• AbsAffineAlgebraicSet
• AbsAffineRationalPoint
• AbsAffineScheme
• AbsAffineSchemeMor
• AbsAffineVariety
• AbsAlgebraicCycle
• AbsCoveredScheme
• AbsGluing
• AbsIdealSheaf
• AbsNumFieldOrder
• AbsPreSheaf
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• AbsWeilDivisor
• AffinePlaneCurve
• AffineRationalPoint
• AffineScheme
• AffineSchemeMor
• Array
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• BasicGAPGroupElem
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• CompositeCoveredSchemeMorphism
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• Covering
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• Dedent
• DirectProductGroup
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• EllipticSurface
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• FinGenAbGroup
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• GAPGroup
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• Gluing
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• Graph
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• Lowercase
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• MPolyBuildCtx
• MSet
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• MatrixGroup
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• MorphismFromRationalFunctions
• Partition
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• PcGroup
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• Perm
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• Polyhedron
• PreSheafOnScheme
• PrimeIdealSheafFromChart
• ProjectiveCurve
• ProjectivePlaneCurve
• ProjectiveRationalPoint
• ProjectiveSchemeMor
• QuadSpaceWithIsom
• Scheme
• SchemeMor
• SemidirectProductGroup
• SesquilinearForm
• SheafOfModules
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• StructureSheafOfRings
• SubFPGroup
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• SymmetricGroup
• TorQuadModule
• UpgradeScript
• Vector
• Vector
• WreathProductGroup
• YoungTableau
• ZZGenus
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• ZZMatrix
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• *
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• *
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• *
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• >>
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• ADE_type
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• GF
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• O
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• R10_matroid
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• ^
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• _numpart
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• abelian_closure
• abelian_d10_pi6
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• abelian_group
• abelian_group
• abelian_group
• abelian_group
• abelian_group
• abelian_group
• abelian_group
• abelian_groups
• abelian_invariants
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• abelian_lie_algebra
• abs
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• accuracy_bits
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• add!
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• add_gluing!
• add_resolution
• add_row
• add_row!
• add_scaled_col!
• add_scaled_row
• add_scaled_row
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• add_verbosity_scope
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• adjacency_matrix
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• agm
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• airy_ai
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• airy_bi
• airy_bi
• airy_bi
• airy_bi
• airy_bi_prime
• airy_bi_prime
• airy_bi_prime
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• alexander_dual
• algebraic_closure
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• algebraic_lattice_primitive_closure!
• algebraic_matrix
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• algebraic_set
• algebraic_set
• algebraic_set
• algebraic_set
• algebraic_set
• algebraic_set
• algebraic_split
• all_atlas_group_infos
• all_blocks
• all_character_table_names
• all_cohomologies
• all_neighbors
• all_od_infos
• all_perfect_groups
• all_primitive_groups
• all_small_groups
• all_subsets_matroid
• all_table_of_marks_names
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• all_triangulations
• alternating_form
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• ambient_dim
• ambient_dim
• ambient_dim
• ambient_dim
• ambient_dim
• ambient_dim
• ambient_dim
• ambient_embedding
• ambient_isometry
• ambient_ring
• ambient_scheme
• ambient_scheme
• ambient_scheme
• ambient_space
• ambient_space
• ambient_space
• ambient_space
• ambient_space
• ambient_space
• ambient_space_models_of_g4_fluxes
• analyze_fibers
• angle
• annihilator
• anti_symmetric_parts
• anticanonical_bundle
• anticanonical_divisor
• anticanonical_divisor_class
• any_order
• approximate_class_fusion
• archimedean_solid
• arithmetic_genus
• arrangement_polynomial
• arxiv_doi
• arxiv_id
• arxiv_link
• arxiv_model_equation_number
• arxiv_model_page
• arxiv_model_section
• arxiv_version
• ascending_compositions
• asin
• asinpi
• associahedron
• associated_literature_models
• atan
• atan2
• atan2
• atanpi
• atlas_description
• atlas_group
• atlas_irrationality
• atlas_subgroup
• augmented_chow_ring
• aut
• automorphism_group
• automorphism_group
• automorphism_group
• automorphism_group
• automorphism_group
• automorphism_group
• automorphism_group_generators
• automorphism_group_generators
• automorphism_group_generators
• automorphism_group_generators
• automorphism_group_generators
• automorphism_group_order
• automorphism_group_order
• automorphism_list
• b_invariants
• ball
• barnes_g
• barnes_g
• base
• base
• base_change
• base_change
• base_change
• base_change
• base_field
• base_field
• base_field
• base_field
• base_field
• base_field
• base_field
• base_field
• base_lie_algebra
• base_map
• base_ring
• base_ring
• base_ring
• base_ring
• base_ring
• base_ring
• base_ring
• base_ring
• base_ring
• base_ring
• base_ring_morphism
• base_ring_type
• base_scheme
• base_space
• bases
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis
• basis_coordinate_ring_kodaira
• basis_coordinate_ring_kodaira_ffl
• basis_lie_highest_weight
• basis_lie_highest_weight_ffl
• basis_lie_highest_weight_lusztig
• basis_lie_highest_weight_nz
• basis_lie_highest_weight_operators
• basis_lie_highest_weight_string
• basis_mat_inv
• basis_mat_inv
• basis_mat_inv
• basis_matrix
• basis_matrix
• basis_matrix
• basis_matrix
• basis_matrix
• basis_matrix
• basis_matrix_of_rational_span
• basis_nf
• basis_of_global_sections_via_homogeneous_component
• basis_of_global_sections_via_rational_functions
• basis_of_h22
• basis_of_h4
• basis_pmatrix
• basis_representation
• bell
• bell
• bell
• bell
• bell
• bell
• bernoulli
• bernoulli
• bernoulli
• bernoulli_cache
• bessel_i
• bessel_i
• bessel_j
• bessel_j
• bessel_k
• bessel_k
• bessel_y
• bessel_y
• betti_number
• betti_numbers
• betti_table
• bielliptic_d10_pi6
• bielliptic_d15_pi21
• billera_lee_polytope
• bin
• binary_markov_graph_polytope
• binomial
• binomial
• binomial
• binomial
• binomial
• binomial
• binomial_exponents_to_ideal
• binomial_primary_decomposition
• biproduct
• biproduct
• biproduct
• biproduct
• biproduct
• biproduct
• bipyramid
• birational_literature_models
• birkhoff_polytope
• block_diagonal_matrix
• block_diagonal_matrix
• block_diagonal_matrix
• block_distribution
• blocks
• blow_up
• blow_up
• blow_up
• blow_up
• blow_up
• blow_up
• blow_up
• blowup
• blowup_points
• bond_matroid
• borcherds_method
• bordiga
• bound_inf_norm
• bound_inf_norm
• boundary_lattice_points
• bracket
• bracket
• brown_invariant
• build_doc
• bump!
