exports.jl

# Entries are sorted with uppercase before lowercase. To resort it,
# execute:  LC_COLLATE=C sort < src/exports.jl > dummy ; mv dummy src/exports.jl
export *
export @check
export @free_group
export @pbw_relations
export @perm
export @permutation_group
export @register_serialization_type
export @tropical
export ANTIC
export AbsAffineAlgebraicSet
export AbsAffineCurve
export AbsAffineRationalPoint
export AbsAffineScheme
export AbsAffineSchemeMor
export AbsAffineVariety
export AbsAlgebraicCycle
export AbsCoveredCurve
export AbsCoveredScheme
export AbsCoveredSchemeMorphism
export AbsCoveredVariety
export AbsGluing
export AbsLocalizedIdeal
export AbsLocalizedRing
export AbsLocalizedRingElem
export AbsLocalizedRingHom
export AbsMultSet
export AbsPreSheaf
export AbsProjectiveAlgebraicSet
export AbsProjectiveCurve
export AbsProjectiveScheme
export AbsProjectiveSchemeMorphism
export AbsProjectiveVariety
export AbsRationalMap
export AbstractAlgebra
export AffineAlgebraicSet
export AffineHalfspace
export AffineHyperplane
export AffineNormalToricVariety
export AffinePlaneCurve
export AffineScheme
export AffineSchemeOpenSubscheme
export AffineSchemeOpenSubschemeMor
export AffineSchemeOpenSubschemeRing
export AffineSchemeOpenSubschemeRingElem
export AffineVariety
export AlgebraicCycle
export AutomorphismGroup
export AutomorphismGroupElem
export BettiTable
export BlowupMorphism
export BorcherdsCtx
export CartierDivisor
export ClosedEmbedding
export ClosedSubvarietyOfToricVariety
export CohomologyClass
export Composition
export Cone
export CoveredScheme
export CoveredSchemeMorphism
export Covering
export CoveringMorphism
export CyclicQuotientSingularity
export DirectProductGroup
export DirectSumSheaf
export Directed
export DualRootSpaceElem
export Edge
export EffectiveCartierDivisor
export EllipticSurface
export EmptyScheme
export FPGroup
export FPGroupElem
export FreeMod
export FreeModElem
export FreeModElem_dec
export FreeMod_dec
export FreeModuleHom
export FreeModuleHom_dec
export FreeResolution
export GAP
export GAPGroupConjClass
export GAPGroupElem
export GAPGroupHomomorphism
export GL
export GO
export GSet
export GU
export GapObj
export Gluing
export Graph
export GroupConjClass
export GroupCoset
export GroupDoubleCoset
export Halfspace
export Hecke
export HilbertData
export Hyperplane
export IdealSheaf
export IncidenceMatrix
export InfiniteDimensionError
export K3Chamber
export K3_surface_automorphism_group
export LazyPoly
export LazyPolyRing
export LinearHalfspace
export LinearHyperplane
export LinearProgram, linear_program
export LinearSystem
export MPolyDecRing
export MPolyDecRingElem
export MPolyIdeal
export MPolyQuoIdeal
export MPolyQuoRing
export MPolyQuoRingElem
export MPolyRingElem
export MatrixGroup
export MatrixGroupElem
export Matroid
export MixedIntegerLinearProgram, mixed_integer_linear_program
export ModuleFP
export ModuleFPElem
export ModuleFPHom
export ModuleOrdering
export MonomialOrdering
export Nemo
export NormalToricVariety
export OO
export PBWAlgElem
export PBWAlgQuo
export PBWAlgQuoElem
export PBWAlgRing
export Partition
export PcGroup
export PcGroupElem
export PermGroup
export PermGroupElem
export PointVector
export PolyhedralComplex, polyhedral_complex
export PolyhedralFan, polyhedral_fan
export Polyhedron
export Polymake
export PreSheafOnScheme
export PrincipalOpenSubset
export ProjectiveAlgebraicSet
export ProjectiveCurve
export ProjectivePlaneCurve
export ProjectiveScheme
export ProjectiveSchemeMor
export ProjectiveVariety
export PullbackSheaf
export PushforwardSheaf
export QQ
export R10_matroid
export RationalEquivalenceClass
export RayVector
export RootSpaceElem
export RootSystem
export SIM_body_polytope
export SL
export SLPoly
export SLPolyRing
export SO
export SU
export Scheme
export SchemeMor
export SemidirectProductGroup
export SesquilinearForm
export SimpleGluing
export SimplicialComplex
export Singular
export Sp
export StructureSheafOfRings
export SubFPGroup
export SubFPGroupElem
export SubObjectIterator
export SubPcGroup
export SubPcGroupElem
export SubQuoHom
export SubdivisionOfPoints, subdivision_of_points
export SubquoModule
export SubquoModuleElem
export ToricDivisor
export ToricDivisorClass
export ToricLineBundle
export ToricMorphism
export ToricVanishingSet
export TropicalCurve, tropical_curve
export TropicalHypersurface, tropical_hypersurface
export TropicalLinearSpace, tropical_linear_space
export TropicalSemiring, TropicalSemiringElem, tropical_semiring
export TropicalSemiringMap, tropical_semiring_map
export TropicalVariety
export Undirected
export VarietyFunctionField
export VarietyFunctionFieldElem
export WeakComposition
export WeightLattice, WeightLatticeElem
export WeilDivisor
export WeylGroup, WeylGroupElem
export WreathProductGroup
export YoungTableau
export ZZ
export abelian_group
export abelian_invariants
export abelian_invariants_schur_multiplier
export absolute_primary_decomposition
export acting_group
export acting_subgroup
export action
export action_function
export action_homomorphism
export add_edge!
