLIQUES  graph  property of Graph  no category 
max_GC_rank(Int d)  polytope  Functions  Producing a polytope from scratch 
MAX_INTERIOR_SIMPLICES  polytope  property of Cone  Combinatorics 
MAX_INTERIOR_SIMPLICES  polytope  property of PointConfiguration  Combinatorics 
max_interior_simplices(Polytope P)  polytope  Functions  Triangulations, subdivisions and volume 
max_interior_simplices(PointConfiguration P)  polytope  Functions  Triangulations, subdivisions and volume 
max_metric(Int n)  fan  Functions  Finite metric spaces 
MAXIMAL_AT_CODIM_ONE  tropical  property of Cycle  Combinatorics 
MAXIMAL_CELLS  fan  property of SubdivisionOfVectors  Combinatorics 
maximal_chains_of_lattice(Lattice F)  graph  Functions  Combinatorics 
MAXIMAL_CONE_LABELS  fan  property of PolyhedralFan  Visualization 
MAXIMAL_CONES  fan  property of PolyhedralFan  Combinatorics 
MAXIMAL_CONES_ACTION  group  property of Group  Symmetry 
MAXIMAL_CONES_ACTION  fan  property of PolyhedralFan  Symmetry 
MAXIMAL_CONES_COMBINATORIAL_DIMS  fan  property of PolyhedralFan  Combinatorics 
MAXIMAL_CONES_FACETS  fan  property of PolyhedralFan  Geometry 
MAXIMAL_CONES_GENERATORS  group  property of Action  Symmetry 
MAXIMAL_CONES_IN_ORBITS  fan  property of PolyhedralFan  Symmetry 
MAXIMAL_CONES_INCIDENCES  fan  property of PolyhedralFan  Combinatorics 
MAXIMAL_CONES_LINEAR_SPAN_NORMALS  fan  property of PolyhedralFan  Geometry 
MAXIMAL_CONES_ORBIT_SIZES  fan  property of PolyhedralFan  Symmetry 
MAXIMAL_CONES_REPS  fan  property of PolyhedralFan  Symmetry 
MAXIMAL_CONES_REPS_DIMS  fan  property of PolyhedralFan  Symmetry 
MAXIMAL_CONES_REPS_FACETS  fan  property of PolyhedralFan  Symmetry 
MAXIMAL_CONES_REPS_LINEAR_SPAN_NORMALS  fan  property of PolyhedralFan  Symmetry 
MAXIMAL_CONES_THRU_RAYS  fan  property of PolyhedralFan  Combinatorics 
MAXIMAL_COVECTOR_CELLS  tropical  property of Polytope  Combinatorics 
MAXIMAL_COVECTORS  tropical  property of Polytope  Combinatorics 
MAXIMAL_FACE  polytope  property of LinearProgram  no category 
MAXIMAL_POLYTOPES  fan  property of PolyhedralComplex  Combinatorics 
MAXIMAL_POLYTOPES_ACTION  fan  property of PolyhedralComplex  Symmetry 
MAXIMAL_POLYTOPES_AFFINE_HULL_NORMALS  fan  property of PolyhedralComplex  Geometry 
MAXIMAL_POLYTOPES_COMBINATORIAL_DIMS  fan  property of PolyhedralComplex  Combinatorics 
MAXIMAL_POLYTOPES_FACETS  fan  property of PolyhedralComplex  Geometry 
MAXIMAL_POLYTOPES_GENERATORS  fan  property of PolyhedralComplex  Symmetry 
MAXIMAL_POLYTOPES_IN_ORBITS  fan  property of PolyhedralComplex  Symmetry 
MAXIMAL_POLYTOPES_INCIDENCES  fan  property of PolyhedralComplex  Combinatorics 
MAXIMAL_POLYTOPES_ORBIT_SIZES  fan  property of PolyhedralComplex  Symmetry 
MAXIMAL_POLYTOPES_REPS  fan  property of PolyhedralComplex  Symmetry 
MAXIMAL_POLYTOPES_REPS_AFFINE_SPAN_NORMALS  fan  property of PolyhedralComplex  Symmetry 
MAXIMAL_POLYTOPES_REPS_DIMS  fan  property of PolyhedralComplex  Symmetry 
MAXIMAL_POLYTOPES_REPS_FACETS  fan  property of PolyhedralComplex  Symmetry 
MAXIMAL_POLYTOPES_THRU_VERTICES  fan  property of PolyhedralComplex  Combinatorics 
MAXIMAL_SOLUTION  polytope  property of MixedIntegerLinearProgram  no category 
MAXIMAL_TRANSVERSAL_PRESENTATION  matroid  property of Matroid  Advanced properties 
MAXIMAL_VALUE  polytope  property of MixedIntegerLinearProgram  no category 
MAXIMAL_VALUE  polytope  property of LinearProgram  no category 
MAXIMAL_VERTEX  polytope  property of LinearProgram  no category 
maximum(ARRAY array)  common  Functions  Utilities 
median(ARRAY array)  common  Functions  Utilities 
metapost(Visual::Object vis_obj …)  graph  Functions  Visualization 
metric_extended_tight_span(Matrix<Rational> M)  fan  Functions  Finite metric spaces 