• c_invariants
• calabi_yau_hypersurface
• calabi_yau_hypersurface
• calabi_yau_hypersurface
• can_compute_horizontal_map
• can_compute_index
• can_compute_vertical_map
• can_scale_totally_positive
• can_solve
• can_solve_with_solution
• can_solve_with_solution_and_kernel
• canonical_bundle
• canonical_bundle
• canonical_bundle
• canonical_class
• canonical_divisor
• canonical_divisor_class
• canonical_injection
• canonical_injection
• canonical_injection
• canonical_injection
• canonical_injection
• canonical_injections
• canonical_injections
• canonical_injections
• canonical_matrix
• canonical_projection
• canonical_projection
• canonical_projection
• canonical_projection
• canonical_projection
• canonical_projections
• canonical_projections
• cartan_bilinear_form
• cartan_matrix
• cartan_matrix
• cartan_symmetrizer
• cartan_type
• cartan_type_with_ordering
• cartesian_power
• cartier_divisor
• cartier_divisor
• castelnuovo
• catalan_solid
• cauchy_ideal
• cavender_farris_neyman_model
• ceil
• ceil
• cellular_associated_primes
• cellular_decomposition
• cellular_hull
• cellular_minimal_associated_primes
• cellular_primary_decomposition
• center
• center
• center
• center
• center_data
• center_unnormalized
• centralizer
• centralizer
• centralizer
• centralizer
• centralizer
• centralizer
• centralizer
• chain_complex
• chamber
• change_base_ring
• change_base_ring
• change_base_ring
• change_base_ring
• change_base_ring
• change_base_ring
• change_coefficient_ring
• change_coefficient_ring
• character
• character
• character
• character_field
• character_lattice
• character_parameters
• character_table
• character_table
• character_table
• character_table
• character_to_rational_function
• character_to_rational_function
• characteristic
• characteristic
• characteristic
• characteristic
• characteristic_polynomial
• characteristic_polynomial
• characteristic_polynomial
• characteristic_subgroups
• charpoly
• charpoly
• charpoly
• cheap_realization
• chebyshev_t
• chebyshev_t
• chebyshev_t
• chebyshev_t2
• chebyshev_t2
• chebyshev_u
• chebyshev_u
• chebyshev_u
• chebyshev_u2
• chebyshev_u2
• chern_character
• chern_class
• chern_class
• chern_class
• chern_classes
• chern_classes
• chief_series
• chow_ring
• chow_ring
• chow_ring
• ci_ideal
• ci_statements
• ci_statements
• ci_stmt
• circuits
• cispi
• cispi
• class_group
• class_group
• class_group
• class_group
• class_group_ideal_relation
• class_lengths
• class_lengths
• class_multiplication_coefficient
• class_names
• class_number
• class_parameters
• class_positions_of_center
• class_positions_of_center
• class_positions_of_derived_subgroup
• class_positions_of_kernel
• class_positions_of_normal_subgroups
• class_positions_of_pcore
• class_positions_of_solvable_residuum
• classes_of_model_sections
• clog
• close_vectors
• closed_embedding
• closed_subvariety_of_toric_variety
• closed_subvariety_of_toric_variety
• closure
• closure
• closure
• clrbit!
• cm_regularity
• cm_regularity
• cmp
• cobases
• cochain_complex
• cocircuits
• cocycle_matroid
• codifferent
• codim
• codim
• codim
• codim
• codim
• codim
• codomain
• codomain
• codomain
• coeff
• coeff
• coeff
• coeff
• coeff
• coeff
• coeff
• coeff
• coeff
• coefficient_field
• coefficient_ideals
• coefficient_ideals
• coefficient_ring
• coefficients
• coefficients
• coefficients
• coefficients
• coefficients
• coefficients
• coefficients
• coefficients
• coerce_to_lie_algebra_elem
• cohomology
• cohomology
• cohomology_class
• cohomology_class
• cohomology_class
• cohomology_class
• cohomology_class
• cohomology_class
• cohomology_indices
• cohomology_ring
• cohyperplanes
• coinvariant_lattice
• coinvariant_lattice
• coinvariant_lattice
• cokernel
• cokernel
• collength
• colon
• coloops
• column
• combinatorial_symmetries
• combit!
• comm
• common_components
• common_components
• compact_presentation
• complement
• complement_classes
• complement_of_point_ideal
• complement_of_prime_ideal
• complement_system
• complements
• complete_bipartite_graph
• complete_graph
• complete_intersection
• complex_conjugation
• complex_embeddings
• complex_normal_form
• complex_places
• complex_projective_plane
• component
• components
• components
• components
• components_of_dual_graph
• components_of_simplified_dual_graph
• compose
• compose
• compose
• compose
• compose
• compose
• compose
• compose
• composition
• composition_series
• compositions
• compositions
• compositum
• compositum
• compute_equivalent_classes
• concentration_matrix
• conductor
• conductor
• cone
• cone_from_equations
• cone_from_inequalities
• cones
• cones
• conj
• conj
• conj
• conj
• conj
• conj
• conj
• conjugacy_class
• conjugacy_class
• conjugacy_classes
• conjugacy_classes
• conjugate
• conjugate_transpose
• conjugates
• conjugates
• conjugates
• conjugates_arb
• conjugates_arb_log
• conjugates_arb_log_normalise
• conjugates_complex
• conjugates_log
• conjugates_real
• connected_components
• connected_sum
• connectivity_function
• const_catalan
• const_catalan
• const_e
• const_e
• const_euler
• const_euler
• const_euler
• const_glaisher
• const_glaisher
• const_khinchin
• const_khinchin
• const_log10
• const_log10
• const_log2
• const_log2
• const_pi
• const_pi
• const_pi
• const_pi
• const_pi
• constant_coefficient
• constant_coefficient
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains
• contains_negative
• contains_negative
• contains_nonnegative
• contains_nonnegative
• contains_nonpositive
• contains_nonpositive
• contains_positive
• contains_positive
• contains_zero
• contains_zero
• contains_zero
• contains_zero
• content
• content
• continued_fraction_hirzebruch_jung
• continued_fraction_hirzebruch_jung_to_rational
• contraction
• convention
• convex_hull
• convex_hull
• coordinate_names
• coordinate_names_of_torus
• coordinate_ring
• coordinate_ring_of_torus
• coordinate_ring_of_torus
• coordinates
• coordinates
• coordinates
• coordinates
• coordinates
• coordinates
• cophenetic_matrix
• coprime_base
• coprime_base
• coprime_base_push!
• corank
• core
• corresponding_bilinear_form
• corresponding_quadratic_form
• cos
• cos_integral
• cos_integral
• cos_minpoly
• cosh_integral
• cosh_integral
• cospi
• cotangent_bundle
• cotangent_bundle
• cotangent_sheaf
• covariance_matrix
• cover
• covered_scheme
• covered_scheme
• covered_scheme_morphism
• covering_morphism
• coverings
• cox_ring
• cox_ring
• cox_ring
• cox_ring_of_qq_factorial_terminalization
• cox_variety
• coxeter_number
• cperm
• cross_polytope
• crt
• crt
• crt
• crt
• crt_with_lcm
• crt_with_lcm
• csgn
• csgn
• cube
• cubic_scroll
• cycle_matroid
• cycle_structure
• cycle_structures
• cycles
• cycles
• cyclic_caratheodory_polytope
• cyclic_flats
• cyclic_generator
• cyclic_group
• cyclic_polytope
• cyclic_quotient_singularity
• cyclotomic
• cyclotomic_field
• cyclotomic_field
• cyclotomic_real_subfield
• data
• dec
• decide_du_val_singularity
• decide_du_val_singularity
• decomposition_group
• decomposition_matrix
• dedekind_eta
• dedekind_eta
• dedekind_sum
• default_covering
• default_ordering
• defining_classes
• defining_equation
• defining_equation
• defining_ideal
• defining_ideal
• defining_ideal
• defining_modulus
• defining_polynomial
• defining_polynomial
• defining_polynomial
• defining_polynomial
• defining_polynomials
• defining_section_parametrization
• deflate
• deflate
• deflate
• deflate
• deflate
• deflate
• deflate
• deflate
• deflation
• deflation
• degeneracy_locus
• deginvlex
• deglex
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degree
• degrees
• degrees_of_generators
• degrees_of_generators
• degrees_of_kbar_restrictions_to_ci_curves
• degrees_of_kbar_restrictions_to_components_of_dual_graph
• degrees_of_kbar_restrictions_to_components_of_simplified_dual_graph
• degrevlex
• dehomogenization_map
• dehomogenizer
• del_pezzo_polytope
• del_pezzo_surface
• deletion
• deletion
• denominator
• denominator
• denominator
• denominator
• denominator
• dense_matrix_type
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• density
• depth
• derivative
• derivative
• derivative
• derivative
• derivative
• derived_algebra
• derived_length
• derived_series
• derived_series
• derived_subgroup
• describe
• det
• det
• det
• det
• det
• det
• det
• det
• det
• det
• det
• det
• det
• det
• det_divisor
• det_given_divisor
• det_given_divisor
• det_mc
• det_representative
• det_representative
• dets
• diagonal
• diagonal
• diagonal
• diagonal_form
• diagonal_matrix
• diagonal_of_rational_span
• diagonal_with_transform
• different
• digamma
• digamma
• digamma
• digamma
• dihedral_group
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim
• dim_of_torusfactor
• dimension_of_center
• dimension_over_center
• dimension_specht_module
• direct_product
• direct_product
• direct_product
• direct_product
• direct_product
• direct_product
• direct_product
• direct_product
• direct_product
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum
• direct_sum_components
• directed_edges_matrix
• disc_log
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant
• discriminant_group
• discriminant_group
• discriminant_representation
• disjoint_union
• disjoint_union
• div
• div!
