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Oscar.jl
  • Welcome to OSCAR
    • Architecture
    • Notes for users of other computer algebra systems
    • Printing Options
    • Frequently Asked Questions
    • Saving and loading files
    • Complex Algorithms
    • Introduction
    • Basics
    • Subgroups
    • Quotients
    • Products of groups
    • Permutation groups
    • Finitely presented groups
    • Polycyclic groups
    • Matrix groups
    • Group actions
    • Group homomorphisms
    • Groups of automorphisms
    • Group libraries
      • Introduction
      • Elements
      • Morphisms
      • Structural Computations
    • Group characters
    • Group recognition
    • Tables of Marks
    • Introduction
    • Ring functionality
    • Integers
      • Univariate polynomial functionality
      • Sparse distributed multivariate polynomials
      • Power series
      • Generic Puiseux series
      • Power series and Laurent series
      • Puiseux series
    • Introduction
    • Field functionality
    • Rationals
    • Factored Elements
    • Class Field Theory
    • Generic fraction fields
      • Padics
      • Qadics
    • Finite fields
    • Algebraic numbers
    • Algebraic closure of finite prime fields
    • Introduction
    • Matrix functionality
    • Matrix Spaces
    • Linear solving
    • Generic matrix algebras
    • Sparse linear algebra
      • Finitely presented modules
      • Free Modules and Vector Spaces
      • Submodules
      • Quotient modules
      • Direct Sums
      • Module Homomorphisms
      • Introduction
      • Spaces
      • Lattices
      • Genera for hermitian lattices
      • Integer Lattices
      • Genera of Integer Lattices
      • Discriminant Groups
      • Vinberg's algorithm
    • Matrix implementation
    • Introduction
      • Introduction
      • Number field operations
      • Element operations
      • Internals
      • Introduction
      • Orders
      • Elements
      • Ideals
      • Fractional ideals
      • Introduction
      • Basics
      • Elliptic curves over finite fields
    • Abelian closure of the rationals
    • Galois Theory
    • Introduction
      • Introduction
      • Constructions
      • Polyhedron and polymake's Polytope
      • Auxiliary functions
    • Cones
    • Polyhedral Fans
    • Polyhedral Complexes
    • Subdivisions of Points
      • Linear Programs
      • Mixed Integer Linear Programs
    • Introduction
    • Creating Multivariate Rings
    • Ideals in Multivariate Rings
    • Affine Algebras and Their Ideals
    • Localized Rings and Their Ideals
      • Introduction
      • Free Modules
      • Subquotients
      • Ideals and Quotient Rings as Modules
      • Operations on Modules
      • Operations on Module Maps
      • Chain and Cochain Complexes
    • Homological Algebra
      • Monomial Orderings
      • Gröbner/Standard Bases Over Fields
      • Gröbner/Standard Bases Over $\mathbb Z$
      • Binomial Primary Decomposition
      • A Framework for Localizing Rings
      • Localizations of modules over computable rings
    • Introduction
    • Invariants of Finite Groups
    • Invariants of Tori
    • Invariants of Linearly Reductive Groups
    • Introduction
      • General schemes
      • Affine schemes
      • Morphisms of affine schemes
      • Rational Points on Affine Schemes
      • Covered schemes
      • Coverings
      • Morphisms of covered schemes
      • Projective schemes
      • Morphisms of projective schemes
      • Rational Points on Projective Schemes
      • Sheaves on covered schemes
      • Cycles and divisors
      • Affine Algebraic Sets
      • Projective Algebraic Sets
      • Affine Varieties
      • Projective Varieties
      • Affine plane curves
      • Projective Curves
      • Projective Plane Curves
      • Rational Parametrizations of Rational Plane Curves
      • Automorphism Groups of K3 surfaces
      • Borcherds' method for Enriques surfaces
      • Elliptic Surfaces
      • Adjunction Process for Surfaces
      • Rational Parametrization of Rational Surfaces
      • Nongeneral Type Surfaces in $\mathbb P^4$
      • Classifier/identifier specifically for du Val singularities
      • Sheaves on Projective Space
      • Introduction
      • Normal Toric Varieties
      • Cyclic Quotient Singularities
      • Toric Divisors
      • Toric Divisor Classes
      • Toric Line Bundles
      • Line bundle cohomology with cohomCalg
      • Cohomology Classes
      • Subvarieties
      • The Chow ring
      • ToricMorphisms
      • Toric Schemes
      • Toric Ideal Sheaves (Experimental)
      • Toric Blowups (Experimental)
      • Some Special Ideals
      • Architecture of affine schemes