metric_tight_span(Matrix<Rational> M)  fan  Functions  Finite metric spaces 
metric_vector  tropical  method of RationalCurve  Conversion 
MILP  polytope  property of Polytope  Optimization 
Min  common  Property_types  Arithmetic 
MIN_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_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 MixedIntegerLinearProgram  no category 
MINIMAL_VALUE  polytope  property of LinearProgram  no category 
MINIMAL_VERTEX  polytope  property of LinearProgram  no category 
MINIMAL_VERTEX_ANGLE  polytope  property of Polytope  Geometry 
minimal_vertex_angle(Polytope P)  polytope  Functions  Geometry 
minimum(ARRAY array)  common  Functions  Utilities 
MINKOWSKI_CONE  polytope  property of Polytope  Geometry 
MINKOWSKI_CONE_COEFF(Vector<Rational> coeff)  polytope  method of Polytope  Geometry 
MINKOWSKI_CONE_POINT(Vector<Rational> point)  polytope  method of Polytope  Geometry 
minkowski_sum(PointConfiguration P1, PointConfiguration P2)  polytope  Functions  Producing a point configuration 
minkowski_sum(Scalar lambda, PointConfiguration P1, Scalar mu, PointConfiguration P2)  polytope  Functions  Producing a point configuration 
minkowski_sum(Polytope P1, Polytope P2)  polytope  Functions  Producing a polytope from polytopes 
minkowski_sum(Scalar lambda, Polytope P1, Scalar mu, Polytope P2)  polytope  Functions  Producing a polytope from polytopes 
minkowski_sum(TropicalNumber<Addition,Scalar> lambda, Polytope<Addition,Scalar> P, TropicalNumber<Addition,Scalar> mu, Polytope<Addition,Scalar> Q)  tropical  Functions  Producing a tropical polytope 
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 Rational  no category 
minus_inf  common  method of Integer  no category 
minus_inf  common  method of Float  no category 
MIXED_GRAPH  topaz  property of SimplicialComplex  Visualization 
mixed_graph(SimplicialComplex complex)  topaz  Functions  Other 
mixed_integer_hull(Polytope P, Array<Int> int_coords)  polytope  Functions  Producing a polytope from polytopes 
mixed_subdivision(Polytope P_0, Polytope P_1, Array<Set> VIF, Scalar t_0, Scalar t_1)  fan  Functions  Producing a polyhedral complex 
mixed_subdivision(Int m, Polytope C, Array<Set> a)  fan  Functions  Producing a polyhedral complex 
mixed_subdivision(Array<Polytope> A, Array<Set> VIF)  fan  Functions  Producing a polyhedral complex 
mixed_volume(Polytope<Scalar> P1, Polytope<Scalar> P2, Polytope<Scalar> Pn)  polytope  Functions  Triangulations, subdivisions and volume 
MixedIntegerLinearProgram<Scalar>  polytope  Objects  Optimization 
MODULE_GENERATORS  fulton  property of NormalToricVariety  Combinatorics 
MOEBIUS_STRIP_EDGES  polytope  property of Polytope  Combinatorics 
MOEBIUS_STRIP_QUADS  polytope  property of Polytope  Combinatorics 
MongoClient  common  Property_types  Database 
MONOID_GRADING  polytope  property of Cone  Lattice points in cones 
MONOMIAL  ideal  property of Ideal  Commutative algebra 
monomial(Int var_index, Int n_vars)  common  method of Polynomial  no category 
monomial  common  method of UniPolynomial  no category 
monomials<Coefficient, Exponent>(Int n)  common  Functions  Arithmetic 
MONOMIALS  tropical  property of Hypersurface  no category 
monomials_as_matrix()  common  method of Polynomial  no category 
monomials_as_vector()  common  method of UniPolynomial  no category 
moore_penrose_inverse(Matrix M)  common  Functions  Linear Algebra 
MORI_CONE  fulton  property of NormalToricVariety  Algebraic Geometry 
Morphism<Addition>  tropical  Objects  no category 
morphism_from_affine<Addition>(Matrix<Rational> A, Vector<Rational> v, Int domain_chart, Int target_chart)  tropical  Functions  Affine and projective coordinates 
MORSE_MATCHING()  topaz  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 