• divexact
• divexact!
• divides
• divisibility
• division_points
• divisor_class
• divisor_lenstra
• divisor_of_character
• divisor_sigma
• divrem
• doctest_fix
• dodecahedron
• domain
• domain
• domain
• dominates
• dot
• dot
• dot
• double_coset
• double_cosets
• dst
• dual
• dual
• dual
• dual
• dual
• dual_basis
• dual_continued_fraction_hirzebruch_jung
• dual_graph
• dual_graph
• dual_matroid
• dual_subdivision
• dwarfed_cube
• dwarfed_product_polygons
• echelon_with_transform
• edges
• effective_cartier_divisor
• effective_cartier_divisor
• ehrhart_polynomial
• ehrhart_polynomial
• eigenvalues
• eigenvalues
• eigenvalues
• eigenvalues_simple
• eigenvalues_with_multiplicities
• eigenvalues_with_multiplicities
• eigenvalues_with_multiplicities
• eisenstein_g
• eisenstein_g
• elem_in_nf
• elem_type
• elem_type
• element_to_homomorphism
• elementary_abelian_group
• elementary_divisors
• elementary_divisors
• elements!
• eliminate
• eliminate
• elliptic_curve
• elliptic_curve_from_j_invariant
• elliptic_d10_pi10
• elliptic_d10_pi9
• elliptic_d11_pi12
• elliptic_d12_pi13
• elliptic_d12_pi14_ss_0
• elliptic_d12_pi14_ss_inf
• elliptic_d7_pi6
• elliptic_d8_pi7
• elliptic_d9_pi7
• elliptic_e
• elliptic_e
• elliptic_k
• elliptic_k
• elliptic_parameter
• elliptic_surface
• emb
• emb!
• embed
• embed
• embed_in_unimodular
• embedding
• embedding
• enriques_d10_pi8
• enriques_d11_pi10
• enriques_d13_pi16
• enriques_d13_pi16_two
• enriques_d9_pi6
• enumerate_classes_of_lattices_with_isometry
• enumerate_partitioned_permutations
• enumerate_prime_power_isometries
• epimorphism_from_free_group
• equation
• equidimensional_decomposition_radical
• equidimensional_decomposition_weak
• equidimensional_hull
• equidimensional_hull_radical
• equivariant_primitive_extensions
• erf
• erf
• erf
• erfc
• erfi
• erfi
• erfi
• error_covariance_matrix
• estimated_number_of_triangulations
• eta_qexp
• eta_qexp
• euler_characteristic
• euler_characteristic
• euler_characteristic
• euler_characteristic
• euler_characteristic
• euler_phi
• euler_phi
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate
• evaluate2
• evaluate2
• evaluate_mod
• evaluate_naive
• evaluation_function
• exceptional_prime_divisor
• excess
• exp
• exp
• exp
• exp
• exp
• exp
• exp
• exp_integral_e
• exp_integral_e
• exp_integral_ei
• exp_integral_ei
• exp_pi_i
• explicit_model_sections
• explicit_zonotope
• exponent
• exponent
• exponent_vectors
• exponent_word
• exponent_words
• exponents
• ext
• ext_of_degree
• extend
• exterior_algebra
• exterior_power
• exterior_power
• exterior_power
• exterior_power
• extra_name
• f_vector
• f_vector
• f_vector
• f_vector
• f_vector
• f_vector
• face_fan
• facet_degrees
• facet_sizes
• facets
• factor
• factor
• factor
• factor
• factor
• factor
• factor
• factor_base_bound_bach
• factor_base_bound_grh
• factor_coprime
• factor_coprime
• factor_coprime
• factor_coprime
• factor_distinct_deg
• factor_distinct_deg
• factor_distinct_deg
• factor_distinct_deg
• factor_distinct_deg
• factor_distinct_deg
• factor_of_direct_product
• factorial
• factorial
• factorial
• factorial
• factorial
• family_of_spaces
• fano_matroid
• fano_simplex
• fat_ideal
• fat_ideal
• fat_scheme
• feasible_region
• feasible_region
• fflu
• fglm
• fiber_ambient_space
• fiber_cartier
• fiber_components
• fiber_product
• fiber_product
• fibonacci
• fibonacci
• fibonacci
• fibonacci
• fibonacci
• fibonacci
• fibration
• fibration_on_weierstrass_model
• field
• fill!
• find_isomorphism
• find_name
• find_random_variables
• find_row_starting_with
• find_state
• finish
• finite_field
• fits
• fits
• fitting_ideal
• fitting_subgroup
• fixed_field
• fixed_field
• fixed_field
• fixed_field
• fixed_field
• fixed_ring
• flag_pluecker_ideal
• flat
• flats
• flog
• floor
• floor
• forget_grading
• forget_grading
• forget_toric_structure
• forget_toric_structure
• forget_toric_structure
• fourier_map
• fourier_parameters
• fourier_ring
• fractional_cut_polytope
• fractional_ideal
• fractional_ideal
• fractional_ideal
• fractional_ideal
• fractional_ideal
• fractional_ideal
• fractional_ideal
• fractional_knapsack_polytope
• fractional_matching_polytope
• frattini_subgroup
• free_abelian_group
• free_extension
• free_group
• free_module
• free_module
• free_module
• free_resolution
• frobenius
• from_roots
• from_roots
• full_group
• fundamental_circuit
• fundamental_cocircuit
• fundamental_group
• fundamental_invariants
• fundamental_invariants
• fundamental_invariants
• g4_flux
• g_vector
• galois_group
• galois_group
• galois_ideal
• galois_orbit_sum
• galois_quotient
• galois_quotient
• galois_quotient
• galois_quotient
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma
• gamma_lower
• gamma_lower
• gamma_lower
• gamma_lower
• gamma_lower_regularized
• gamma_lower_regularized
• gamma_lower_regularized
• gamma_lower_regularized
• gamma_regularized
• gamma_regularized
• gamma_regularized
• gamma_regularized
• gauge_algebra
• gaussian_ring
• gcd
• gcd
• gcd
• gcd
• gcd
• gcd
• gcd
• gcd!
• gcdinv
• gcdx
• gcdx
• gcdx
• gelfand_tsetlin_polytope
• gen
• gen
• gen
• gen
• gen
• gen
• gen
• gen
• gen
• gen
• gen
• gen_index
• genera_of_ci_curves
• genera_of_components_of_dual_graph
• genera_of_components_of_simplified_dual_graph
• general_linear_group
• general_linear_lie_algebra
• general_markov_model
• generalized_jordan_block
• generalized_jordan_form
• generating_sections
• generators
• generic_fiber
• generic_section
• gens
• gens
• gens
• gens
• gens
• gens
• gens
• gens
• gens
• gens_of_rational_equivalence_classes
• gens_with_data
• genus
• genus
• genus
• genus
• genus
• genus
• genus_field
• genus_representatives
• genus_representatives
• geometric_genus
• geometric_irreducible_components
• geometric_irreducible_components
• get_assertion_level
• get_attribute
• get_attribute!
• get_html_as_latex
• get_name
• get_seeded_rng
• get_variable
• get_verbosity_level
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex
• getindex_safe
• girth
• global_gauge_quotients
• global_tate_model
• global_tate_model
• global_tate_model
• global_tate_model
• global_tate_model_over_del_pezzo_surface
• global_tate_model_over_hirzebruch_surface
• global_tate_model_over_projective_space
• glue_map
• gluing_domains
• gluing_morphisms
• gluings
• goldfarb_cube
• goldfarb_sit_cube
• gorenstein_index
• grade
• grade
• grade
• grade
• grade
• graded_free_module
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• graded_polynomial_ring
• grading_group
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• grading_group
• grading_group
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• gram
• gram_determinant_specht_module
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• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix_bilinear
• gram_matrix_of_generators
• gram_matrix_of_rational_span
• gram_matrix_quadratic
• gram_schmidt_orthogonalisation
• graph
• graph
• graph
• graph_from_adjacency_matrix
• graph_from_edges
• graphical_model
• graphical_model
• grassmann_pluecker_ideal
• grid_morphism
• groebner_basis
• groebner_basis
• groebner_basis
• groebner_basis
• groebner_basis_f4
• groebner_basis_hilbert_driven
• groebner_basis_with_transformation_matrix
• groebner_walk
• group
• group
• group
• group_algebra
• group_of_model
• gset
• guess
• h_star_polynomial
• h_star_polynomial
• h_vector
• h_vector
• hadamard
• hadamard_bound2
• hall_subgroup_classes
• hall_subgroups
• hall_system
• harmonic
• has_attribute
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• has_complement
• has_du_val_singularities
• has_edge
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• has_index
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• has_norm
• has_number_of_perfect_groups
• has_number_of_primitive_groups
• has_number_of_small_groups
• has_number_of_transitive_groups
• has_perfect_group_identification
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• has_preimage_with_preimage
• has_primitive_group_identification
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• has_quick_triangulation
• has_quotient
• has_right_bound
• has_small_group_identification
• has_small_groups
• has_terminal_singularities
• has_torusfactor
• has_transitive_group_identification
• has_transitive_groups
• has_upper_bound
• has_vertex
• has_vertical_map
• has_zero_entropy
• hash
• hasse_invariant
• hasse_invariant
• hasse_invariant
• hcat
• hcat!