export add_gluing!
export add_vertex!
export add_vertices!
export adjacency_matrix
export adjacency_tree
export adjacent_chamber
export adjoint_ideal
export adjunction_process
export affine_algebra
export affine_charts
export affine_cone
export affine_equation_matrix
export affine_geometry
export affine_halfspace
export affine_hull
export affine_hyperplane
export affine_inequality_matrix
export affine_normal_toric_variety
export affine_open_covering
export affine_patch
export affine_patches
export affine_scheme
export affine_scheme_open_subscheme_ring_type
export affine_space
export alexander_dual
export algebraic_cycle
export algebraic_ideal
export algebraic_lattice
export algebraic_matrix
export algebraic_matroid
export algebraic_pluecker_vector
export algebraic_polynomial
export algebraic_set
export all_atlas_group_infos
export all_blocks
export all_character_table_names
export all_cohomologies
export all_groups_with_class_number
export all_neighbors
export all_perfect_groups
export all_primitive_groups
export all_small_groups
export all_subsets_matroid
export all_table_of_marks_names
export all_transitive_groups
export all_triangulations
export allow_unicode
export alternating_form
export alternating_group
export ambient_coordinate_ring
export ambient_coordinates
export ambient_dim
export ambient_embedding
export ambient_free_module
export ambient_module
export ambient_representative
export ambient_representatives_generators
export ambient_scheme
export ambient_space
export ambient_type
export annihilator
export anti_symmetric_parts
export anticanonical_bundle
export anticanonical_divisor
export anticanonical_divisor_class
export approximate_class_fusion
export archimedean_solid
export arithmetic_genus
export arrangement_polynomial
export as_dictionary
export as_gset
export ascending_compositions
export associahedron
export associated_points
export associated_primes
export atlas_description
export atlas_group
export atlas_irrationality
export atlas_program
export atlas_subgroup
export augmented_chow_ring
export aut
export automorphism_group
export barycentric_subdivision
export base_ring
export base_scheme
export bases
export basis_of_global_sections
export basis_of_global_sections_via_homogeneous_component
export basis_of_global_sections_via_rational_functions
export basis_of_h4
export bell
export betti
export betti_number
export betti_numbers
export betti_table
export billera_lee_polytope
export binary_markov_graph_polytope
export binomial_exponents_to_ideal
export binomial_primary_decomposition
export bipyramid
export birkhoff_polytope
export block_distribution
export blocks
export bond_matroid
export borcherds_method
export boundary_lattice_points
export build_ctx
export build_doc
export bump!
export canonical_bundle
export canonical_divisor
export canonical_divisor_class
export canonical_isomorphism
export canonical_matrix
export cartan_bilinear_form
export cartan_matrix
export cartan_symmetrizer
export cartan_type
export cartan_type_with_ordering
export cartesian_power
export cartier_divisor
export catalan_solid
export cauchy_ideal
export cellular_associated_primes
export cellular_decomposition
export cellular_decomposition_macaulay
export cellular_hull
export cellular_minimal_associated_primes
export cellular_primary_decomposition
export center, has_center, set_center
export centralizer
export chain_complex
export chain_range
export chamber
export character_field
export character_lattice
export character_parameters
export character_table
export character_to_rational_function
export characteristic_subgroups, has_characteristic_subgroups, set_characteristic_subgroups
export charpoly
export chern_class
export chern_classes
export chief_series, has_chief_series, set_chief_series
export chow_ring
export circuits
export class_group
export class_lengths
export class_multiplication_coefficient
export class_names
export class_parameters
export class_positions_of_center
export class_positions_of_derived_subgroup
export class_positions_of_kernel
export class_positions_of_normal_subgroups
export class_positions_of_pcore
export class_positions_of_solvable_residuum
export closed_subvariety_of_toric_variety
export closure
export cm_regularity
export cobases
export cochain_complex
export cocircuits
export cocycle_matroid
export codim
export codomain
export codomain_covering
export coefficient_field
export coefficient_ring
export coefficient_ring_type
export coefficients
export coefficients_and_exponents
export cohomology
export cohomology_class
export cohomology_indices
export cohomology_ring
export cohyperplanes
export cokernel
export collector
export coloops
export column
export combinatorial_symmetries
export comm
export comm!
export common_components
export common_refinement
export complement
export complement_classes
export complement_equation
export complement_equations
export complement_ideal
export complement_of_point_ideal
export complement_of_prime_ideal
export complement_scheme
export complement_system, has_complement_system, set_complement_system
export complements
export complete_bipartite_graph
export complete_graph
export complex_projective_plane
export components
export components
export compose
export composition
export composition_series, has_composition_series, set_composition_series
export compositions
export cone
export cone_from_equations
export cone_from_inequalities
export cones
export conjugacy_class
export conjugacy_classes
export conjugacy_classes_subgroups
export conjugate
export conjugate_dominant_weight, conjugate_dominant_weight!