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  matroid  property of Matroid  Enumerative properties 
n_automorphisms(Graph graph)  graph  Functions  Comparing 
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  matroid  property of Matroid  Advanced properties 
N_CONNECTED_COMPONENTS()  topaz  method of SimplicialComplex  Topology 
N_CONNECTED_COMPONENTS  graph  property of Graph  no category 
N_CRITICAL_FACES  topaz  property of MorseMatching  no category 
N_CYCLIC_FLATS  matroid  property of Matroid  Enumerative properties 
N_EDGES  polytope  property of Cone  Combinatorics 
N_EDGES  graph  property of Graph  no category 
N_ELEMENTS  matroid  property of Matroid  Enumerative properties 
N_ELEMENTS  tropical  property of MatroidRingCycle  Matroid data 
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_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_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  polytope  property of Cone  Geometry 
N_INPUT_RAYS  fan  property of PolyhedralFan  Geometry 
N_INPUT_RAYS_GENERATORS  group  property of Action  Symmetry 
N_INTERIOR_LATTICE_POINTS  polytope  property of Polytope  Lattice points in polytopes 
N_ISOLATED  tropical  property of LinesInCubic  Counts of lines 
N_LATTICE_POINTS  polytope  property of Polytope  Lattice points in polytopes 
N_LATTICE_POINTS_IN_DILATION(Int n)  polytope  method of Polytope  Lattice points in cones 
N_LEAVES  tropical  property of RationalCurve  Combinatorics 
N_LINEALITY_SPACE_GENERATORS  group  property of Action  Symmetry 
N_LOOPS  matroid  property of Matroid  Enumerative properties 
N_MATROID_HYPERPLANES  matroid  property of Matroid  Enumerative properties 
N_MAX_BOUNDARY_SIMPLICES  polytope  property of PointConfiguration  Combinatorics 
N_MAX_INTERIOR_SIMPLICES  polytope  property of PointConfiguration  Combinatorics 
N_MAXIMAL_CELLS  fan  property of SubdivisionOfVectors  Combinatorics 
N_MAXIMAL_CONE_ORBITS  fan  property of PolyhedralFan  Symmetry 
N_MAXIMAL_CONES  fan  property of PolyhedralFan  Combinatorics 
N_MAXIMAL_CONES_GENERATORS  group  property of Action  Symmetry 
N_MAXIMAL_POLYTOPES  fan  property of PolyhedralComplex  Combinatorics 
N_MAXIMAL_POLYTOPES_ORBITS  fan  property of PolyhedralComplex  Symmetry 
N_MAXIMAL_TORUS_ORBITS  fulton  property of NormalToricVariety  Basic properties 
N_MINIMAL_NON_FACES  topaz  property of SimplicialComplex  Combinatorics 
N_NESTED_SUMMANDS  tropical  property of MatroidRingCycle  Matroid data 
N_NODES  graph  property of Graph  no category 
N_ORBIT_REPRESENTATIVES  group  property of Action  Symmetry 
N_ORBITS  group  property of Action  Symmetry 
N_POINTS  polytope  property of PointConfiguration  Geometry 
N_POINTS  polytope  property of Polytope  Geometry 
N_POINTS  fan  property of PolyhedralComplex  Geometry 
N_POINTS  fan  property of SubdivisionOfPoints  Geometry 
N_POINTS_GENERATORS  polytope  property of Polytope  no category 
N_POINTS_GENERATORS  fan  property of PolyhedralComplex  Symmetry 
N_POINTS_GENERATORS  fan  property of PolyhedralComplex  Symmetry 
N_POLYTOPES  fan  property of PolyhedralComplex  Combinatorics 
n_poset_homomorphisms(Graph<Directed> P, Graph<Directed> Q)  topaz  Functions  Combinatorics 
N_RAY_FACET_INC  polytope  property of Cone  Combinatorics 
N_RAY_ORBITS  fan  property of PolyhedralFan  Symmetry 
N_RAYS  polytope  property of Cone  Combinatorics 
N_RAYS  fan  property of PolyhedralFan  Geometry 
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  polytope  property of VoronoiPolyhedron  no category 
N_STRONG_GENERATORS  group  property of PermutationAction  no category 
N_SYMMETRIES  fan  property of PolyhedralFan  Symmetry 
N_UNIMODULAR  topaz  property of GeometricSimplicialComplex  no category 