    • Introduction
    • Tropical semirings, matrices, and polynomials
    • Tropical semiring maps
    • Tropical varieties
    • Tropical hypersurfaces
    • Tropical curves
    • Tropical linear spaces
    • Tropical Groebner theory
    • Tropicalization of polynomial ideals
    • Positive tropicalizations of linear ideals
    • Introduction
      • Introduction
      • Creating PBW-Algebras
      • Ideals in PBW-algebras
      • GR-Algebras: Quotients of PBW-Algebras
    • Free Associative Algebras
    • Introduction
    • Cartan matrices
    • Root systems
    • Weight lattices
    • Weyl groups
    • Graphs
    • Matroids
    • Simplicial Complexes
    • Phylogenetic Trees
      • Partitions
      • Multipartitions
      • Tableaux
      • Schur polynomials
      • Compositions
    • Introduction
    • GAP's SLPs
    • AbstractAlgebra's polynomial interface
  • References
  • Index
    • Introduction for new developers
    • Developer Style Guide
    • Documenting Code
    • Printing Details
    • Debugging Code
    • Caching Parent Objects
    • Serialization
    • Design Decisions
    • GAP Integration
    • Release management
    • Updating CHANGELOG.md
      • AbstractCollection
      • SubObjectIterator
    • Writing parallel methods
    • Adding new projects to experimental
      • Introduction
      • Graphical Models
      • Gaussian Graphical Models
      • Conditional independence statements
      • Discrete random variables
      • Algebraic Phylogenetics
      • Double complexes – the user's interface
      • Advice for the programmer
      • Introduction
      • An example documentation
      • Usage
      • Special ideals used for benchmarking
      • Introduction
      • Construction and basic functionality
      • Cox rings
      • Matroid Realization Spaces
      • Introduction
      • Access to precomputed OD data
      • Criteria for computing orthogonal discriminants
      • Miscellaneous functions
      • Parallelization in Oscar
      • $q$-analogs
      • Quadratic forms and isometries
      • Quadratic spaces with isometry
      • Lattices with isometry
      • Enumeration of isometries
      • Nikulin's theory on primitive embeddings
      • -
      • Introduction
      • Lie algebras
      • Ideals and Lie subalgebras
      • Lie algebra homomorphisms
      • Lie algebra modules
      • Lie algebra module homomorphisms
      • Weyl groups (experimental features)
      • Introduction
      • Functions for a monomial basis of highest weight modules
      • Introduction
      • Exterior Shifting
      • Partial Shift Graph
      • Partitioned Permutations
      • Welcome to FTheoryTools
      • Functionality for all F-theory models
      • Weierstrass models
      • Global Tate models
      • Hypersurface models
      • Literature constructions
      • G4-Fluxes
      • Introduction
      • Abstract Varieties
      • Abstract Bundles
      • Abstract Variety Maps
      • Blow-Ups
      • Schubert Calculus
      • Localization and Bott's Formula
      • Illustrating Examples From Enumerative Geometry
Version
  • Index
  • Index
GitHub
  • AbsAffineAlgebraicSet
  • AbsAffineRationalPoint
  • AbsAffineScheme
  • AbsAffineSchemeMor
  • AbsAffineVariety
  • AbsAlgebraicCycle
  • AbsCoveredScheme
  • AbsGluing
  • AbsIdealSheaf
  • AbsNumFieldOrder
  • AbsPreSheaf
  • AbsProjectiveAlgebraicSet
  • AbsProjectiveRationalPoint
  • AbsProjectiveVariety
  • AbsWeilDivisor
  • AffinePlaneCurve
  • AffineRationalPoint
  • AffineScheme
  • AffineSchemeMor
  • Array
  • Array
  • BasicGAPGroupElem
  • CartierDivisor
  • CompositeCoveredSchemeMorphism
  • CoveredClosedEmbedding
  • CoveredScheme
  • CoveredScheme
  • Covering
  • Covering
  • CoveringMorphism
  • Dedent
  • DirectProductGroup
  • DirectSumSheaf
  • DualRootSpaceElem
  • DualRootSpaceElem
  • EffectiveCartierDivisor
  • EllipticSurface
  • EnriquesBorcherdsCtx
  • FPGroup
  • FPGroupElem
  • Fac
  • FacElem
  • FacElem
  • FinGenAbGroup
  • FinGenAbGroup
  • GAPGroup
  • GAPGroupCharacterTable
  • GAPGroupTableOfMarks
  • Gluing
  • Gluing
  • GroupConjClass
  • GroupCoset
  • GroupDoubleCoset
  • HomSheaf
  • IdealSheaf
  • IncidenceMatrix
  • Indent
  • K3Chamber
  • LinearSystem
  • Lowercase
  • LowercaseOff
  • MPolyBuildCtx
  • MSet
  • Matrix
  • Matrix
  • MatrixGroup
  • MatrixGroupElem
  • Matroid
  • MorphismFromRationalFunctions
  • OscarWorkerPool
  • Partition
  • PartitionedPermutation
  • PcGroup
  • PcGroupElem
  • Perm
  • PermGroup
  • PermGroupElem
  • Polyhedron
  • PreSheafOnScheme
  • PrimeIdealSheafFromChart
  • ProductIdealSheaf
  • ProjectiveCurve
  • ProjectivePlaneCurve
  • ProjectiveRationalPoint
  • ProjectiveSchemeMor
  • PullbackIdealSheaf