export conjugate_dominant_weight_with_elem, conjugate_dominant_weight_with_elem!
export conjugate_group
export conjugate_transpose
export connected_components
export connected_sum
export connectivity
export connectivity_function
export contains
export continued_fraction_hirzebruch_jung
export continued_fraction_hirzebruch_jung_to_rational
export contraction
export contributing_denominators
export convention
export convert
export convex_hull
export coordinate_names
export coordinate_names_of_torus
export coordinate_ring
export coordinate_ring_of_torus
export coordinates
export cophenetic_matrix
export corank
export core
export coroot
export coroots
export corresponding_bilinear_form
export corresponding_quadratic_form
export cotangent_sheaf
export covered_projection_to_base
export covered_scheme
export covered_scheme_morphism
export covering_morphism
export coverings
export cox_ring
export cox_variety
export cperm
export cross_polytope
export cube
export cycle_length
export cycle_matroid
export cycle_structure
export cycle_structures
export cyclic_caratheodory_polytope
export cyclic_flats
export cyclic_generator
export cyclic_group
export cyclic_polytope
export cyclic_quotient_singularity
export data
export de_rham_complex
export decide_du_val_singularity
export decomposition_matrix
export decorate
export decoration
export default_covering
export default_ordering
export defines_automorphism
export defining_equation
export defining_ideal
export deginvlex
export deglex
export degree
export degrees_of_generators
export degrevlex
export dehomogenization_map
export dehomogenizer
export del_pezzo_polytope
export del_pezzo_surface
export deletion
export demazure_character
export denest
export denominator
export denominators
export depth
export derived_length, has_derived_length, set_derived_length
export derived_series, has_derived_series, set_derived_series
export derived_subgroup, has_derived_subgroup, set_derived_subgroup
export describe
export desimulate_valuation
export det
export diameter
export dihedral_group
export dim
export dim_of_torusfactor
export direct_product
export direct_sum
export direct_sum_components
export disjoint_union
export div_left
export div_left!
export div_right
export div_right!
export divexact
export divides
export divisor_class
export divisor_of_character
export divisor_sigma
export divrem
export dodecahedron
export domain
export domain_covering
export dominates
export double_coset
export double_cosets
export double_dual
export dst
export dual
export dual_continued_fraction_hirzebruch_jung
export dual_graph
export dual_matroid
export dual_subdivision
export dwarfed_cube
export dwarfed_product_polygons
export edges
export effective_cartier_divisor
export ehrhart_polynomial
export element_to_homomorphism
export elementary_abelian_group
export elementary_symmetric
export elements
export eliminate
export elliptic_parameter
export elliptic_surface
export embedding
export embedding_orthogonal_group
export epimorphism_from_free_group
export equidimensional_decomposition_radical
export equidimensional_decomposition_weak
export equidimensional_hull
export equidimensional_hull_radical
export euler_characteristic
export euler_phi
export exceptional_divisor
export expand
export explicit_zonotope
export exponent, has_exponent, set_exponent
export exponents
export ext
export ext_of_degree
export extend!
export extension_field
export exterior_derivative
export exterior_power
export f_vector
export face_fan
export faces
export facet_degrees
export facet_indices
export facet_sizes
export facets
export factor_of_direct_product
export factorizations
export fano_matroid
export fano_simplex
export fat_ideal
export fat_scheme
export feasible_region
export fglm
export fiber_components
export fiber_product
export fibonacci
export fibration_type
export filtrate
export find_morphism
export find_morphisms
export fits
export fitting_ideal
export fitting_subgroup
export fitting_subgroup, has_fitting_subgroup, set_fitting_subgroup
export fixed_field
export flag_pluecker_ideal
export flats
export forget_decoration
export forget_grading
export forget_toric_structure
export fp_group
export fraction
export fraction_field
export fractional_cut_polytope
export fractional_ideal
export fractional_knapsack_polytope
export fractional_matching_polytope
export frattini_subgroup, has_frattini_subgroup, set_frattini_subgroup
export free_abelian_group
export free_extension
export free_group
export free_module
export free_module_dec
export free_resolution
export free_resolution_via_kernels
export full_group
export function_field
export fundamental_circuit
export fundamental_cocircuit
export fundamental_group
export fundamental_invariants
export fundamental_weight
export fundamental_weights
export g_vector
export galois_group
export galois_ideal
export galois_orbit_sum
export galois_quotient
export gelfand_tsetlin_polytope
export gen
export general_linear_group
export generalized_jordan_block
export generalized_jordan_form
export generating_system
export generator_matrix
export generic_fiber
export generic_fraction
export generic_fractions
export generic_section
export gens, has_gens
export gens_of_rational_equivalence_classes
export geometric_genus
export geometric_irreducible_components
export get_conjugate
export get_power
export get_relative_order
export get_relative_orders
export getindex_safe
export girth
export gkz_vector
export gluing_domains
export gluing_graph