N_VARIABLES  ideal  property of Ideal  Commutative algebra 
n_vars()  common  method of Polynomial  no category 
n_vars  common  method of UniPolynomial  no category 
N_VECTORS  polytope  property of VectorConfiguration  Geometry 
N_VECTORS  fan  property of SubdivisionOfVectors  Geometry 
N_VERTEX_FACET_INC  polytope  property of Polytope  Combinatorics 
N_VERTICES  polytope  property of Polytope  Combinatorics 
N_VERTICES  topaz  property of SimplicialComplex  Combinatorics 
N_VERTICES  fan  property of PolyhedralComplex  Geometry 
n_vertices()  common  method of FacetList  no category 
N_VERTICES_GENERATORS  polytope  property of Polytope  no category 
N_VERTICES_GENERATORS  fan  property of PolyhedralComplex  Symmetry 
N_VERTICES_GENERATORS  fan  property of PolyhedralComplex  Symmetry 
N_VERTICES_ORBITS  fan  property of PolyhedralComplex  Symmetry 
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>(Graph graph)  common  Functions  Graph Operations 
node_exists(Int node)  common  method of Graph  no category 
NODE_IN_DEGREES  graph  property of Graph  no category 
NODE_LABELS  graph  property of Graph  no category 
NODE_OUT_DEGREES  graph  property of Graph  no category 
node_out_of_range(Int node)  common  method of Graph  no category 
NodeHashMap<Dir, Element>  common  Property_types  Graph Types 
NodeMap<Dir, Element>  common  Property_types  Graph Types 
nodes()  common  method of Graph  no category 
nodes(Graph graph)  common  Functions  Graph Operations 
NODES_BY_LEAVES  tropical  property of RationalCurve  Combinatorics 
NODES_BY_SETS  tropical  property of RationalCurve  Combinatorics 
nodes_of_dim(Int d)  polytope  method of Cone  Combinatorics 
nodes_of_dim  topaz  method of SimplicialComplex  no category 
nodes_of_dim(Int d)  fan  method of PolyhedralFan  Combinatorics 
nodes_of_dim  tropical  method of CovectorLattice  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_dim_range(Int d1, Int d1)  fan  method of PolyhedralFan  Combinatorics 
nodes_of_dim_range  tropical  method of CovectorLattice  Combinatorics 
nodes_of_rank(Int r)  graph  method of Lattice  Combinatorics 
nodes_of_rank(Int r)  graph  method of InverseRankMap  Combinatorics 
nodes_of_rank_range(Int r1, Int r2)  graph  method of Lattice  Combinatorics 
nodes_of_rank_range(Int r1, Int r2)  graph  method of InverseRankMap  Combinatorics 
NON_BASES  matroid  property of Matroid  Axiom systems 
non_fano_matroid()  matroid  Functions  Producing a matroid from scratch 
non_p8_matroid()  matroid  Functions  Producing a matroid from scratch 
non_pappus_matroid()  matroid  Functions  Producing a matroid from scratch 
NON_SATURATED  polytope  property of SlackIdeal  no category 
non_vamos_matroid()  matroid  Functions  Producing a matroid from scratch 
NON_VERTICES  polytope  property of PointConfiguration  Geometry 
Nonsequential  graph  Property_types  Artificial 
NonSymmetric  common  Property_types  Artificial 
NOP_GRAPH  polytope  property of Polytope  no category 
norm(Vector<TropicalNumber<Addition,Scalar>> v)  tropical  Functions  Tropical operations 
NORMAL  polytope  property of Polytope  Lattice points in cones 
normal_cone(PointConfiguration p, Set<Int> F)  polytope  Functions  Producing a cone 
normal_cone(Cone p, Set<Int> F)  polytope  Functions  Producing a cone 
normal_fan<Coord>(Polytope p)  fan  Functions  Producing a fan 
normaliz_compute(Cone C)  polytope  Functions  Geometry 
normalized(Matrix<Float> A)  common  Functions  Linear Algebra 
NormalToricVariety  fulton  Objects  no category 
null_space(Matrix A)  common  Functions  Linear Algebra 
null_space(Vector b)  common  Functions  Linear Algebra 
null_space_integer(Matrix A)  common  Functions  Linear Algebra 
numbered(Vector data)  common  Functions  Formatting 