  • PullbackSheaf
  • PushforwardSheaf
  • QuadSpaceWithIsom
  • RadicalOfIdealSheaf
  • RootSpaceElem
  • RootSpaceElem
  • RootSpaceElem
  • Scheme
  • SchemeMor
  • SemidirectProductGroup
  • SesquilinearForm
  • SheafOfModules
  • SimpleGluing
  • SimplifiedIdealSheaf
  • SingularLocusIdealSheaf
  • SkewDiagram
  • StructureSheafOfRings
  • SubFPGroup
  • SubFPGroupElem
  • SubPcGroup
  • SubPcGroupElem
  • SumIdealSheaf
  • SymmetricGroup
  • TorQuadModule
  • ToricIdealSheafFromCoxRingIdeal
  • UpgradeScript
  • Vector
  • Vector
  • WeightLatticeElem
  • WeightLatticeElem
  • WeightLatticeElem
  • WeightLatticeElem
  • WeightLatticeElem
  • WreathProductGroup
  • YoungTableau
  • ZZGenus
  • ZZLatWithIsom
  • ZZLocalGenus
  • ZZMatrix
  • ZZMatrix
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • +
  • +
  • +
  • +
  • +
  • +
  • +
  • +
  • +
  • +
  • -
  • -
  • <
  • <<
  • <<
  • <<
  • <=
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • >>
  • >>
  • >>
  • ADE_type
  • GF
  • GF
  • K3_surface_automorphism_group
  • MN1inner
  • ModuleHomomorphism
  • ModuleIsomorphism
  • O
  • O
  • O
  • O
  • O
  • O
  • OO
  • R10_matroid
  • SIM_body_polytope
  • ^
  • ^
  • ^
  • ^
  • ^
  • ^
  • _numpart
  • a_invariants
  • abelian_closure
  • abelian_d10_pi6
  • abelian_d15_pi21_quintic_1
  • abelian_d15_pi21_quintic_3
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_groups
  • abelian_invariants
  • abelian_invariants_schur_multiplier
  • abelian_lie_algebra
  • abs
  • abs
  • abs2
  • absolute_basis
  • absolute_basis
  • absolute_basis_matrix
  • absolute_charpoly
  • absolute_coordinates
  • absolute_degree
  • absolute_degree
  • absolute_discriminant
  • absolute_minpoly
  • absolute_norm
  • absolute_norm
  • absolute_norm
  • absolute_primary_decomposition
  • absolute_primitive_element
  • absolute_simple_field
  • absolute_tr
  • absolute_tr
  • absolute_tr
  • abstract_bundle
  • abstract_flag_bundle
  • abstract_flag_variety
  • abstract_grassmannian
  • abstract_hirzebruch_surface
  • abstract_module
  • abstract_module
  • abstract_point
  • abstract_projective_bundle
  • abstract_projective_space
  • abstract_variety
  • accuracy_bits
  • accuracy_bits
  • accuracy_bits
  • accuracy_bits
  • acos
  • acospi
  • acting_group
  • acting_group
  • acting_group
  • acting_subgroup
  • acting_subgroup
  • action_function
  • action_homomorphism
  • add!
  • add_assertion_scope
  • add_column
  • add_column!
  • add_edge!
  • add_error!
  • add_error!
  • add_gluing!
  • add_resolution
  • add_row
  • add_row!
  • add_scaled_col!
  • add_scaled_row
  • add_scaled_row
  • add_scaled_row!
  • add_verbosity_scope
  • add_vertex!
  • add_vertices!
  • addmul!
  • adjacency_matrix
  • adjacency_tree
  • adjacent_chamber
  • adjacent_chamber
  • adjoint_ideal
  • adjunction_process
  • adjusted_length
  • admissible_equivariant_primitive_extensions
  • admissible_triples
  • affine_algebra
  • affine_algebra
  • affine_charts
  • affine_charts
  • affine_cone
  • affine_geometry
  • affine_halfspace
  • affine_hull
  • affine_hyperplane
  • affine_normal_toric_variety
  • affine_normal_toric_variety
  • affine_open_covering
  • affine_phylogenetic_model!
  • affine_space
  • affine_space
  • affine_space
  • agm
  • agm
  • agm
  • agm
  • agm
  • agm
  • airy_ai
  • airy_ai
  • airy_ai
  • airy_ai
  • airy_ai_prime
  • airy_ai_prime
  • airy_ai_prime
  • airy_ai_prime
  • airy_bi
  • airy_bi
  • airy_bi
  • airy_bi
  • airy_bi_prime
  • airy_bi_prime
  • airy_bi_prime
  • airy_bi_prime
  • alexander_dual
  • algebraic_closure
  • algebraic_cycle
  • algebraic_cycle
  • algebraic_cycle
  • algebraic_ideal
  • algebraic_lattice
  • algebraic_lattice_primitive_closure
  • algebraic_lattice_primitive_closure!
  • algebraic_matrix
  • algebraic_pluecker_vector
  • algebraic_polynomial
  • algebraic_set
  • algebraic_set
  • algebraic_set
  • algebraic_set
  • algebraic_set
  • algebraic_set
  • algebraic_split
  • all_atlas_group_infos
  • all_blocks
  • all_blocks
  • all_character_table_names
  • all_cohomologies
  • all_groups_with_class_number
  • all_neighbors
  • all_od_infos
  • all_perfect_groups
  • all_primitive_groups
  • all_small_groups
  • all_subsets_matroid
  • all_table_of_marks_names
  • all_transitive_groups
  • all_triangulations
  • allow_unicode
  • alternating_form
  • alternating_group
  • ambient_coordinate_ring
  • ambient_dim
  • 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
  • analyze_fibers
  • angle
  • annihilator
  • anti_symmetric_parts
  • anticanonical_bundle
  • anticanonical_divisor
  • anticanonical_divisor_class
  • any_order
  • apply_braid_move!