export gluing_morphisms
export gluings
export goldfarb_cube
export goldfarb_sit_cube
export gomory_chvatal_closure
export gorenstein_index
export grade
export graded_cokernel
export graded_free_module
export graded_image
export graded_map
export graded_polynomial_ring
export grading_group
export graph
export graph_from_adjacency_matrix
export graph_from_edges
export grassmann_pluecker_ideal
export grid_morphism
export groebner_basis
export groebner_basis_f4
export groebner_basis_hilbert_driven
export groebner_basis_modular
export groebner_basis_with_transformation_matrix
export groebner_fan
export group
export group_with_class_number
export gset
export h_star_polynomial
export h_vector
export halfspace
export halfspace_matrix_pair
export hall_subgroup
export hall_subgroup_classes
export hall_subgroups
export hall_system, has_hall_system, set_hall_system
export has_edge
export has_groups_with_class_number
export has_nonempty_intersection
export has_perfect_groups
export has_preimage_with_preimage
export has_primitive_groups
export has_small_groups
export has_torusfactor
export has_transitive_groups
export has_vertex
export height
export hermitian_form
export hessian
export hessian_matrix
export hilbert_basis
export hilbert_function
export hilbert_polynomial
export hilbert_series
export hilbert_series_expanded
export hilbert_series_reduced
export hirzebruch_surface
export hom
export hom_product
export hom_tensor
export hom_without_reversing_direction
export homogeneity_space
export homogeneity_vector
export homogeneous_component
export homogeneous_components
export homogeneous_coordinate_ring
export homogeneous_coordinates
export homogenization_map
export homogenize
export homogenizer
export homology
export homomorphism_of_semidirect_product
export homomorphism_of_wreath_product
export homomorphism_to_element
export hook_length
export hook_lengths
export hyperplane
export hyperplanes
export hypersimplex
export hypersurface_complement
export hypertruncated_cube
export icosahedron
export id_hom
export ideal
export ideal_as_module
export ideal_membership
export ideal_of_linear_relations
export ideal_sheaf
export identifier
export identity_map
export image
export image_ideal
export image_in_Oq
export images
export img_gens
export immaculate_line_bundles
export incidence_matrix
export inclusion_morphism
export independent_sets
export index
export index_of_gen
export index_of_leading_term
export indicator
export induce
export induce_shift
export induced_automorphism
export induced_cyclic
export induced_map_on_exterior_power
export induced_ring_ordering
export initial
export inneighbors
export inner_automorphism
export inner_automorphism_group
export inner_cartesian_power
export inner_direct_product
export inradical
export integer_hull
export integral_basis
export integrate
export interior_lattice_points
export interreduce!
export intersect
export intersection_form
export intersection_multiplicity
export intersections
export inv
export inv!
export invariant_alternating_forms
export invariant_bilinear_forms
export invariant_hermitian_forms
export invariant_quadratic_forms
export invariant_ring
export invariant_sesquilinear_forms
export invariant_symmetric_forms
export inverse
export inverse_on_image
export invert
export invert_birational_map
export inverted_set
export invlex
export irreducible_components
export irreducible_decomposition
export irreducible_secondary_invariants
export irreducibles
export irrelevant_ideal
export is_abelian, has_is_abelian, set_is_abelian
export is_admissible_ordering
export is_affine
export is_algebraically_independent
export is_algebraically_independent_with_relations
export is_almost_simple, has_is_almost_simple, set_is_almost_simple
export is_alternating
export is_ample
export is_archimedean_solid
export is_atlas_character_table
export is_ball
export is_basepoint_free
export is_bicoset
export is_bijective
export is_binary
export is_binomial
export is_bounded
export is_canonically_isomorphic
export is_canonically_isomorphic_with_map
export is_cartan_matrix
export is_cartan_type
export is_cartier
export is_cellular
export is_character_table_name
export is_characteristic_subgroup
export is_closed_embedding
export is_clutter
export is_cohen_macaulay
export is_coloopless
export is_complete
export is_congruent
export is_conjugate
export is_conjugate_subgroup
export is_conjugate_subgroup_with_data
export is_conjugate_with_data
export is_connected
export is_coroot
export is_coroot_with_index
export is_cyclic, has_is_cyclic, set_is_cyclic
export is_degenerate
export is_dense
export is_dihedral_group, has_is_dihedral_group, set_is_dihedral_group
export is_dominant
export is_du_val_singularity
export is_duplicate_table
export is_effective
export is_elementary_abelian, has_is_elementary_abelian, set_is_elementary_abelian
export is_elimination_ordering
export is_embedded
export is_empty
export is_equal_with_morphism
export is_equidimensional
export is_equidistant
export is_faithful
export is_fano
export is_feasible
export is_finalized
export is_finite, has_is_finite, set_is_finite
export is_finite_dimensional_vector_space
export is_finite_order
export is_finitely_generated, has_is_finitely_generated, set_is_finitely_generated
export is_flat
export is_full_direct_product
export is_full_semidirect_product
export is_full_wreath_product
export is_fulldimensional
export is_fundamental_weight
export is_fundamental_weight_with_index