numerator(Rational a)  common  Functions  Arithmetic 
numerator(RationalFunction f)  common  Functions  Arithmetic 
numerator(PuiseuxFraction f)  common  Functions  Arithmetic 
NUMERATOR  tropical  property of RationalFunction  Defining morphisms and functions 
o7_matroid()  matroid  Functions  Producing a matroid from scratch 
obliterate_extension(String path)  core  Functions  Interactive 
occluding_cone(Cone P, Set F)  polytope  Functions  Geometry 
octahedron()  polytope  Functions  Producing regular polytopes and their generalizations 
ODD_SUBCOMPLEX  topaz  property of SimplicialComplex  Combinatorics 
on_cols  group  Property_types  no category 
on_container  group  Property_types  no category 
on_elements  group  Property_types  no category 
on_nonhomog_cols  group  Property_types  no category 
on_nonhomog_container  group  Property_types  no category 
on_rows  group  Property_types  no category 
ONE_RAY  polytope  property of Cone  Geometry 
ONE_VERTEX  polytope  property of Polytope  Geometry 
ones_matrix<Element>(Int m, Int n)  common  Functions  Linear Algebra 
ones_vector<Element>(Int d)  common  Functions  Linear Algebra 
optimal_permutations(Matrix<TropicalNumber> matrix)  tropical  Functions  Tropical operations 
ORBIFOLD  fulton  property of NormalToricVariety  Basic properties 
orbit<action_type>(Array G, Core::Object O)  group  Functions  Orbits 
orbit(Group G, Any C)  group  Functions  Orbits 
orbit<Scalar>(Array<Matrix<Scalar>> G, Vector<Scalar> V)  group  Functions  Orbits 
orbit_complex(PolyhedralComplex input_complex, Array<Array<Int>> gens)  fan  Functions  Symmetry 
orbit_complex(PolyhedralFan input_fan, PermutationAction a)  fan  Functions  Symmetry 
orbit_fan(PolyhedralFan input_fan, Array<Array<Int>> gens)  fan  Functions  Symmetry 
orbit_fan<Scalar>(PolyhedralFan input_fan, Array<Matrix<Scalar>> gens)  fan  Functions  Symmetry 
orbit_permlib(Group G, Set S)  group  Functions  Orbits 
orbit_permlib(Group G, Set<Set> S)  group  Functions  Orbits 
orbit_polytope(Vector input_point, PermutationAction a)  polytope  Functions  Symmetry 
orbit_polytope(Matrix input_points, PermutationAction a)  polytope  Functions  Symmetry 
orbit_polytope(Vector input_point, Group g)  polytope  Functions  Symmetry 
orbit_polytope(Matrix input_points, Group g)  polytope  Functions  Symmetry 
orbit_polytope(Matrix input_points, Array<Array<Int>> gens)  polytope  Functions  Symmetry 
orbit_polytope<Scalar>(Vector input_point, MatrixActionOnVectors a)  polytope  Functions  Symmetry 
orbit_polytope<Scalar>(Matrix<Scalar> input_points, MatrixActionOnVectors<Scalar> a)  polytope  Functions  Symmetry 
ORBIT_REPRESENTATIVE_LABELS  group  property of Action  Symmetry 
ORBIT_REPRESENTATIVES  group  property of Action  Symmetry 
orbit_representatives(Array<GeneratorType> G)  group  Functions  Orbits 
orbit_reps_and_sizes<Container>(Array<Array<Int>> generators, Container S)  group  Functions  Symmetry 
ORBIT_SIZES  group  property of Action  Symmetry 
ORBITS  group  property of Action  Symmetry 
ORBITS_F_VECTOR  fan  property of PolyhedralFan  Symmetry 
orbits_in_orbit_order(PermutationAction a, Matrix M)  group  Functions  Orbits 
orbits_of_action(PermutationAction a)  group  Functions  Orbits 
orbits_of_coordinate_action(PermutationAction a, Matrix<Scalar> M)  group  Functions  Orbits 
orbits_of_induced_action(PermutationAction a, IncidenceMatrix I)  group  Functions  Orbits 
ORDER  group  property of Group  Symmetry 
ORDER_MATRIX  ideal  property of Groebner  Input properties 
ORDER_NAME  ideal  property of Groebner  Input properties 
ORDER_VECTOR  ideal  property of Groebner  Input properties 
ORIENTATION  topaz  property of SimplicialComplex  Topology 
orientation()  common  method of TropicalNumber  no category 