  • 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_ambient
  • basis_of_h22_ambient_indices
  • basis_of_h22_hypersurface
  • basis_of_h22_hypersurface_indices
  • 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_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
  • blocks
  • blow_up
  • blow_up
  • blow_up
  • blow_up
  • blow_up
  • blow_up
  • blow_up_along_minimal_supercone_coordinates
  • blow_up_points
  • bond_matroid
  • borcherds_method
  • borcherds_method
  • bordiga
  • bound_inf_norm
  • bound_inf_norm
  • boundary_lattice_points
  • bracket
  • bracket
  • braid_moves
  • breaks_non_abelian_gauge_group
  • breaks_non_abelian_gauge_group
  • 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_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
  • central_character
  • centralizer
  • centralizer
  • centralizer
  • centralizer
  • centralizer
  • centralizer
  • centralizer
  • chain_complex
  • chamber
  • chamber_invariants
  • 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
  • character_field
  • character_lattice
  • character_parameters
  • character_table
  • character_table
  • character_table
  • character_table
  • character_table_complex_reflection_group
  • character_table_wreath_symmetric
  • 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_class
  • chern_classes
  • chern_classes
  • chief_series
  • chosen_g4_flux_basis
  • 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
  • classes_of_tunable_sections_in_basis_of_Kbar_and_defining_classes
  • 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
  • coeff
  • coeff
  • coeff
  • coefficient_field
  • coefficient_ideals
  • coefficient_ideals
  • coefficient_ring
  • coefficients
  • coefficients
  • coefficients
  • 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
  • collector
  • collector
  • 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
  • compound_matrix
  • compute_distributed!
  • 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
  • conjugate_dominant_weight
  • conjugate_dominant_weight_with_elem
  • 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
  • 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
  • contracted_partial_shift_graph
  • contraction
  • convention
  • converter_dict_h22_ambient
  • converter_dict_h22_hypersurface
  • 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
  • coroot
  • coroots
  • 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_module_homomorphism
  • 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
  • d3_tadpole_constraint
  • d3_tadpole_constraint
  • data
  • dec
  • decide_du_val_singularity
  • decide_du_val_singularity
  • decomposition_group
  • decomposition_matrix
  • dedekind_eta
  • dedekind_eta
  • dedekind_sum
  • default_covering
  • default_ordering
  • defect_group
  • defining_classes
  • defining_equation
  • defining_equation
  • defining_ideal
  • defining_ideal
  • defining_ideal
  • defining_modulus
  • defining_polynomial
  • defining_polynomial
  • defining_polynomial
  • defining_polynomial
  • defining_polynomials
  • 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
  • degree_of_character_field
  • 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
  • demazure_character
  • demazure_character
  • demazure_operator
  • denominator
  • denominator
  • denominator
  • denominator
  • denominator
  • dense_matrix_type
  • dense_row
  • 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
  • dim_of_simple_module
  • 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
  • dominant_character
  • dominant_weights
  • dominates
  • dot
  • dot
  • dot
  • double_coset
  • double_cosets
  • dst
  • dual
  • dual
  • dual
  • dual
  • dual
  • dual
  • dual
  • dual
  • dual_basis
  • dual_continued_fraction_hirzebruch_jung
  • dual_geometric_representation
  • 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
  • enriques_surface_automorphism_group
  • enumerate_classes_of_lattices_with_isometry
  • enumerate_partitioned_permutations
  • enumerate_prime_power_isometries
  • enumerate_quadratic_triples
  • epimorphism_from_free_group
  • equation
  • equation_order
  • 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_number
  • 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_classes
  • exceptional_divisor_indices
  • 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
  • exterior_shift
  • extra_name
  • f_vector
  • f_vector
  • f_vector
  • f_vector
  • f_vector
  • f_vector
  • face_fan
  • facet_degrees
  • facet_sizes
  • facets
  • 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
  • falling_factorial
  • family_of_g4_fluxes
  • 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_points
  • fixed_ring
  • flag_pluecker_ideal
  • flat
  • flats
  • flog
  • floor
  • floor
  • flux_instance
  • 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
  • fundamental_weight
  • fundamental_weights
  • g4_flux
  • g4_flux_family
  • g_vector
  • galois_group
  • galois_group
  • galois_ideal
  • galois_orbit_sum
  • galois_quotient
  • galois_quotient
  • galois_quotient
  • galois_quotient
  • galois_representative_and_multiplicity
  • 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
  • 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_enriques_surface
  • generic_fiber
  • generic_section
  • generic_unipotent_matrix
  • gens
  • gens
  • 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
  • geometric_representation
  • get_assertion_level
  • get_attribute
  • get_attribute!