export is_geometrically_integral
export is_geometrically_reduced
export is_global
export is_gorenstein
export is_graded
export is_groebner_basis
export is_homogeneous
export is_identity_map
export is_immaculate
export is_in_linear_system
export is_injective
export is_inner_automorphism
export is_integral
export is_invariant
export is_inverse_of
export is_invertible
export is_irreducible
export is_isomorphic
export is_isomorphic_to_alternating_group, has_is_isomorphic_to_alternating_group, set_is_isomorphic_to_alternating_group
export is_isomorphic_to_symmetric_group, has_is_isomorphic_to_symmetric_group, set_is_isomorphic_to_symmetric_group
export is_isomorphic_with_map
export is_isomorphic_with_permutation
export is_isomorphism
export is_johnson_solid
export is_k_separation
export is_lattice_polytope
export is_leaf
export is_left
export is_linearly_normal
export is_local
export is_locally_free
export is_loopless
export is_manifold
export is_maximal_subgroup
export is_minor
export is_mixed
export is_modular
export is_natural_alternating_group, has_is_natural_alternating_group, set_is_natural_alternating_group
export is_natural_symmetric_group, has_is_natural_symmetric_group, set_is_natural_symmetric_group
export is_nef
export is_negative_coroot
export is_negative_coroot_with_index
export is_negative_root
export is_negative_root_with_index
export is_nilpotent, has_is_nilpotent, set_is_nilpotent
export is_non_zero_divisor
export is_normal
export is_normal_subgroup
export is_normalized_by
export is_one
export is_open_embedding
export is_orbifold
export is_perfect, has_is_perfect, set_is_perfect
export is_pgroup, has_is_pgroup, set_is_pgroup
export is_pgroup_with_prime
export is_platonic_solid
export is_pointed
export is_positive_coroot
export is_positive_coroot_with_index
export is_positive_root
export is_positive_root_with_index
export is_positively_graded
export is_primary
export is_prime
export is_primitive
export is_principal
export is_probable_prime
export is_projective
export is_projective_space
export is_pure
export is_q_cartier
export is_q_gorenstein
export is_quasisimple, has_is_quasisimple, set_is_quasisimple
export is_quaternion_group, has_is_quaternion_group, set_is_quaternion_group
export is_quotient
export is_radical
export is_ready
export is_reduced
export is_regular
export is_regular_sequence
export is_right
export is_root
export is_root_with_index
export is_semiregular
export is_semisimple
export is_semistandard
export is_shifted
export is_simple, has_is_simple, set_is_simple
export is_simple_coroot
export is_simple_coroot_with_index
export is_simple_root
export is_simple_root_with_index
export is_simplicial
export is_singular
export is_smooth
export is_solvable, has_is_solvable, set_is_solvable
export is_sphere
export is_sporadic_simple, has_is_sporadic_simple, set_is_sporadic_simple
export is_square
export is_standard
export is_standard_basis
export is_standard_graded
export is_strongly_connected
export is_subscheme
export is_subset
export is_supersolvable, has_is_supersolvable, set_is_supersolvable
export is_surjective
export is_table_of_marks_name
export is_ternary
export is_total
export is_transitive
export is_transverse_intersection
export is_trivial
export is_tropically_generic
export is_two_sided
export is_unipotent
export is_unit
export is_unital
export is_vertex_transitive
export is_vertical_k_separation
export is_very_ample
export is_weakly_connected
export is_welldefined
export is_z_graded
export is_zero
export is_zm_graded
export isfinite
export isometry_group
export isomorphic_matroid
export isomorphic_subgroups
export isomorphism
export isone
export isqrtrem
export issubset
export iszero
export iterate_basis
export jacobi_symbol
export jacobian_ideal
export jacobian_matrix
export jennings_series, has_jennings_series, set_jennings_series
export johnson_solid
export k_cyclic_polytope
export k_skeleton
export kaehler_differentials
export katsura
export kernel
export klee_minty_cube
export klein_bottle
export known_class_fusion
export known_class_fusions
export koszul_complex
export koszul_homology
export koszul_matrix
export labeled_matrix_formatted
export laplacian_matrix
export lattice_points
export lattice_volume
export leading_coefficient
export leading_coefficient_and_exponent
export leading_exponent
export leading_ideal
export leading_module
export leading_monomial
export leading_term
export lecture_hall_simplex
export left_acting_group
export left_coset
export left_cosets
export left_ideal
export left_transversal
export length
export letters
export lex
export lift
export lift_homomorphism_contravariant
export lift_homomorphism_covariant
export lifted_denominator
export lifted_numerator
export lineality_dim
export lineality_space
export linear_characters
export linear_equation_matrix
export linear_halfspace
export linear_hyperplane
export linear_inequality_matrix
export linear_span
export linear_symmetries
export linear_system
export link_subcomplex
export load
export load_lp
export load_mps
export localization
export localized_ring
export longest_element
export loops
export low_index_subgroup_classes
export low_index_subgroups
export lower_central_series, has_lower_central_series, set_lower_central_series
export lower_triangular_matrix
export map
export map_from_character_lattice_to_torusinvariant_weil_divisor_group
export map_from_picard_group_to_class_group
export map_from_torusinvariant_cartier_divisor_group_to_class_group