• height
• height
• height_bits
• height_bits
• hermitian_form
• hermitian_genera
• hermitian_lattice
• hermitian_lattice
• hermitian_lattice
• hermitian_lattice
• hermitian_local_genera
• hermitian_space
• hermitian_space
• hermitian_structure
• hessenberg
• hex
• highest_root
• hilbert
• hilbert_basis
• hilbert_basis
• hilbert_class_field
• hilbert_class_polynomial
• hilbert_function
• hilbert_polynomial
• hilbert_polynomial
• hilbert_polynomial
• hilbert_series
• hilbert_series_expanded
• hilbert_series_reduced
• hilbert_symbol
• hirzebruch_surface
• hnf
• hnf
• hnf
• hnf!
• hnf_extend!
• hnf_kannan_bachem
• hnf_modular
• hnf_modular_eldiv
• hnf_with_transform
• hnf_with_transform
• hodge_h11
• hodge_h12
• hodge_h13
• hodge_h22
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom
• hom_direct_sum
• hom_direct_sum
• hom_product
• hom_tensor
• hom_tensor
• hom_tensor
• hom_without_reversing_direction
• homogeneous_component
• homogeneous_component
• homogeneous_component
• homogeneous_component
• homogeneous_components
• homogeneous_components
• homogeneous_coordinate_ring
• homogeneous_coordinates_on_affine_cone
• homogenization_map
• homogenizer
• homogenizer
• homology
• homology
• homology
• homomorphism_of_semidirect_product
• homomorphism_of_wreath_product
• homomorphism_to_element
• hook_length
• hook_lengths
• hooklength
• horizontal_direction
• horizontal_map
• howell_form
• howell_form
• hyperbolic_plane_lattice
• hyperelliptic_polynomials
• hypergeometric_1f1
• hypergeometric_1f1
• hypergeometric_1f1_regularized
• hypergeometric_1f1_regularized
• hypergeometric_2f1
• hypergeometric_2f1
• hypergeometric_u
• hypergeometric_u
• hyperkaehler_lattice
• hyperplane_class
• hyperplanes
• hypersimplex
• hypersurface_complement
• hypersurface_complement
• hypersurface_equation
• hypersurface_equation_parametrization
• hypersurface_model
• hypersurface_model
• hypertruncated_cube
• icosahedron
• id_hom
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal_as_module
• ideal_membership
• ideal_membership
• ideal_membership
• ideal_membership
• ideal_of_linear_relations
• ideal_of_linear_relations
• ideal_of_linear_relations
• ideal_sheaf
• ideal_sheaf
• ideal_sheaf
• idempotents
• idempotents
• identifier
• identifier
• identity_map
• identity_map
• identity_map
• identity_map
• identity_map
• identity_matrix
• identity_matrix
• identity_matrix
• identity_matrix
• imag
• imag
• image
• image
• image
• image
• image
• image
• image
• image
• image
• image
• image
• image_centralizer_in_Oq
• image_ideal
• image_ideal
• immaculate_line_bundles
• in
• in
• in
• in
• in
• in
• in
• in
• in
• in
• in
• in
• in
• incidence_matrix
• inclusion_morphism
• independent_sets
• index
• index
• index_of_new_ray
• indicator
• indices_of_trivial_ci_curves
• induce
• induce
• induced_automorphism
• induced_cyclic
• induced_ring_ordering
• inequations
• inertia_subgroup
• infinite_places
• infinity
• infinity
• infinity
• inflate
• inflate
• inflate
• inflate
• inflate
• inflate
• initial
• initial
• inneighbors
• inner_automorphism
• inner_automorphism_group
• inner_cartesian_power
• inner_direct_product
• inner_point
• inner_product
• inner_product
• integer_genera
• integer_lattice
• integer_lattice
• integer_lattice_with_isometry
• integer_lattice_with_isometry
• integral
• integral
• integral
• integral
• integral_basis
• integral_split
• integrate
• interior_lattice_points
• interpolate
• interreduce!
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersect
• intersection_form
• intersection_matrix
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• intersection_multiplicity
• inv
• inv
• inv
• inv
• inv
• inv
• inv
• inv
• inv
• inv
• inv!
• inv_coeff_ideals
• invariant_alternating_forms
• invariant_bilinear_form
• invariant_bilinear_forms
• invariant_coinvariant_pair
• invariant_coinvariant_pair
• invariant_factors
• invariant_hermitian_forms
• invariant_lattice
• invariant_lattice
• invariant_lattice
• invariant_quadratic_form
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• invariant_sesquilinear_form
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• invariant_symmetric_forms
• invariants
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• inverse
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• invert_birational_map
• invlex
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• involution
• involution
• iroot
• iroot
• irreducible_components
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• is_simplicial
• is_simplicial
• is_singular
• is_skew_symmetric
• is_smooth
• is_smooth
• is_smooth
• is_smooth
• is_smooth
• is_snf
• is_snf
• is_snf
• is_snf
• is_solvable
• is_solvable
• is_solvable
• is_sphere
• is_split
• is_sporadic_simple
• is_sporadic_simple
• is_square
• is_square
• is_square
• is_square
• is_square
• is_square
• is_square_with_sqrt
• is_squarefree
• is_standard
• is_standard_graded
• is_subfield
• is_subfield
• is_subfield_normal
• is_subgroup
• is_sublattice
• is_sublattice_with_relations
• is_submodule
• is_subscheme
• is_subset
• is_subset
• is_subset
• is_subset
• is_subset
• is_supersolvable
• is_supersolvable
• is_surjective
• is_surjective
• is_symmetric
• is_symmetric
• is_table_of_marks_name
• is_tamely_ramified
• is_tamely_ramified
• is_term
• is_term
• is_term
• is_term_recursive
• is_ternary
• is_terse
• is_torsion
• is_torsion_unit
• is_totally_complex
• is_totally_positive
• is_totally_real
• is_transitive
• is_transverse_intersection
• is_transverse_intersection
• is_trivial
• is_trivial
• is_uinf
• is_undefined
• is_unimodular
• is_unipotent
• is_unit
• is_unit
• is_unit
• is_unit
• is_unital
• is_univariate
• is_univariate
• is_unknown
• is_upper_triangular
• is_upper_triangular
• is_vertical_k_separation
• is_very_ample
• is_very_ample
• is_very_ample
• is_weak_popov
• is_weakly_ramified
• is_z_graded
• is_zero
• is_zero
• is_zero
• is_zero
• is_zero
• is_zero
• is_zero
• is_zero
• is_zm_graded
• isempty
• isempty
• isequal
• isequal
• isequal
• isequal
• iseven
• iseven
• iseven
• iseven
• iseven
• isfinite
• isfinite
• isfinite
• isfinite
• isinf
• isinteger
• isinteger
• isinteger
• isinteger
• isinteger
• isinteger
• isinteger
• iso_gap_oscar
• iso_oscar_gap
• isodd
• isodd
• isometry
• isometry
• isometry_group
• isomorphism
• isomorphism
• isomorphism
• isomorphism_from_generic_fibers
• isomorphisms
• isone
• isone
• isone
• isone
• isone
• isone
• isqrt
• isqrtrem
• isreal
• isreal
• isreal
• issubset
• issubset
• iszero
• iszero
• iszero
• iszero
• iszero
• iszero
• iterate_basis
• iterate_basis
• j_invariant
• j_invariant
• j_invariant
• jacobi_symbol
• jacobi_symbol
• jacobi_theta
• jacobi_theta
• jennings_series
• johnson_solid
• jordan_decomposition
• journal_doi
• journal_link
• journal_model_equation_number
• journal_model_page
• journal_model_section
• journal_name
• journal_pages
• journal_report_numbers
• journal_volume
• journal_year
• jukes_cantor_model
• k3_d10_pi9_quart_1
• k3_d10_pi9_quart_2
• k3_d11_pi11_ss_0
• k3_d11_pi11_ss_1
• k3_d11_pi11_ss_2
• k3_d11_pi11_ss_3
• k3_d11_pi12
• k3_d12_pi14
• k3_d13_pi16
• k3_d14_pi19
• k3_d7_pi5
• k3_d8_pi6
• k3_d9_pi8
• k3_lattice
• k_cyclic_polytope
• katsura
• katsura
• kbar3
• kernel
• kernel
• kernel
• kernel
• kernel
• kernel
• kernel
• kernel_lattice
• kernel_lattice
• kernel_lattice
• kimura2_model
• kimura3_model
• kissing_number
• klee_minty_cube
• klein_bottle
• known_class_fusion
• known_class_fusions
• kodaira_neron_model
• koszul_complex
• koszul_homology
• koszul_matrix
• kronecker_symbol
• kummer_failure
• laplacian_matrix
• lattice
• lattice
• lattice
• lattice
• lattice
• lattice
• lattice
• lattice
• lattice_in_same_ambient_space
• lattice_points
• lattice_volume
• laurent_polynomial_ring
• lcm
• lcm
• lcm
• lcm
• lcm!