  • get_conjugate
  • get_html_as_latex
  • get_name
  • get_power
  • get_relative_order
  • get_relative_orders
  • 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_group_quotient
  • 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
  • gomory_chvatal_closure
  • gorenstein_index
  • grade
  • grade
  • grade
  • grade
  • grade
  • graded_free_module
  • graded_free_module
  • graded_polynomial_ring
  • grading_group
  • grading_group
  • grading_group
  • grading_group
  • grading_group
  • grading_group
  • gram
  • gram_determinant_specht_module
  • gram_matrix
  • 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
  • graph_curve
  • graph_from_adjacency_matrix
  • graph_from_edges
  • graph_from_labeled_edges
  • graphical_model
  • graphical_model
  • grassmann_pluecker_ideal
  • groebner_basis
  • groebner_basis
  • groebner_basis
  • groebner_basis
  • groebner_basis_f4
  • groebner_basis_hilbert_driven
  • groebner_basis_with_transformation_matrix
  • groebner_walk
  • gromov_witten_invariant
  • group
  • group
  • group
  • group_algebra
  • group_of_model
  • group_with_class_number
  • 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
  • has_canonical_singularities
  • has_complement
  • has_du_val_singularities
  • has_edge
  • has_gens
  • has_groups_with_class_number
  • has_horizontal_map
  • has_index
  • has_left_bound
  • has_lower_bound
  • has_minimum
  • has_nonempty_intersection
  • has_norm
  • has_number_of_groups_with_class_number
  • has_number_of_perfect_groups
  • has_number_of_primitive_groups
  • has_number_of_small_groups
  • has_number_of_transitive_groups
  • has_perfect_group_identification
  • has_perfect_groups
  • has_preimage_with_preimage
  • has_primitive_group_identification
  • has_primitive_groups
  • has_princ_gen_special
  • has_quick_triangulation
  • has_quotient
  • has_right_bound
  • has_root_system_type
  • 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
  • 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
  • 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
  • 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_exceptional_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_direct_product
  • inner_point
  • inner_product
  • inner_product
  • instanton_number
  • integer_genera
  • integer_hull
  • integer_lattice
  • integer_lattice
  • integer_lattice_with_isometry
  • integer_lattice_with_isometry
  • integral
  • integral
  • integral
  • integral
  • integral
  • integral_basis
  • integral_coefficients
  • 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
  • intersection_multiplicity
  • 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_lattice_of_K3_cover
  • invariant_quadratic_form
  • invariant_quadratic_forms
  • invariant_ring
  • invariant_ring
  • invariant_ring
  • invariant_ring
  • invariant_sesquilinear_form
  • invariant_sesquilinear_forms
  • invariant_symmetric_forms
  • invariants
  • inverse
  • inverse
  • inverse_specialized_fourier_transform
  • invert_birational_map
  • invlex
  • invmod
  • involution
  • involution
  • iroot
  • iroot
  • irreducible_components
  • irreducible_components
  • irreducible_components
  • irreducible_decomposition
  • irreducible_factors
  • irreducible_secondary_invariants
  • irrelevant_ideal
  • irrelevant_ideal
  • irrelevant_ideal
  • is_GLZ_conjugate
  • is_abelian
  • is_abelian
  • is_abelian
  • is_abelian
  • is_absolute
  • is_absolute
  • is_admissible_triple
  • is_affine
  • is_algebraic
  • is_algebraic_integer
  • is_algebraically_independent
  • is_algebraically_independent_with_relations
  • is_almost_simple
  • is_almost_simple
  • is_alternating
  • is_alternating
  • is_ample
  • is_ample
  • is_anti_isometric_with_anti_isometry
  • is_archimedean_solid
  • is_associated
  • is_associated
  • is_atlas_character_table
  • is_ball
  • is_base_space_fully_specified
  • is_basepoint_free
  • is_basepoint_free
  • is_bass
  • is_bicoset
  • is_bijective
  • is_bijective
  • is_binary
  • is_binomial
  • is_binomial
  • is_bipartite
  • is_bounded
  • is_calabi_yau
  • is_cartan_matrix
  • is_cartan_type
  • is_cartier
  • is_cellular
  • is_central
  • is_central
  • is_character_table_name
  • is_characteristic_subgroup
  • is_closed_embedding
  • is_clutter
  • is_cm_field
  • is_cohen_macaulay
  • is_coloopless
  • is_commutative
  • is_compatible
  • is_complete
  • is_complete
  • is_complete
  • is_complex
  • is_conductor
  • is_congruent
  • is_conjugate
  • is_conjugate
  • is_conjugate
  • is_conjugate_with_data
  • is_conjugate_with_data
  • is_conjugate_with_data
  • is_connected
  • is_constant
  • is_constant
  • is_contained
  • is_coroot
  • is_coroot_with_index
  • is_cyclic
  • is_cyclic
  • is_cyclic
  • is_cyclic
  • is_defining_polynomial_nice
  • is_definite
  • is_definite
  • is_definite
  • is_definite
  • is_definite
  • is_definite
  • is_degenerate
  • is_degenerate
  • is_diagonal
  • is_diagonal
  • is_divisible_by
  • is_divisible_by
  • is_divisible_by
  • is_divisible_by
  • is_dominant
  • is_du_val_singularity
  • is_du_val_singularity
  • is_duplicate_table
  • is_dyadic
  • is_effective
  • is_effective
  • is_effective
  • is_elementary
  • is_elementary
  • is_elementary
  • is_elementary
  • is_elementary_abelian
  • is_elementary_abelian
  • is_elementary_with_prime
  • is_elementary_with_prime
  • is_elementary_with_prime