export map_from_torusinvariant_cartier_divisor_group_to_picard_group
export map_from_torusinvariant_cartier_divisor_group_to_torusinvariant_weil_divisor_group
export map_from_torusinvariant_weil_divisor_group_to_class_group
export map_gens_of_chow_ring_to_cox_ring
export map_on_affine_cones
export map_range
export map_word
export marks_vector
export mat_elem_type
export mathieu_group
export matrix_group
export matrix_kernel
export matrix_ordering
export matroid_base_polytope
export matroid_from_bases
export matroid_from_circuits
export matroid_from_hyperplanes
export matroid_from_matrix_columns
export matroid_from_matrix_rows
export matroid_from_matroid_hex
export matroid_from_nonbases
export matroid_from_prime_ideal
export matroid_from_revlex_basis_encoding
export matroid_groundset
export matroid_hex
export max_GC_rank_polytope
export maxes
export maximal_abelian_quotient, has_maximal_abelian_quotient, set_maximal_abelian_quotient
export maximal_associated_points
export maximal_blocks
export maximal_cells
export maximal_cones
export maximal_extension
export maximal_groebner_cone
export maximal_normal_subgroups, has_maximal_normal_subgroups, set_maximal_normal_subgroups
export maximal_polyhedra, maximal_polyhedra_and_multiplicities
export maximal_subgroup_classes, has_maximal_subgroup_classes, set_maximal_subgroup_classes
export maximal_subgroups
export metadata
export min_revlex_basis_encoding
export min_weights
export minimal_betti_table
export minimal_block_reps
export minimal_faces
export minimal_generating_set
export minimal_generator
export minimal_size_generating_set, has_minimal_size_generating_set, set_minimal_size_generating_set
export minimal_supercone_coordinates, minimal_supercone_indices, is_minimal_supercone_coordinate_vector
export minimal_nonfaces
export minimal_normal_subgroups, has_minimal_normal_subgroups, set_minimal_normal_subgroups
export minimal_primes
export minimal_subalgebra_generators
export minkowski_sum
export minor
export module_syzygies
export modulus
export moebius_kantor_matroid
export moebius_mu
export molien_series
export monomial_basis
export monomial_ordering
export monomials
export monomials_of_degree
export mordell_weil_sublattice
export mori_cone
export morphism
export morphism_from_cox_variety
export morphism_from_rational_functions
export morphism_on_class_group
export morphism_on_picard_group
export morphism_on_torusinvariant_cartier_divisor_group
export morphism_on_torusinvariant_weil_divisor_group
export morphism_type
export moved_points, has_moved_points, set_moved_points
export mpoly_dec_ring_type
export mpoly_dec_type
export mpoly_ring_type
export mpoly_type
export mul!
export multi_hilbert_function
export multi_hilbert_series
export multi_hilbert_series_reduced
export multiplication_induced_morphism
export multiplication_morphism
export multiplicative_jordan_decomposition
export multiplicities
export multiplicities_eigenvalues
export multiplicity
export n_cones
export n_connected_components
export n_edges
export n_facets
export n_gon
export n_maximal_cells
export n_maximal_cones
export n_maximal_polyhedra
export n_points
export n_polyhedra
export n_rays
export n_vertices
export name
export names_of_fusion_sources
export natural_character
export nef_cone
export negative_coroot
export negative_coroots
export negative_root
export negative_roots
export negbias
export negdeglex
export negdegrevlex
export neginvlex
export neglex
export negwdeglex
export negwdegrevlex
export neighbors
export newick
export newton_polytope
export newton_subdivision
export nice_gens
export nilpotency_class, has_nilpotency_class, set_nilpotency_class
export noether_normalization
export non_fano_matroid
export non_flat_locus
export non_pappus_matroid
export nonbases
export norm_equation
export norm_equation_fac_elem
export normal_closure
export normal_cone
export normal_fan
export normal_subgroup
export normal_subgroups, has_normal_subgroups, set_normal_subgroups
export normal_toric_varieties_from_glsm
export normal_toric_varieties_from_star_triangulations
export normal_toric_variety
export normal_toric_variety_from_glsm
export normal_toric_variety_from_star_triangulation
export normal_vector
export normalization
export normalization_with_delta
export normalize!
export normalized_volume
export normalizer
export nullity
export number_of_atlas_groups
export number_of_complement_equations
export number_of_compositions
export number_of_conjugacy_classes, has_number_of_conjugacy_classes, set_number_of_conjugacy_classes
export number_of_factors
export number_of_generators
export number_of_groups_with_class_number, has_number_of_groups_with_class_number
export number_of_moved_points, has_number_of_moved_points, set_number_of_moved_points
export number_of_partitions
export number_of_patches
export number_of_perfect_groups, has_number_of_perfect_groups
export number_of_positive_roots
export number_of_primitive_groups, has_number_of_primitive_groups
export number_of_roots
export number_of_simple_roots
export number_of_small_groups, has_number_of_small_groups
export number_of_standard_tableaux
export number_of_transitive_groups, has_number_of_transitive_groups
export number_of_weak_compositions
export numerator
export objective_function
export omega_group
export on_indeterminates
export on_lines
export on_echelon_form_mats
export on_sets
export on_sets_sets
export on_simplicial_complex
export on_subgroups
export on_tuples
export one!