orientation  common  method of Max  no category 
orientation  common  method of Min  no category 
ORIENTED_PSEUDO_MANIFOLD  topaz  property of SimplicialComplex  Topology 
ORIGIN  polytope  property of AffineLattice  no category 
ORTH_LINEALITY_SPACE  fan  property of PolyhedralFan  Geometry 
orthant_subdivision<Addition>(Vector<Rational> point, Int chart, Integer weight)  tropical  Functions  Creation functions for specific cycles 
orthantify(Polytope P, Int v)  polytope  Functions  Transformations 
ortho_project(Polytope p)  polytope  Functions  Symmetry 
orthonormal_col_basis(Matrix M)  polytope  Functions  Transformations 
orthonormal_row_basis(Matrix M)  polytope  Functions  Transformations 
out_adjacent_nodes(Int node)  common  method of Graph  no category 
out_degree(Int node)  common  method of Graph  no category 
out_edges(Int node)  common  method of Graph  no category 
OUTER_DESCRIPTION()  polytope  method of Polytope  Geometry 
outitudes(Array<Array<Int>> dcel_data)  topaz  Functions  Other 
outitudes(String surface)  topaz  Functions  Other 
p()  common  method of ExtGCD  no category 
p7_matroid()  matroid  Functions  Producing a matroid from scratch 
p8_matroid()  matroid  Functions  Producing a matroid from scratch 
P_RESOLUTION  fulton  property of VersalComponent  Combinatorics 
Pair<First, Second>  common  Property_types  Basic Types 
pappus_matroid()  matroid  Functions  Producing a matroid from scratch 
parallel_extension(Matroid m_1, Int e_1, Matroid m_2, Int e_2)  matroid  Functions  Producing a matroid from matroids 
parallel_extension(Matroid m, Int e)  matroid  Functions  Producing a matroid from matroids 
partition_representatives(Array<Array<Int>> gens, Set<Int> S)  group  Functions  Symmetry 
PATCHWORK  tropical  property of Hypersurface  Combinatorics 
Patchwork  tropical  Objects  no category 
path_graph(Int n)  graph  Functions  Producing a graph 
PAVING  matroid  property of Matroid  Advanced properties 
PENNER_COORDINATES  topaz  property of HyperbolicSurface  no category 
perles_irrational_8_polytope()  polytope  Functions  Producing a polytope from scratch 
PermBase  common  Objects  Combinatorics 
permutahedron(Int d)  polytope  Functions  Producing a polytope from scratch 
PERMUTATION  common  property of PermBase  no category 
PERMUTATION_ACTION  group  property of Group  Symmetry 
permutation_cycle_lengths(Array<Int> p)  common  Functions  Combinatorics 
permutation_cycles(Array<Int> p)  common  Functions  Combinatorics 
permutation_matrix<Scalar>(Array<Int> p)  common  Functions  Combinatorics 
permutation_order(Array<Int> p)  common  Functions  Combinatorics 
permutation_sign(Array<Int> p)  common  Functions  Combinatorics 
PERMUTATION_TO_ORBIT_ORDER  group  property of Action  Symmetry 
PermutationAction  group  Objects  no category 
PermutationActionOnSets  group  Objects  no category 
permute_inv_nodes  common  method of Graph  no category 
permute_nodes  common  method of Graph  no category 
permuted  common  method of Plucker  no category 
persistent_homology(Filtration<Matrix<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 
pl_homeomorphic(SimplicialComplex complex1, SimplicialComplex complex2)  topaz  Functions  Comparing 
placing_triangulation(Matrix Points)  polytope  Functions  Triangulations, subdivisions and volume 
planar_net(Polytope p)  fan  Functions  Producing a fan 
PlanarNet<Scalar>  fan  Objects  Geometry 
platonic_solid(String s)  polytope  Functions  Producing regular polytopes and their generalizations 
Plucker<Scalar>  common  Property_types  Algebraic Types 
pluecker(Matrix V)  common  Functions  Linear Algebra 
pluecker_ideal(Int d, Int n)  ideal  Functions  Producing an ideal from scratch 