  • is_elementary_with_prime
  • is_elimination_ordering
  • is_embedded
  • is_empty
  • is_equal_abs
  • is_equal_abs_imag
  • is_equal_abs_real
  • is_equal_imag
  • is_equal_real
  • is_equation_order
  • is_equidistant
  • is_even
  • is_exact
  • is_exact
  • is_exact
  • is_exact
  • is_faithful
  • is_fano
  • is_feasible
  • is_finalized
  • is_finite
  • is_finite
  • is_finite
  • is_finite
  • is_finite
  • is_finite_dimensional_vector_space
  • is_finite_order
  • is_finite_order
  • is_finitely_generated
  • is_flat
  • is_full_direct_product
  • is_full_semidirect_product
  • is_full_wreath_product
  • is_fulldimensional
  • is_fulldimensional
  • is_fundamental_weight
  • is_fundamental_weight_with_index
  • is_gen
  • is_gen
  • is_gen
  • is_gen
  • is_gen
  • is_gen
  • is_gen
  • is_gen
  • is_genus
  • is_global
  • is_gorenstein
  • is_gorenstein
  • is_graded
  • is_graded
  • is_graded
  • is_hadamard
  • is_hermitian
  • is_hermitian
  • is_hermitian
  • is_hermitian
  • is_hessenberg
  • is_hnf
  • is_hnf
  • is_homogeneous
  • is_homogeneous
  • is_homogeneous
  • is_homogeneous
  • is_homogeneous
  • is_homogeneous
  • is_homogeneous
  • is_identity_map
  • is_imaginary
  • is_imaginary
  • is_immaculate
  • is_in_linear_system
  • is_independent
  • is_index_divisor
  • is_inert
  • is_injective
  • is_injective
  • is_inner_automorphism
  • is_integral
  • is_integral
  • is_integral
  • is_integral
  • is_integral
  • is_integral
  • is_integral
  • is_invariant
  • is_invariant
  • is_inverse_of
  • is_invertible
  • is_invertible
  • is_invertible
  • is_invertible_with_inverse
  • is_invertible_with_inverse
  • is_involution
  • is_irreducible
  • is_irreducible
  • is_isometric
  • is_isometric
  • is_isometric
  • is_isometric
  • is_isometric_with_isometry
  • is_isometric_with_isometry
  • is_isomorphic
  • is_isomorphic
  • is_isomorphic
  • is_isomorphic
  • is_isomorphic
  • is_isomorphic
  • is_isomorphic
  • is_isomorphic
  • is_isomorphic_to_alternating_group
  • is_isomorphic_to_symmetric_group
  • is_isomorphic_with_map
  • is_isomorphic_with_map
  • is_isomorphic_with_permutation
  • is_isomorphism
  • is_isomorphism
  • is_isomorphism
  • is_isotropic
  • is_isotropic
  • is_johnson_solid
  • is_k_separation
  • is_kummer_extension
  • is_lattice_polytope
  • is_left
  • is_less_abs
  • is_less_abs_imag
  • is_less_abs_real
  • is_less_imag
  • is_less_real
  • is_less_root_order
  • is_linearly_disjoint
  • is_linearly_normal
  • is_local
  • is_local_norm
  • is_local_norm
  • is_local_norm
  • is_locally_hyperbolic
  • is_locally_isometric
  • is_locally_isometric
  • is_locally_represented_by
  • is_loopless
  • is_lower_triangular
  • is_manifold
  • is_maximal
  • is_maximal
  • is_maximal_integral
  • is_maximal_integral
  • is_maximal_subgroup
  • is_minimal_supercone_coordinate_vector
  • is_minor
  • is_mixed
  • is_modular
  • is_modular
  • is_monic
  • is_monomial
  • is_monomial
  • is_monomial
  • is_monomial
  • is_monomial_recursive
  • is_natural_alternating_group
  • is_natural_symmetric_group
  • is_neat
  • is_nef
  • is_negative
  • is_negative
  • is_negative
  • is_negative
  • is_negative_coroot
  • is_negative_coroot_with_index
  • is_negative_definite
  • is_negative_definite
  • is_negative_definite
  • is_negative_definite
  • is_negative_definite
  • is_negative_root
  • is_negative_root_with_index
  • is_nilpotent
  • is_nilpotent
  • is_nilpotent
  • is_nilpotent
  • is_non_zero_divisor
  • is_nonnegative
  • is_nonnegative
  • is_nonpositive
  • is_nonpositive
  • is_nonzero
  • is_nonzero
  • is_norm
  • is_norm_divisible
  • is_normal
  • is_normal
  • is_normal
  • is_normal
  • is_normal
  • is_normal
  • is_normal_subgroup
  • is_normalized_by
  • is_number
  • is_of_hermitian_type
  • is_of_same_type
  • is_of_type
  • is_on_curve
  • is_one
  • is_one
  • is_open_embedding
  • is_orbifold
  • is_orthogonally_stable
  • is_partially_resolved
  • is_perfect
  • is_perfect
  • is_perfect
  • is_perfect_power
  • is_pgroup
  • is_pgroup_with_prime
  • is_platonic_solid
  • is_pointed
  • is_pointed
  • is_positive
  • is_positive
  • is_positive
  • is_positive
  • is_positive_coroot
  • is_positive_coroot_with_index
  • is_positive_definite
  • is_positive_definite
  • is_positive_definite
  • is_positive_definite
  • is_positive_definite
  • is_positive_root
  • is_positive_root_with_index
  • is_positively_graded
  • is_power
  • is_power
  • is_power
  • is_primary
  • is_primary
  • is_primary
  • is_primary
  • is_primary
  • is_primary_with_prime
  • is_primary_with_prime
  • is_primary_with_prime
  • is_primary_with_prime
  • is_prime
  • is_prime
  • is_prime
  • is_prime
  • is_prime
  • is_prime_known
  • is_prime_power
  • is_prime_power_with_data
  • is_primitive
  • is_primitive
  • is_primitive
  • is_primitive
  • is_principal
  • is_principal
  • is_principal_fac_elem
  • is_principal_with_data
  • is_probable_prime
  • is_projective
  • is_projective_space
  • is_pure
  • is_pure
  • is_pure
  • is_q_cartier
  • is_q_gorenstein
  • is_quadratic
  • is_quadratic
  • is_quasisimple
  • is_quasisimple
  • is_radical_extension
  • is_ramified
  • is_ramified
  • is_rational
  • is_rational
  • is_rational
  • is_rationally_isometric
  • is_rationally_isometric
  • is_ready
  • is_real
  • is_realizable
  • is_reduced
  • is_regular