export open_subset_type
export opposite_algebra
export opposite_ordering
export optimal_solution
export optimal_value
export optimal_vertex
export orbit_polytope
export orbit_representatives_and_stabilizers
export orbits
export order, has_order, set_order
export order_field_of_definition
export order_of_vanishing
export ordering
export orders_centralizers
export orders_class_representatives
export orders_perfect_groups
export ordinary_table
export orthogonal_components
export orthogonal_group
export orthogonal_sign
export outneighbors
export p_central_series
export pappus_matroid
export parallel_extension
export parametrization
export parametrization_conic
export parent
export partition
export partitions
export patches
export pbw_algebra
export pc_group
export pcore
export pentagonal_hexecontahedron
export pentagonal_icositetrahedron
export perfect_group
export perfect_group_identification, has_perfect_group_identification
export perles_matroid
export perles_nonrational_8_polytope
export perm
export permutahedron
export permutation
export permutation_group
export permutation_matrix
export permutation_of_terms
export permuted
export phylogenetic_tree
export picard_class
export picard_group
export picard_index
export pile_polytope
export pitman_stanley_polytope
export plane_curve
export platonic_solid
export pluecker_indices
export point_coordinates
export point_matrix
export point_vector
export points
export pol_elementary_divisors
export polarize
export poly_type
export polyhedra
export polyhedra_of_dim
export polyhedral_fan_from_rays_action
export polyhedron
export polynomial
export polynomial_ring
export positive_coroot
export positive_coroots
export positive_hull
export positive_root
export positive_roots
export positive_tropical_variety
export possible_class_fusions
export power_sum
export powers_of_element
export preimage
export present_as_cokernel
export presentation
export present_finite_extension_ring
export preserved_quadratic_forms
export preserved_sesquilinear_forms
export primary_decomposition
export primary_invariants
export prime_ideal
export prime_of_pgroup, has_prime_of_pgroup, set_prime_of_pgroup
export primitive_collections
export primitive_generator
export primitive_generator_with_scaling_factor
export primitive_group
export primitive_group_identification, has_primitive_group_identification
export primorial
export principal_extension
export print_constraints
export product
export proj
export project_full
export projection
export projection_to_base
export projective_closure
export projective_curve
export projective_general_linear_group
export projective_geometry
export projective_omega_group
export projective_orthogonal_group
export projective_plane
export projective_scheme
export projective_space
export projective_special_linear_group
export projective_special_orthogonal_group
export projective_special_unitary_group
export projective_symplectic_group
export projective_unitary_group
export projectivization
export prune_with_map
export pseudo_del_pezzo_polytope
export pullback
export pyramid
export quadratic_form
export quantum_automorphism_group
export quantum_symmetric_group
export quaternion_group
export quo
export quo_object
export quotient
export quotient_ring_as_module
export radical
export radical_membership
export rand
export rand01_polytope
export rand_box_polytope
export rand_cyclic_polytope
export rand_homogeneous
export rand_metric
export rand_metric_int
export rand_normal_polytope
export rand_pseudo
export rand_spherical_polytope
export rand_subpolytope
export rank
export rank_action
export rational_equivalence_class
export rational_map
export rational_point_conic
export rational_solutions
export rational_to_continued_fraction_hirzebruch_jung
export ray_degrees
export ray_indices
export ray_vector
export rays
export rays_modulo_lineality
export read_metadata
export reading_word
export real_projective_plane
export real_solutions
export recession_cone
export recognize
export reduce
export reduce_fraction
export reduce_with_quotients
export reduce_with_quotients_and_unit
export reduced_characteristic_polynomial
export reduced_expressions
export reduced_groebner_basis
export reduced_scheme
export reducible_fibers
export reflect, reflect!
export reflection
export register_morphism!
export regular_120_cell
export regular_24_cell
export regular_600_cell
export regular_character
export regular_triangulation
export regular_triangulations
export relations
export relative_ambient_dimension
export relative_interior_point
export relative_invariants
export relators
export rem_edge!
export rem_vertex!
export rem_vertices!
export renest
export repres
export representative
export representative_field
export representative_patch
export represents_element
export restrict
export restrict_automorphism
export restrict_automorphism_group
export restrict_codomain
export restrict_domain
export restrict_endomorphism
export restrict_homomorphism
export restricted_map
export restricted_map_type
export restriction
export restriction_map
export restrictions
export reverse
export reverse_direction!
export revlex_basis_encoding
export reynolds_operator
export right_acting_group
export right_coset
export right_coset_action
export right_cosets
export right_ideal
export right_transversal
export ring
export ring_elem_type
export ring_type
export rising_factorial
export root
export root_system
export root_system_type, has_root_system_type
export root_system_type_with_ordering
export roots
export row
export rss_associahedron
export saturated_ideal
export saturation
export saturation_with_index
export save
export save_lp
export save_mps
export scalar_product
export scheme
export scheme_type
export schensted
export schur_cover
export schur_index
export schur_multiplier
export schur_polynomial
export secondary_cone
export secondary_invariants
export secondary_polytope
export section
export sectional_genus
export semi_invariants
export semidirect_product
export semistandard_tableaux
export separating_hyperplanes
export series_extension
export set_base_scheme!