• leading_coefficient
• leading_coefficient
• leading_coefficient
• leading_ideal
• leading_ideal
• leading_monomial
• leading_term
• lecture_hall_simplex
• leech_lattice
• left_acting_group
• left_bound
• left_coset
• left_cosets
• left_ideal
• left_transversal
• leglength
• length
• length
• length
• length
• length
• length
• length
• length
• length
• level
• level
• lex
• lgamma
• lgamma
• lgamma
• lgamma
• lie_algebra
• lie_algebra
• lie_algebra
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift_homomorphism_contravariant
• lift_homomorphism_covariant
• lindep
• lindep
• lindep
• lindep
• lindep
• lindep
• line_bundle
• lineality_dim
• lineality_dim
• lineality_dim
• lineality_dim
• lineality_dim
• lineality_space
• lineality_space
• lineality_space
• lineality_space
• lineality_space
• linear_characters
• linear_characters
• linear_halfspace
• linear_hyperplane
• linear_program
• linear_quotient
• linear_symmetries
• linear_system
• linearly_reductive_group
• linearly_reductive_group
• link_subcomplex
• literature_identifier
• literature_model
• lll
• lll
• lll
• lll
• lll!
• lll_basis
• lll_basis
• lll_gram
• lll_gram!
• lll_gram_with_transform
• lll_with_removal
• lll_with_removal_transform
• lll_with_transform
• load
• load_lp
• load_mps
• local_basis_matrix
• local_modification
• local_symbol
• local_symbols
• localization
• localization
• log
• log
• log
• log
• log
• log_barnes_g
• log_barnes_g
• log_integral
• log_integral
• log_integral_offset
• log_integral_offset
• log_pi_i
• log_sinpi
• log_sinpi
• loops
• lorenz_module
• low_index_subgroup_classes
• low_index_subgroups
• lower_bound
• lower_central_series
• lower_central_series
• lower_triangular_matrix
• lower_triangular_matrix
• lu
• make_elementary
• map
• map
• map!
• map_coefficients
• map_coefficients
• map_coefficients
• map_entries
• map_entries
• map_from_character_lattice_to_torusinvariant_weil_divisor_group
• map_from_func
• map_from_torusinvariant_cartier_divisor_group_to_picard_group
• map_from_torusinvariant_cartier_divisor_group_to_torusinvariant_weil_divisor_group
• map_from_torusinvariant_weil_divisor_group_to_class_group
• map_gens_of_chow_ring_to_cox_ring
• map_on_affine_cones
• map_word
• map_word
• marginal
• markov_ring
• mass
• mass
• mass
• matrix
• matrix
• matrix
• matrix
• matrix
• matrix
• matrix
• matrix
• matrix_group
• matrix_ordering
• matrix_repr
• matrix_repr
• matrix_repr
• matrix_repr
• matrix_repr_basis
• matrix_repr_basis
• matroid_base_polytope
• matroid_from_bases
• matroid_from_circuits
• matroid_from_hyperplanes
• matroid_from_matrix_columns
• matroid_from_matrix_rows
• matroid_from_matroid_hex
• matroid_from_nonbases
• matroid_from_revlex_basis_encoding
• matroid_groundset
• matroid_hex
• max_GC_rank_polytope
• max_exp
• max_lattice_pts_in_facet
• max_precision
• maxabs_exp
• maxes
• maximal_abelian_quotient
• maximal_abelian_subfield
• maximal_abelian_subfield
• maximal_blocks
• maximal_cells
• maximal_cones
• maximal_extension
• maximal_integral_lattice
• maximal_integral_lattice
• maximal_integral_lattice
• maximal_integral_lattice
• maximal_normal_subgroups
• maximal_polyhedra
• maximal_polyhedra
• maximal_polyhedra_and_multiplicities
• maximal_subgroup_classes
• maximal_subgroups
• maximum
• maximum
• maximum
• maximum
• maximum
• midpoint
• midpoint
• min_exp
• min_weights
• minimal_betti_table
• minimal_betti_table
• minimal_block_reps
• minimal_faces
• minimal_faces
• minimal_faces
• minimal_generating_set
• minimal_generating_set
• minimal_nonfaces
• minimal_normal_subgroups
• minimal_polynomial
• minimal_polynomial
• minimal_primes
• minimal_size_generating_set
• minimal_subalgebra_generators
• minimum
• minimum
• minimum
• minimum
• minimum
• minimum
• minimum
• minimum
• minkowski_map
• minkowski_map
• minkowski_matrix
• minor
• minors
• minpoly
• minpoly
• minpoly
• minpoly
• minpoly
• minpoly
• mixed_integer_linear_program
• mod
• mod
• mod
• mod
• mod!
• mod!
• mod_sym!
• mod_sym!
• mod_sym!
• model
• model_parameters
• modular_delta
• modular_delta
• modular_lambda
• modular_lambda
• modular_proj
• modular_weber_f
• modular_weber_f
• modular_weber_f1
• modular_weber_f1
• modular_weber_f2
• modular_weber_f2
• module_syzygies
• modulus
• modulus
• modulus
• modulus
• modulus_bilinear_form
• modulus_quadratic_form
• moebius_kantor_matroid
• moebius_mu
• moebius_mu
• molien_series
• monomial_basis
• monomial_basis
• monomial_basis
• monomial_to_newton!
• mordell_weil_sublattice
• mordell_weil_torsion
• mori_cone
• morphism
• morphism
• morphism
• morphism
• morphism_from_cox_variety
• morphism_on_class_group
• morphism_on_picard_group
• morphism_on_torusinvariant_cartier_divisor_group
• morphism_on_torusinvariant_weil_divisor_group
• mukai_lattice
• mul!
• mul_red!
• mullow
• mullow
• mulmod
• multi_hilbert_function
• multi_hilbert_series
• multi_hilbert_series_reduced
• multiplicative_group
• multiplicative_group_generators
• multiplicative_jordan_decomposition
• multiplicities
• multiplicities
• multiplicities_eigenvalues
• multiplicity
• multiplicity
• multiplicity
• multiply_column
• multiply_column!
• multiply_row
• multiply_row!
• multiset
• n_cones
• n_connected_components
• n_edges
• n_facets
• n_facets
• n_facets
• n_gon
• n_maximal_cells
• n_maximal_cones
• n_maximal_polyhedra
• n_maximal_polyhedra
• n_polyhedra
• n_polyhedra
• n_rays
• n_rays
• n_rays
• n_vertices
• n_vertices
• n_vertices
• n_vertices
• n_vertices
• name
• names_of_fusion_sources
• narrow_class_group
• natural_character
• natural_character
• natural_character
• natural_character
• nbits
• nef_cone
• neg!