  • is_regular
  • is_regular
  • is_regular
  • is_regular
  • is_regular
  • is_regular_sequence
  • is_represented_by
  • is_right
  • is_rimhook
  • is_rimhook
  • is_root
  • is_root_of_unity
  • is_root_with_index
  • is_rref
  • is_rref
  • is_self_normalizing
  • is_semi_regular
  • is_semiregular
  • is_semiregular
  • is_semisimple
  • is_semisimple
  • is_semistandard
  • is_separable
  • is_signed_inf
  • is_simple
  • is_simple
  • is_simple
  • is_simple
  • is_simple
  • is_simple
  • is_simple
  • is_simple_coroot
  • is_simple_coroot_with_index
  • is_simple_root
  • is_simple_root_with_index
  • is_simplicial
  • is_simplicial
  • 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_split_with_zero_divisor
  • 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_transitive
  • is_transverse_intersection
  • is_transverse_intersection
  • is_trivial
  • is_trivial
  • is_uinf
  • is_undefined
  • is_unicode_allowed
  • 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_well_quantized
  • is_well_quantized
  • 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
  • isomorphic_subgroups
  • isomorphism
  • isomorphism
  • isomorphism
  • isomorphism
  • isomorphism
  • isomorphism_classes_elliptic_fibrations
  • isomorphism_classes_polarizations
  • isomorphism_from_generic_fibers
  • isomorphisms
  • isone
  • isone
  • isone
  • isone
  • isone
  • isone
  • isone
  • isotropic_rays
  • isqrt
  • isqrtrem
  • isreal
  • isreal
  • isreal
  • issubset
  • issubset
  • iszero
  • iszero
  • iszero
  • 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
  • kontsevich_moduli_space
  • koszul_complex
  • koszul_homology
  • koszul_matrix
  • kronecker_symbol
  • kummer_failure
  • label!
  • labelings
  • laplacian_matrix
  • lattice
  • lattice
  • lattice
  • lattice
  • lattice
  • lattice
  • lattice
  • lattice
  • lattice_homomorphism
  • 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
  • length
  • letters
  • letters
  • 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_subspaces_on_hypersurface
  • 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
  • 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
  • longest_element
  • 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
  • mass
  • mat_elem_type
  • matrix
  • matrix
  • matrix
  • matrix
  • matrix
  • matrix
  • matrix
  • matrix
  • matrix_group
  • matrix_integral
  • matrix_ordering
  • matrix_rational
  • 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_blocks
  • maximal_cells
  • maximal_cones
  • maximal_extension
  • maximal_integral_lattice
  • maximal_integral_lattice
  • maximal_integral_lattice
  • maximal_integral_lattice
  • maximal_normal_subgroups
  • maximal_order
  • maximal_order
  • 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_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
  • minimal_supercone_coordinates
  • minimal_supercone_coordinates_of_exceptional_ray
  • minimal_supercone_indices
  • 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
  • model_parameters
  • model_section_parametrization
  • model_sections
  • 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_dense
  • mul_red!
  • mul_sparse
  • mullow
  • mullow
  • mulmod
  • multi_hilbert_function
  • multi_hilbert_series
  • multi_hilbert_series_reduced
  • multipartition
  • multipartitions
  • multiplicative_group
  • multiplicative_group_generators
  • multiplicative_jordan_decomposition
  • multiplicities
  • multiplicities
  • multiplicities_eigenvalues
  • multiplicity
  • multiplicity
  • multiplicity
  • multiply_column
  • multiply_column!
  • multiply_row
  • multiply_row!
  • multiset
  • my_access_func
  • 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!
  • negative_coroot
  • negative_coroots
  • negative_root
  • negative_roots
  • 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_generators
  • number_of_groups_with_class_number
  • number_of_multipartitions
  • number_of_partitions
  • number_of_partitions
  • number_of_partitions
  • number_of_perfect_groups
  • number_of_positive_roots
  • number_of_primitive_groups
  • number_of_roots
  • number_of_rows
  • number_of_rows
  • number_of_rows
  • number_of_simple_roots
  • 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
  • numerical_lattice
  • numerical_lattice_of_K3_cover
  • 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
  • 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
  • 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
  • oscar_worker_pool
  • 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
  • parabolic_subgroup
  • parabolic_subgroup_with_projection
  • parallel_all
  • parallel_any
  • parallel_extension
  • parametrization
  • parametrization
  • parametrization
  • parametrization
  • parent
  • parent
  • parent
  • parent
  • parent
  • parent
  • parent_type
  • parity
  • partial_shift_graph
  • partial_shift_graph_vertices
  • partition
  • partitions
  • partitions
  • partitions
  • partitions
  • partitionseq
  • passes_tadpole_cancellation_check
  • passes_transversality_checks
  • passes_transversality_checks
  • patches
  • pbw_algebra
  • pc_group
  • 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
  • polynomial_ring
  • polynomial_ring
  • polynomial_ring
  • polynomial_ring
  • polynomial_ring_only
  • polynomial_to_power_sums
  • polytope_index
  • pontryagin_class
  • pop_task!