export set_commutator!
export set_conjugate!
export set_coordinate_names
export set_coordinate_names_of_torus
export set_grading
export set_mordell_weil_basis!
export set_name!
export set_ordering
export set_power!
export set_relative_order!
export set_relative_orders!
export set_theoretic_intersection
export sets
export shape
export sheaf_cohomology
export sheaf_of_rings
export short_right_transversal
export shortest_path_dijkstra
export show_morphism
export show_morphism_as_map
export show_subquo
export signed_incidence_matrix
export signed_permutahedron
export simple_coroot
export simple_coroots
export simple_root
export simple_roots
export simplex
export simplicial_complex
export simplicial_product
export simplified_fp_group
export simplify
export simplify!
export simplify_light
export simplify_with_same_ambient_free_module
export simulate_valuation
export singular
export singular_assure
export singular_coeff_ring
export singular_locus
export singular_locus_reduced
export singular_poly_ring
export slpoly_ring
export small_generating_set, has_small_generating_set, set_small_generating_set
export small_group
export small_group_identification, has_small_group_identification
export smaller_degree_permutation_representation
export snub_cube
export snub_dodecahedron
export socle, has_socle, set_socle
export solvable_radical, has_solvable_radical, set_solvable_radical
export solve_ineq
export solve_lp
export solve_milp
export solve_mixed
export solve_non_negative
export space
export spanning_sets
export spec
export special_linear_group
export special_orthogonal_group
export special_unitary_group
export src
export stable_intersection
export stable_set_polytope
export standard_basis
export standard_basis_highest_corner
export standard_basis_with_transformation_matrix
export standard_coordinates
export standard_tableaux
export stanley_reisner_ideal
export stanley_reisner_ring
export star_subcomplex
export star_subdivision
export star_triangulations
export straight_line_program
export strongly_connected_components
export structure_sheaf
export sub
export sub_object
export subalgebra_membership
export subalgebra_membership_homogeneous
export subgroup_classes
export subquo_type
export subquotient
export subscheme
export subsystem
export support_function
export syllables
export sylow_subgroup
export sylow_system, has_sylow_system, set_sylow_system
export symmetric_form
export symmetric_group
export symmetric_parts
export symmetric_power
export symmetrizations
export symplectic_components
export symplectic_group
export syz
export syzygy_generators
export table_of_marks
export tail
export tangent_lines
export tangent_sheaf
export tangent_space
export tautological_bundle
export taxa
export tensor_product
export terms
export tetrahedron
export tighten_simulation
export to_elementary_symmetric
export tor
export toric_divisor
export toric_divisor_class
export toric_ideal
export toric_identity_morphism
export toric_line_bundle
export toric_morphism
export toric_vanishing_set
export toric_variety
export torus # requires a distinction from e.g. an algebraic group
export torusinvariant_cartier_divisor_group
export torusinvariant_prime_divisors
export torusinvariant_weil_divisor_group
export total_degree
export total_space
export transform
export transform_to_weierstrass
export transitive_group
export transitive_group_identification, has_transitive_group_identification
export transitivity
export transport
export transportation_polytope
export trivial_character
export trivial_divisor
export trivial_divisor_class
export trivial_lattice
export trivial_line_bundle
export trivial_morphism
export trivial_subgroup, has_trivial_subgroup, set_trivial_subgroup
export trivializing_covering
export tropical_matrix
export tropical_median_consensus
export tropical_pluecker_vector
export tropical_polynomial
export tropical_variety
export truncate
export turn_denominator_into_polyhedron
export tutte_connectivity
export tutte_lifting
export tutte_polynomial
export twist
export twisting_sheaf
export two_sided_ideal
export underlying_gluing
export underlying_presheaf
export underlying_quotient
export underlying_word
export uniform_matroid
export unit
export unitary_group
export units_of
export unwrap
export update_gluing_graph
export upper_bound_f_vector
export upper_bound_g_vector
export upper_bound_h_vector
export upper_central_series, has_upper_central_series, set_upper_central_series
export upper_triangular_matrix
export valuation_of_roots
export vamos_matroid
export vanishing_ideal
export vanishing_sets
export variety
export vector_matrix
export vector_space_basis
export vector_space_dimension
export vertex_and_ray_indices
export vertex_edge_graph
export vertex_figure
export vertex_indices
export vertex_sizes
export vertexindices
export vertical_connectivity
export vertices
export vertices_and_rays
export vinberg_algorithm
export visualize
export volume
export volume_form
export volume_map
export walls
export wdeglex
export wdegrevlex
export weak_composition
export weak_compositions
export weakly_connected_components
export wedge
export wedge_generator_decompose_function
export wedge_multiplication_map
export wedge_pure_function
export weierstrass_chart
export weierstrass_chart_on_minimal_model
export weierstrass_contraction
export weierstrass_model
export weight
export weight_cone
export weight_lattice
export weight_ordering
export weighted_projective_space
export weil_divisor
export weyl_algebra
export weyl_group
export weyl_orbit
export weyl_vector
export with_ordering
export witt_index
export word
export wreath_product
export write_as_full
export young_tableau
export zero_section
export zonotope
export zonotope_vertices_fukuda_matrix