• negdeglex
• negdegrevlex
• neginvlex
• neglex
• negwdeglex
• negwdegrevlex
• neighbors
• newell_patch
• newell_patch
• newell_patch_with_orderings
• newick
• newton_polytope
• newton_to_monomial!
• next_calkin_wilf
• next_minimal
• next_signed_calkin_wilf
• next_signed_minimal
• nextpow2
• nf
• nf
• nice_gens
• nilpotency_class
• nnz
• noether_normalization
• non_fano_matroid
• non_flat_locus
• non_pappus_matroid
• nonbases
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm
• norm2
• norm_change_const
• norm_equation
• norm_group
• norm_group
• normal_basis
• normal_closure
• normal_closure
• normal_closure
• normal_fan
• normal_form
• normal_form
• normal_form
• normal_form
• normal_subgroup
• normal_subgroup
• normal_subgroups
• normal_toric_varieties_from_glsm
• normal_toric_varieties_from_star_triangulations
• normal_toric_variety
• normal_toric_variety
• normal_toric_variety_from_glsm
• normal_toric_variety_from_star_triangulation
• normalization
• normalization
• normalization
• normalization_with_delta
• normalize!
• normalize!
• normalized_volume
• normalizer
• normalizer
• normalizer
• normalizer
• norms
• nrels
• nrows
• nullity
• nullspace
• nullspace_right_rational
• num_coeff
• number_field
• number_field
• number_field
• number_field
• number_field
• number_of_atlas_groups
• number_of_columns
• number_of_columns
• number_of_columns
• number_of_compositions
• number_of_compositions
• number_of_conjugacy_classes
• number_of_digits
• number_of_factors
• number_of_generators
• number_of_generators
• number_of_partitions
• number_of_partitions
• number_of_partitions
• number_of_perfect_groups
• number_of_primitive_groups
• number_of_rows
• number_of_rows
• number_of_rows
• number_of_small_groups
• number_of_standard_tableaux
• number_of_transitive_groups
• number_of_variables
• number_of_weak_compositions
• number_states
• numerator
• numerator
• numerator
• numerator
• numerator
• numpart
• numpart
• numpart
• numpart
• objective_function
• oct
• od_for_specht_module
• od_from_atlas_group
• od_from_eigenvalues
• od_from_order
• od_from_p_subgroup
• oddity
• omega_group
• on_echelon_form_mats
• on_indeterminates
• on_lines
• on_sets
• on_simplicial_complex
• on_subgroups
• on_tuples
• one
• one
• one
• one
• one
• one!
• onei
• onei
• onei
• ones_matrix
• opposite_algebra
• optimal_solution
• optimal_value
• optimal_value
• optimal_vertex
• orbit
• orbit
• orbit_polytope
• orbits
• order
• order
• order
• order
• order
• order
• order
• order
• order
• order
• order
• order
• order
• order
• order
• order
• order_field_of_definition
• order_of_isometry
• order_of_isometry
• order_of_vanishing
• orders_centralizers
• orders_class_representatives
• orders_class_representatives
• orders_perfect_groups
• ordinary_table
• orthogonal_basis
• orthogonal_complement
• orthogonal_components
• orthogonal_discriminant
• orthogonal_discriminants
• orthogonal_group
• orthogonal_projection
• orthogonal_sign
• orthogonal_submodule
• orthogonal_submodule
• orthogonal_submodule
• orthogonal_submodule
• outneighbors
• overlaps
• overlaps
• overlaps
• overlaps
• overlaps
• overlaps
• overlaps
• overlaps
• overlattice
• p_central_series
• padic_field
• paper_authors
• paper_buzzwords
• paper_description
• paper_title
• pappus_matroid
• parallel_extension
• parametrization
• parametrization
• parametrization
• parametrization
• parent
• parent
• parent
• parent
• parent
• parent
• parent_type
• parity
• partition
• partitions
• partitions
• partitions
• partitions
• partitionseq
• passes_elementary_quantization_checks
• patches
• pbw_algebra
• pcore
• pcore
• pentagonal_hexecontahedron
• pentagonal_icositetrahedron
• perfect_group
• perfect_group_identification
• perles_matroid
• perles_nonrational_8_polytope
• perm
• permtype
• permutahedron
• permutation
• permutation_group
• permutation_matrix
• permuted
• pfaffian
• pfaffians
• phylogenetic_tree
• picard_class
• picard_group
• picard_group
• picard_index
• pile_polytope
• pitman_stanley_polytope
• platonic_solid
• pluecker_indices
• pmaximal_overorder
• point_class
• point_vector
• points
• pol_elementary_divisors
• polarize
• polarize
• polygamma
• polygamma
• polyhedra
• polyhedra_of_dim
• polyhedral_complex
• polyhedral_complex
• polyhedral_fan
• polyhedral_fan
• polyhedral_fan_from_rays_action
• polyhedron
• polyhedron
• polyhedron
• polyhedron
• polylog
• polylog
• polylog
• polylog
• polynomial
• polynomial
• polynomial
• polynomial
• polynomial_ring
• polynomial_ring
• polynomial_ring
• polynomial_ring
• polynomial_ring_only
• polynomial_to_power_sums
• polytope_index
• pontryagin_class
• popcount
• popov
• popov_with_transform
• positive_hull
• possible_class_fusions
• poverorder
• poverorders
• pow
• power_class
• power_product_class
• power_reduce
• power_sums_to_polynomial
• powermod
• powers
• powers_of_element
• ppio
• pradical
• pradical
• precision
• precision
• precision
• precision
• preimage
• preimage
• preimage
• preimage
• preimage_map
• preimage_map
• present_as_cokernel
• present_finite_extension_ring
• presentation
• preserved_quadratic_forms
• preserved_sesquilinear_forms
• pretty
• pretty
• prevpow2
• primary_decomposition
• primary_invariants
• prime
• prime
• prime
• prime
• prime_decomposition_type
• prime_field
• prime_ideals_up_to
• prime_of_pgroup
• primes
• primes
• primitive_closure
• primitive_closure
• primitive_collections
• primitive_embeddings
• primitive_embeddings
• primitive_embeddings
• primitive_extensions
• primitive_group
• primitive_group_identification
• primorial
• primorial
• primpart
• principal_extension
• principal_generator
• principal_generator_fac_elem
• principal_subfields
• print_constraints
• print_constraints
• probability_map
• probability_ring
• product
• product
• product
• project_full
• projective_closure
• projective_general_linear_group
• projective_geometry
• projective_omega_group
• projective_orthogonal_group
• projective_plane
• projective_space
• projective_space
• projective_space
• projective_special_linear_group
• projective_special_orthogonal_group
• projective_special_unitary_group
• projective_symplectic_group
• projective_unitary_group
• projectivization
• projectivization
• prune_with_map
• pseudo_basis
• pseudo_basis
• pseudo_del_pezzo_polytope
• pseudo_hnf
• pseudo_hnf_with_transform
• pseudo_inv
• pseudo_matrix
• pseudo_matrix
• pseudo_matrix
• pseudo_matrix
• pseudodivrem
• pseudorem
• psubgroups
• pullback
• pullback
• pullback
• pullback
• push!
• push_term!