point_collection<Addition>(Matrix<Rational> points, Vector<Integer> weights)  tropical  Functions  Creation functions for specific cycles 
point_functions<Addition>(Vector<Rational> A)  tropical  Functions  Intersection theory 
POINT_LABELS  polytope  property of PointConfiguration  Visualization 
POINT_LABELS  polytope  property of Polytope  Visualization 
POINT_LABELS  fan  property of PolyhedralComplex  Visualization 
POINT_LABELS  fan  property of SubdivisionOfPoints  Visualization 
PointConfiguration<Scalar>  polytope  Objects  no category 
POINTED  polytope  property of Cone  Geometry 
POINTED  polytope  property of Polytope  Geometry 
POINTED  fan  property of PolyhedralFan  Geometry 
pointed_part(Polytope P)  polytope  Functions  Producing a polytope from polytopes 
POINTS  polytope  property of PointConfiguration  Input property 
POINTS  polytope  property of Polytope  Input property 
POINTS  fan  property of PolyhedralComplex  Input property 
POINTS  fan  property of SubdivisionOfPoints  Geometry 
POINTS  tropical  property of Polytope  Geometry 
points2hypersurface(Matrix<TropicalNumber<Addition>> points)  tropical  Functions  Producing a tropical hypersurface 
points2metric(Matrix points)  polytope  Functions  Triangulations, subdivisions and volume 
POINTS_ACTION  polytope  property of PointConfiguration  Symmetry 
POINTS_ACTION  polytope  property of Polytope  Symmetry 
POINTS_ACTION  fan  property of PolyhedralComplex  Symmetry 
POINTS_GENERATORS  polytope  property of Polytope  no category 
POINTS_GENERATORS  fan  property of PolyhedralComplex  Symmetry 
POINTS_GENERATORS  fan  property of PolyhedralComplex  Symmetry 
POINTS_IN_FACETS  polytope  property of Polytope  Geometry 
points_in_pseudovertices(Matrix<TropicalNumber<Addition,Scalar>> points, Matrix<Scalar> pseudovertices)  tropical  Functions  Other 
POINTS_ORBITS  polytope  property of PointConfiguration  Symmetry 
POINTS_REPS  fan  property of PolyhedralComplex  Symmetry 
POLAR_SMOOTH  polytope  property of Polytope  Lattice points in cones 
polarize(Cone C)  polytope  Functions  Transformations 
polarized_toric_variety(Polytope<Rational> P, String name)  fulton  Functions  Producing a normal toric variety 
poly2lp(Polytope P, LinearProgram LP, Bool maximize, String file)  polytope  Functions  Optimization 
poly2metric(Polytope P)  polytope  Functions  Triangulations, subdivisions and volume 
poly2porta(Polytope<Rational> p, String file)  polytope  Functions  Optimization 
POLYHEDRAL_COMPLEX  fan  property of SubdivisionOfPoints  Geometry 
PolyhedralComplex<Scalar>  fan  Objects  Geometry 
PolyhedralFan<Scalar>  fan  Objects  Geometry 
Polynomial<Coefficient, Exponent>  common  Property_types  Algebraic Types 
POLYNOMIAL  tropical  property of LinesInCubic  Defining properties 
POLYNOMIAL  tropical  property of Hypersurface  no category 
POLYTOPAL_SUBDIVISION(Int index)  polytope  method of Visual::PointConfiguration  no category 
POLYTOPAL_SUBDIVISION  polytope  property of PointConfiguration  Triangulation and volume 
POLYTOPAL_SUBDIVISION  polytope  property of Polytope  Triangulation and volume 
POLYTOPE  matroid  property of Matroid  Advanced properties 
Polytope<Scalar>  polytope  Objects  no category 
POLYTOPE  fan  property of PlanarNet  Geometry 
polytope(Int i)  fan  method of PolyhedralComplex  Geometry 
Polytope<Addition, Scalar>  tropical  Objects  no category 
POLYTOPE_COVECTOR_DECOMPOSITION  tropical  property of Polytope  Combinatorics 
POLYTOPE_IN_STD_BASIS(Polytope<Rational> P)  polytope  method of Polytope  Lattice points in cones 
POLYTOPE_MAXIMAL_COVECTOR_CELLS  tropical  property of Polytope  Combinatorics 
POLYTOPE_MAXIMAL_COVECTORS  tropical  property of Polytope  Combinatorics 
polytope_of_divisor_class  fulton  Functions  Combinatorics 