  • popcount
  • popov
  • popov_with_transform
  • positive_coroot
  • positive_coroots
  • positive_hull
  • positive_root
  • positive_roots
  • positive_tropical_variety
  • possible_class_fusions
  • poverorder
  • poverorders
  • pow
  • power_class
  • power_map
  • 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_generator
  • primitive_generator_with_scaling_factor
  • 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
  • process_result!
  • 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_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
  • q_binomial
  • q_factorial
  • q_integer
  • qadic_field
  • qsm_flux
  • 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_algebra
  • 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_flux
  • random_flux_instance
  • random_realization
  • random_variables
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank_action
  • rank_action
  • ranks
  • rational_coefficients
  • 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
  • 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
  • reduced_expressions
  • reducible_fibers
  • reducible_fibers
  • reflect
  • reflect
  • reflect
  • reflect
  • reflect!
  • reflect!
  • reflect!
  • reflect!
  • reflection
  • 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
  • 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_elem_type
  • ring_of_multipliers
  • rising_factorial
  • 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
  • rising_factorial2
  • root
  • root
  • root
  • root
  • root
  • root
  • root_invariant
  • 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
  • root_system
  • root_system
  • root_system
  • root_system
  • root_system
  • root_system
  • root_system
  • root_system_type
  • root_system_type_with_ordering
  • roots
  • roots
  • roots
  • roots
  • roots
  • roots
  • roots
  • roots
  • roots_upper_bound
  • roots_upper_bound
  • rothe_matrix
  • 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_commutator!
  • set_conjugate!
  • set_coordinate_names
  • set_coordinate_names_of_torus
  • set_global_tate_model
  • set_html_as_latex
  • set_mordell_weil_basis!
  • set_name!
  • set_power!
  • set_precision!
  • set_precision!
  • set_relative_order!
  • set_relative_orders!
  • 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_affine
  • short_vectors_affine
  • short_vectors_iterator
  • shortest_path_dijkstra
  • shortest_vectors
  • show
  • show
  • show_OD_info
  • show_atlas_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_incidence_matrix
  • signed_permutahedron
  • signs
  • similarity!
  • simple_coroot
  • simple_coroots
  • simple_extension
  • simple_module
  • simple_root
  • simple_roots
  • 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_flux_family
  • 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
  • splitting_roots_mod2
  • 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_coordinates
  • 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
  • strict_transform
  • strict_transform_with_index
  • 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
  • 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
  • syllables
  • syllables
  • 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_bundle
  • tangent_lines
  • tangent_lines
  • tangent_sheaf
  • 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
  • tautological_bundles
  • taxa
  • teichmuller
  • teichmuller
  • tensor_power
  • tensor_product
  • tensor_product
  • tensor_product
  • tensor_product
  • tensor_product
  • tensor_product
  • tensor_product
  • tensor_product_decomposition
  • tensor_ring
  • terse
  • test_experimental_module
  • test_module
  • tetrahedron
  • theta_qexp
  • tn_bundle
  • tn_bundle
  • tn_flag_variety
  • tn_grassmannian
  • tn_representation
  • tn_variety
  • 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_sections
  • 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_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
  • transitivity
  • translation_morphism
  • transportation_polytope
  • transpose
  • transpose
  • triangular_decomposition
  • 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_prevariety
  • 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
  • tunable_sections
  • tune
  • tune
  • tutte_connectivity
  • tutte_lifting
  • tutte_polynomial
  • twist
  • twisting_sheaf
  • two_neighbor_step
  • two_sided_ideal
  • type
  • undefined
  • underlying_scheme
  • underlying_scheme
  • underlying_scheme
  • uniform_hypergraph
  • 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
  • vertices_and_rays
  • vertices_and_rays
  • vinberg_algorithm
  • visualize
  • visualize
  • visualize
  • visualize
  • volume
  • volume
  • volume_form
  • walls
  • 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_lattice
  • weight_ordering
  • weighted_projective_space
  • weighted_resolution_generating_sections
  • weighted_resolution_zero_sections
  • weighted_resolutions
  • weights
  • weights
  • weil_divisor
  • weil_divisor
  • weil_divisor
  • weil_divisor
  • weyl_algebra
  • weyl_group
  • weyl_group
  • weyl_group
  • weyl_group
  • weyl_orbit
  • weyl_vector
  • weyl_vector
  • wildanger_field
  • with_ordering
  • with_unicode
  • witt_index
  • witt_invariant
  • witt_invariant
  • word
  • wreath_product
  • write_as_full
  • young_tableau
  • zero
  • zero
  • zero
  • zero
  • zero
  • zero
  • zero
  • zero
  • zero
  • zero
  • zero!
  • zero_algebra
  • zero_locus_section
  • zero_map
  • zero_map
  • zero_matrix
  • zero_matrix
  • zero_section
  • zero_section
  • zero_section_class
  • zero_section_index
  • 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
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