• pushforward
• pushforward
• pushforward_on_algebraic_lattices
• put_over_concrete_base
• pyramid
• qadic_field
• quadratic_defect
• quadratic_field
• quadratic_form
• quadratic_form
• quadratic_lattice
• quadratic_lattice
• quadratic_lattice
• quadratic_lattice
• quadratic_product
• quadratic_space
• quadratic_space
• quadratic_space
• quadratic_space_with_isometry
• quadratic_space_with_isometry
• quantum_automorphism_group
• quantum_automorphism_group
• quantum_symmetric_group
• quaternion_group
• quintic_elliptic_scroll
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quotient
• quotient
• quotient
• quotient
• quotient_ring_as_module
• radical
• radical
• radical
• radical_bilinear
• radical_extension
• radical_membership
• radical_quadratic
• radius
• radius
• ramification_group
• ramification_index
• ramified_primes
• rand
• rand
• rand
• rand
• rand
• rand
• rand
• rand
• rand
• rand
• rand01_polytope
• rand_bits
• rand_bits
• rand_bits_prime
• rand_box_polytope
• rand_cyclic_polytope
• rand_metric
• rand_metric_int
• rand_normal_polytope
• rand_pseudo
• rand_row
• rand_spherical_polytope
• rand_subpolytope
• random_realization
• random_variables
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank
• rank_action
• ranks
• rational_d10_pi8
• rational_d10_pi9_quart_1
• rational_d10_pi9_quart_2
• rational_d11_pi11_ss_0
• rational_d11_pi11_ss_1
• rational_d11_pi11_ss_inf
• rational_d7_pi4
• rational_d8_pi5
• rational_d8_pi6
• rational_d9_pi6
• rational_d9_pi7
• rational_equivalence_class
• rational_equivalence_class
• rational_equivalence_class
• rational_equivalence_class
• rational_equivalence_class
• rational_equivalence_class
• rational_equivalence_class
• rational_point_conic
• rational_representative
• rational_span
• rational_span
• rational_span
• rational_spinor_norm
• rational_spinor_norm
• rational_to_continued_fraction_hirzebruch_jung
• rationals_as_number_field
• ray_class_field
• ray_class_field
• ray_class_field
• ray_class_field
• ray_class_field
• ray_class_group
• ray_degrees
• ray_vector
• rays
• rays
• rays
• rays
• rays
• rays
• rays_modulo_lineality
• rays_modulo_lineality
• rays_modulo_lineality
• rays_modulo_lineality
• rays_modulo_lineality
• reading_word
• real
• real
• real_embeddings
• real_places
• real_projective_plane
• realization
• realization
• realization_preview
• realization_space
• realize
• realize_maximally_on_open_subset
• realize_on_open_subset
• realize_on_patch
• recession_cone
• recognize
• reconstruct
• reconstruct
• reduce
• reduce
• reduce
• reduce
• reduce
• reduce!
• reduce_full
• reduce_ideal
• reduce_mod
• reduce_mod
• reduce_with_quotients
• reduce_with_quotients_and_unit
• reduced_characteristic_polynomial
• reduced_discriminant
• reducible_fibers
• regular_120_cell
• regular_24_cell
• regular_600_cell
• regular_character
• regular_character
• regular_triangulation
• regular_triangulations
• regulator
• relations
• relative_ambient_dimension
• relative_class_number
• relative_interior_point
• relative_simple_extension
• relators
• rels
• rem!
• rem_edge!
• rem_vertex!
• rem_vertices!
• remove
• remove
• representation_from_weights
• representation_matrix
• representation_matrix
• representation_matrix
• representation_on_forms
• representative
• representative
• representative
• representative
• representative
• representative
• representative
• representative
• representative
• representative
• representatives
• representatives
• representatives_of_hermitian_type
• representatives_of_hermitian_type
• representatives_of_hermitian_type
• represents
• represents
• rescale
• rescale
• rescale
• rescale
• rescale
• rescale
• rescale
• rescale
• rescale
• reshape_to_varnames
• residue_field
• residue_ring
• resolution_generating_sections
• resolution_zero_sections
• resolutions
• resolve
• resolvent
• restrict
• restrict
• restrict
• restrict
• restrict
• restrict
• restrict_automorphism
• restrict_homomorphism
• restrict_scalars
• restricted_map
• restriction
• resultant
• resx
• reverse
• reverse
• reverse
• reverse
• reverse
• reverse_rows!
• revlex_basis_encoding
• reynolds_operator
• reynolds_operator
• reynolds_operator
• rgamma
• rgamma
• rgamma
• rgamma
• right_acting_group
• right_bound
• right_coset
• right_cosets
• right_ideal
• right_transversal
• ring
• ring_class_field
• ring_class_group
• ring_of_multipliers
• rising_factorial
• rising_factorial
• rising_factorial
• rising_factorial
• rising_factorial
• rising_factorial
• rising_factorial
• rising_factorial
• rising_factorial
• rising_factorial2
• rising_factorial2
• rising_factorial2
• rising_factorial2
• root
• root
• root
• root
• root
• root_lattice
• root_lattice_recognition
• root_lattice_recognition_fundamental
• root_of_unity
• root_of_unity
• root_of_unity
• root_of_unity
• root_of_unity_as_args
• roots
• roots
• roots
• roots
• roots
• roots
• roots_upper_bound
• roots_upper_bound
• row
• rowlength
• rref
• rref_rational
• rsqrt
• rsqrt
• rsqrt
• rsqrt
• rss_associahedron
• saturate
• saturate
• saturated_ideal
• saturation
• saturation
• saturation_with_index
• saturation_with_index
• save
• save_lp
• save_mps
• scalar_matrix
• scalar_product
• scale
• scale
• scale
• scale
• scale
• scale
• scale
• scale
• scale_row!
• scales
• scheme
• scheme
• scheme
• schensted
• schubert_class
• schubert_classes
• schubert_classes
• schur_cover
• schur_index
• schur_multiplier
• schur_polynomial
• secondary_cone
• secondary_cone
• secondary_invariants
• secondary_polytope
• section
• sectional_genus
• segre_class
• semi_invariants
• semidirect_product
• semistandard_tableaux
• separating_hyperplanes
• series_extension
• set_assertion_level
• set_attribute!
• set_coefficient!
• set_coordinate_names
• set_coordinate_names_of_torus
• set_global_tate_model
• set_html_as_latex
• set_mordell_weil_basis!
• set_name!
• set_precision!
• set_precision!
• set_theoretic_intersection
• set_theoretic_intersection
• set_variable!
• set_verbosity_level
• set_weierstrass_model
• setbit!
• setindex!
• setindex!
• setpermstyle
• setunion
• setunion
• setyoungtabstyle
• shape
• sheaf_cohomology
• shift_left
• shift_left
• shift_left
• shift_right
• shift_right
• shift_right
• short_vectors
• short_vectors_iterator
• shortest_path_dijkstra
• shortest_vectors
• show
• show
• show_OD_info
• show_with_ODs
• sign
• sign
• sign
• sign
• sign
• sign
• sign
• sign
• sign_imag
• sign_real
• signature
• signature
• signature
• signature
• signature
• signature
• signature_tuple
• signature_tuple
• signature_tuple
• signatures
• signatures
• signed_permutahedron
• signs
• similarity!
• simple_extension
• simplest_between
• simplest_rational_inside
• simplest_rational_inside
• simplex
• simplicial_complex
• simplified_dual_graph
• simplified_fp_group
• simplified_simple_extension
• simplify
• simplify
• simplify
• simplify
• simplify
• simplify
• sin
• sin_integral
• sin_integral
• sincospi
• singular_loci
• singular_loci
• singular_loci
• sinh_integral
• sinh_integral
• sinpi
• size
• size
• size
• size
• small_generating_set
• small_group
• small_group_identification
• smaller_degree_permutation_representation
• snf
• snf
• snf
• snf
• snf
• snf
• snf_diagonal
• snf_with_transform
• snub_cube
• snub_dodecahedron
• socle
• solvable_radical
• solve
• solve
• solve_dixon_sf
• solve_ineq
• solve_init
• solve_lp
• solve_milp
• solve_mixed
• solve_mixed
• solve_non_negative
• space
• spanning_sets
• sparse
• sparse_matrix
• sparse_matrix
• sparse_matrix
• sparse_matrix
• sparse_matrix
• sparse_row
• sparse_row
• sparse_row
• sparse_row
• sparsity
• spec
• spec
• spec
• special_linear_group
• special_linear_lie_algebra
• special_orthogonal_group
• special_orthogonal_lie_algebra
• special_unitary_group
• specialized_fourier_transform
• splitting_of_hermitian_prime_power
• splitting_of_mixed_prime_power
• splitting_of_prime_power
• splitting_of_pure_mixed_prime_power
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt
• sqrt1pm1
• sqrt1pm1
• sqrtmod
• sqrtpos
• sqrtpos
• src
• stabilizer
• stabilizer
• stable_set_polytope
• stable_submodules
• standard_basis
• standard_basis_with_transformation_matrix
• standard_finite_field
• standard_module
• standard_tableaux
• stanley_reisner_ideal
• stanley_reisner_ideal
• stanley_reisner_ideal
• stanley_reisner_ideal
• stanley_reisner_ring
• stanley_reisner_ring
• star_subcomplex
• star_subdivision
• star_subdivision
• state_space
• straight_line_program
• strictly_lower_triangular_matrix
• strictly_upper_triangular_matrix
• strong_echelon_form
• strong_echelon_form
• structure_constant_algebra
• structure_constant_algebra
• structure_constant_table
• structure_map
• structure_sheaf
• su5_tate_model_over_arbitrary_3d_base
• su5_weierstrass_model_over_arbitrary_3d_base
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub!