polytope_subdivision_as_complex(Int chart)  tropical  method of Polytope  Geometry 
POLYTOPES  fan  property of PolyhedralComplex  Combinatorics 
POLYTOPES_ORBIT_SIZES  fan  property of PolyhedralComplex  Symmetry 
POLYTOPES_REPS  fan  property of PolyhedralComplex  Symmetry 
porta2poly(String file)  polytope  Functions  Optimization 
poset_by_inclusion(Array<T> P)  topaz  Functions  Other 
poset_homomorphisms(Graph<Directed> P, Graph<Directed> Q)  topaz  Functions  Producing a new simplicial complex from others 
POSITIVE  polytope  property of Cone  Geometry 
POSITIVE  polytope  property of VectorConfiguration  Geometry 
positive_circuits(Polytope or, Set<Int> S)  polytope  Functions  Triangulations, subdivisions and volume 
positroid_from_decorated_permutation(Array<Int> perm, Set<Int> loops)  matroid  Functions  Producing a matroid from other objects 
postscript(Visual::Object vis_obj …)  common  Functions  Visualization 
povray(Visual::Object vis_obj …)  common  Functions  Visualization 
POWER  tropical  property of RationalFunction  Defining morphisms and functions 
PowerSet<Element>  common  Property_types  Set Types 
prefer(String label_expression)  core  Functions  Basic 
prefer_now(String label_expression)  core  Functions  Basic 
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(Matrix m)  common  method of Polynomial  no category 
print_ordered(Exponent x)  common  method of UniPolynomial  no category 
prism(Polytope P, Scalar z1, Scalar z2)  polytope  Functions  Producing a polytope from polytopes 
product(Polytope P1, Polytope P2)  polytope  Functions  Producing a polytope from polytopes 
product(PolyhedralFan F1, PolyhedralFan F2)  fan  Functions  Producing a fan 
PROJ_DICTIONARY  topaz  property of SimplicialComplex  Combinatorics 
PROJ_ORBITS  topaz  property of SimplicialComplex  Combinatorics 
project()  common  method of Polynomial  no category 
project_full<Scalar>(VectorConfiguration P)  polytope  Functions  Producing a vector configuration 
project_full(Cone P)  polytope  Functions  Producing a polytope from polytopes 
project_full(PolyhedralFan P)  fan  Functions  Producing a fan 
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 points, Matrix orthogonal)  common  Functions  Linear Algebra 
PROJECTED_EQUATIONS  polytope  property of SymmetrizedCocircuitEquations  no category 
projection<Scalar>(VectorConfiguration P, Array<Int> indices)  polytope  Functions  Producing a vector configuration 
projection(Cone P, Array<Int> indices)  polytope  Functions  Producing a polytope from polytopes 
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<Scalar>(Array<VectorConfiguration> P_Array)  polytope  Functions  Producing a vector configuration 
projection_preimage(Array<Cone> P_Array)  polytope  Functions  Producing a polytope from polytopes 
PROJECTIVE  fulton  property of NormalToricVariety  Algebraic Geometry 
PROJECTIVE_AMBIENT_DIM  tropical  property of Cycle  Affine and projective coordinates 
PROJECTIVE_AMBIENT_DIM  tropical  property of Polytope  Geometry 
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_space(Int d)  fulton  Functions  Producing a normal toric variety 
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::Object  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, RationalFunction r)  tropical  Functions  Intersection theory 
PURE  topaz  property of SimplicialComplex  Combinatorics 
PURE  fan  property of PolyhedralFan  Combinatorics 
pyramid(Polytope P, Scalar z)  polytope  Functions  Producing a polytope from polytopes 
PYRAMID_LATTICE  fulton  property of VersalComponent  Combinatorics 
Q  fulton  property of CyclicQuotient  Input properties 
q()  common  method of ExtGCD  no category 
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 