• subalgebra_membership
• subdivision_of_points
• subdivision_of_points
• subfields
• subfields
• subgroup_classes
• subgroups
• subgroups
• submodules
• submul!
• subquotient
• subscheme
• subscheme
• subsets
• subsets
• subsets
• subst
• subsystem
• sum
• sum_equivalent_classes
• summands
• sunit_group
• sunit_group_fac_elem
• sunit_mod_units_group_fac_elem
• supermodule
• supermodule
• support_function
• swap_cols
• swap_cols!
• swap_cols!
• swap_rows
• swap_rows!
• swap_rows!
• swinnerton_dyer
• sylow_subgroup
• sylow_subgroup
• sylow_system
• sylvester_matrix
• symbol
• symbols
• symbols
• symbols
• symmetric_form
• symmetric_group
• symmetric_parts
• symmetric_power
• symmetric_power
• symmetric_power
• symmetrizations
• symplectic_components
• symplectic_group
• symplectic_lie_algebra
• syzygy_generators
• t2
• table_of_marks
• table_of_marks
• table_of_marks
• tail
• tail
• tan
• tangent_bundle
• tangent_bundle
• tangent_lines
• tangent_lines
• tangent_space
• tangent_space
• tanpi
• tate_ideal_sheaf
• tate_polynomial
• tate_section_a1
• tate_section_a2
• tate_section_a3
• tate_section_a4
• tate_section_a6
• tautological_bundle
• tautological_bundles
• taxa
• teichmuller
• teichmuller
• tensor_power
• tensor_product
• tensor_product
• tensor_product
• tensor_product
• tensor_product
• tensor_product
• tensor_product
• tensor_ring
• terse
• test_experimental_module
• test_module
• tetrahedron
• theta_qexp
• to_univariate
• todd_class
• todd_class
• top_chern_class
• topological_intersection_numbers_among_ci_curves
• topological_intersection_numbers_among_nontrivial_ci_curves
• tor
• toric_divisor
• toric_divisor
• toric_divisor
• toric_divisor_class
• toric_divisor_class
• toric_divisor_class
• toric_divisor_class
• toric_ideal
• toric_ideal
• toric_ideal
• toric_identity_morphism
• toric_line_bundle
• toric_line_bundle
• toric_line_bundle
• toric_line_bundle
• toric_line_bundle
• toric_line_bundle
• toric_morphism
• toric_morphism
• toric_variety
• toric_variety
• toric_variety
• toric_variety
• toric_variety
• toric_variety
• toric_variety
• torsion_free_rank
• torsion_quadratic_module
• torsion_quadratic_module
• torsion_subgroup
• torsion_unit_group
• torsion_unit_order
• torsion_units
• torsion_units_gen_order
• torsion_units_generator
• torus
• torus_group
• torusinvariant_cartier_divisor_group
• torusinvariant_prime_divisors
• torusinvariant_weil_divisor_group
• total_chern_class
• total_complex
• total_pontryagin_class
• total_segre_class
• total_space
• total_transform
• tr
• tr
• tr
• tr
• tr
• tr
• trace_matrix
• trace_of_frobenius
• trace_of_frobenius
• trailing_coefficient
• trailing_coefficient
• trailing_coefficient
• trailing_zeros
• transform_row
• transform_row!
• transition_matrices
• transitive_group
• transitive_group_identification
• transitivity
• translation_morphism
• transportation_polytope
• transpose
• transpose
• trim
• trim
• trim
• trim
• trivial_character
• trivial_character
• trivial_divisor
• trivial_divisor_class
• trivial_lattice
• trivial_line_bundle
• trivial_line_bundle
• trivial_module
• trivial_morphism
• trivial_subgroup
• trivializing_covering
• tropical_hypersurface
• tropical_linear_space
• tropical_matrix
• tropical_median_consensus
• tropical_pluecker_vector
• tropical_polynomial
• tropical_polynomial
• tropical_semiring
• tropical_semiring_map
• tropical_semiring_map
• tropical_semiring_map
• tropical_semiring_map
• tropical_variety
• tropical_variety
• truncate
• truncate
• truncate
• truncate
• truncate
• truncate
• truncate
• tstbit
• tune
• tune
• tune
• tutte_connectivity
• tutte_polynomial
• twist
• twisting_sheaf
• two_neighbor_step
• two_sided_ideal
• type
• undefined
• underlying_morphism
• underlying_scheme
• underlying_scheme
• underlying_scheme
• uniform_matroid
• uniformizer
• unique_integer
• unique_integer
• unique_integer
• unique_integer
• unique_integer
• unique_integer
• unit
• unit
• unit_group
• unit_group_fac_elem
• unit_group_rank
• unitary_group
• universal_polynomial_ring
• unknown
• unknowns
• unramified_extension
• unsigned_infinity
• update_mwl_basis!
• upgrade
• upgrade_data
• upper_bound
• upper_bound
• upper_central_series
• upper_triangular_matrix
• upper_triangular_matrix
• valence_mc
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• value_module
• value_module_quadratic_form
• vamos_matroid
• vanishing_ideal
• vanishing_ideal
• vanishing_ideal
• vanishing_ideal
• vanishing_ideal
• vanishing_sets
• var
• var
• var_index
• variable_names
• variety
• variety
• variety
• variety
• variety
• variety
• variety
• variety
• vars
• vcat
• vcat!
• vector_space
• vector_space_dimension
• verify_euler_characteristic_from_hodge_numbers
• veronese
• versioninfo
• vertex_edge_graph
• vertex_figure
• vertex_sizes
• vertical_connectivity
• vertical_direction
• vertical_map
• vertices
• vertices
• vertices
• vertices
• vertices_and_rays
• vertices_and_rays
• vinberg_algorithm
• visualize
• visualize
• volume
• volume
• volume_form
• walls
• wdeglex
• wdegrevlex
• weak_composition
• weak_compositions
• weak_popov
• weak_popov_with_transform
• weierstrass_chart
• weierstrass_chart_on_minimal_model
• weierstrass_contraction
• weierstrass_ideal_sheaf
• weierstrass_model
• weierstrass_model
• weierstrass_model
• weierstrass_model
• weierstrass_model
• weierstrass_model
• weierstrass_model_over_del_pezzo_surface
• weierstrass_model_over_hirzebruch_surface
• weierstrass_model_over_projective_space
• weierstrass_p
• weierstrass_p
• weierstrass_polynomial
• weierstrass_section_f
• weierstrass_section_g
• weight
• weight_cone
• weight_ordering
• weighted_projective_space
• weighted_resolution_generating_sections
• weighted_resolution_zero_sections
• weighted_resolutions
• weights
• weil_divisor
• weil_divisor
• weil_divisor
• weil_divisor
• weyl_algebra
• weyl_vector
• wildanger_field
• with_ordering
• witt_index
• witt_invariant
• witt_invariant
• wreath_product
• write_as_full
• young_tableau
• zero
• zero
• zero
• zero
• zero
• zero
• zero
• zero!
• zero_algebra
• zero_locus_section
• zero_map
• zero_map
• zero_matrix
• zero_matrix
• zero_section
• zeta
• zeta
• zeta
• zeta
• zeta
• zeta
• zeta
• zeta
• zeta
• zeta
• zeta_log_residue
• zonotope
• zonotope_vertices_fukuda_matrix
• @CI_str
• @attr
• @attributes
• @free_group
• @hassert
• @import_all_serialization_functions
• @perm
• @perm_str
• @permutation_group
• @polynomial_ring
• @register_serialization_type
• @req
• @show_name
• @show_special
• @show_special_elem
• @v_do
• @varnames_interface
• @vprint
• @vprintln