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Oscar.jl
  • Welcome to OSCAR
    • Architecture
    • Notes for users of other computer algebra systems
    • Frequently Asked Questions
    • Serialization
    • Complex Algorithms in OSCAR
    • 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
    • Abelian Groups
    • Group characters
    • 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
    • Introduction
    • Sparse linear algebra
    • Matrix functionality
    • Generic matrix algebras
      • 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
    • Introduction
      • Introduction
      • Number field operations
      • Element operations
      • Internals
      • Introduction
      • Orders
      • Elements
      • Ideals
      • Fractional ideals
    • Abelian closure of the rationals
    • Galois Theory
    • Introduction
      • Introduction
      • Constructions
      • Polyhedron and polymake's Polytope
      • Auxiliary functions
      • Saving and loading
      • Visualization
    • Cones
    • Polyhedral Fans
    • Polyhedral Complexes
    • Linear Programs
    • Mixed Integer Linear Programs
    • Subdivisions of Points
    • Introduction
    • Creating Multivariate Rings
    • Monomial Orderings
    • Gröbner/Standard Bases Over Fields
    • Gröbner/Standard Bases Over $\mathbb Z$
    • Ideals in Multivariate Rings
      • Introduction
      • Free Modules
      • Subquotient Modules
      • Chain and Cochain Complexes
      • Operations on Modules
      • Operations on Module Maps
    • Affine Algebras
    • Binomial Primary Decomposition
    • Localization
    • Localizations of modules over computable rings
    • Introduction
    • Invariants of Finite Groups
    • Invariants of Linearly Reductive Groups
    • Introduction
      • General schemes
      • Affine schemes
      • Morphisms of affine schemes
      • Architecture of affine schemes
      • Covered schemes
      • Coverings
      • 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
      • Introduction
      • Curves
      • Rational Parametrizations of Rational Plane Curves
      • Standard Constructions in Algebraic Geometry
    • Introduction
      • Introduction
      • Creating PBW-Algebras
      • Ideals in PBW-algebras
      • Quotients of PBW-Algebras
    • Free Associative Algebras
    • Graphs
    • Matroids
    • Simplicial Complexes
    • Introduction
    • GAP's SLPs
    • AbstractAlgebra's polynomial interface
  • References
  • Index
    • Introduction for new developers
    • Developer Style Guide
    • Design Decisions
    • Documenting OSCAR code
    • Debugging OSCAR Code
    • Serialization
      • AbstractCollection
      • SubObjectIterator
Version
  • Index
  • Index
Edit on GitHub
  • AbsCoveredScheme
  • AbsGlueing
  • AbsSpec
  • AbsSpecMor
  • AffineCurveDivisor
  • AffineNormalToricVariety
  • AffineNormalToricVariety
  • AffinePlaneCurve
  • Array
  • Array
  • BasicGAPGroupElem
  • ClosedSubvarietyOfToricVariety
  • CohomologyClass
  • CohomologyClass
  • CohomologyClass
  • CoveredScheme
  • CoveredScheme
  • Covering
  • Covering
  • CyclicQuotientSingularity
  • DirectProductGroup
  • DivisorOnTropicalCurve
  • FPGroup
  • FPGroupElem
  • Fac
  • FacElem
  • FacElem
  • FlintPadicField
  • FlintQadicField
  • GAPGroup
  • GAPGroupCharacterTable
  • Glueing
  • Glueing
  • Graph
  • GroupConjClass
  • GroupCoset
  • GroupDoubleCoset
  • GrpAbFinGen
  • GrpAbFinGen
  • LaurentPolynomialRing
  • LinearProgram
  • MPolyBuildCtx
  • MapFromFunc
  • Matrix
  • MatrixGroup
  • MatrixGroupElem
  • Matroid
  • MixedIntegerLinearProgram
  • NfAbsOrd
  • NormalToricVariety
  • NormalToricVariety
  • NormalToricVariety
  • NormalToricVariety
  • Partition
  • PcGroup
  • PcGroupElem
  • Perm
  • PermGroup
  • PermGroupElem
  • Point
  • Point_EllCurve
  • PolyhedralComplex
  • PolyhedralFan
  • Polyhedron
  • Polyhedron
  • Polyhedron
  • ProjCurve
  • ProjCurveDivisor
  • ProjEllipticCurve
  • ProjPlaneCurve
  • ProjPlaneCurve
  • RationalEquivalenceClass
  • RationalEquivalenceClass
  • RationalEquivalenceClass
  • RationalEquivalenceClass
  • RationalEquivalenceClass
  • RationalEquivalenceClass
  • Scheme
  • SchemeMor
  • SemidirectProductGroup
  • SesquilinearForm
  • SimpleGlueing
  • SimplicialComplex
  • SkewDiagram
  • Spec
  • Spec
  • Spec
  • Spec
  • SpecMor
  • SpecMor
  • SubdivisionOfPoints
  • SubdivisionOfPoints
  • SymmetricGroup
  • TorQuadMod
  • ToricDivisor
  • ToricDivisorClass
  • ToricLineBundle
  • ToricLineBundle
  • ToricMorphism
  • ToricMorphism
  • ToricMorphism
  • ToricMorphism
  • ToricMorphism
  • ToricMorphism
  • ToricMorphism
  • ToricMorphism
  • TropicalCurve
  • TropicalCurve
  • TropicalHypersurface
  • TropicalLinearSpace
  • TropicalSemiring
  • TropicalSemiringMap
  • Vector
  • WreathProductGroup
  • YoungTableau
  • ZGenus
  • ZpGenus
  • fmpz_mat
  • fmpz_mat
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • *
  • +
  • +
  • +
  • +
  • +
  • +
  • +
  • +
  • <<
  • <<
  • <<
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • ==
  • >>
  • >>
  • >>
  • ADE_type
  • CyclotomicField
  • CyclotomicRealSubfield
  • DirectSum
  • DivisorOfCharacter
  • ECM
  • ECPP
  • EquationOrder
  • FlintFiniteField
  • FreeModule
  • GF
  • GradedPolynomialRing
  • IntMult_Point_EllCurveZnZ
  • Localization
  • MN1inner
  • MaximalOrder
  • MaximalOrder
  • Miller_Rabin_test
  • ModuleHomomorphism
  • ModuleIsomorphism
  • NormalToricVarietiesFromStarTriangulations
  • NormalToricVarietyFromGLSM
  • NumberField
  • NumberField
  • NumberField
  • O
  • O
  • O
  • O
  • O
  • O
  • OO
  • Order
  • Order
  • Order
  • Pollard_p_1
  • Pollard_rho
  • PolynomialRing
  • PolynomialRing
  • PseudoMatrix
  • PseudoMatrix
  • PseudoMatrix
  • ResidueField
  • ResidueRing
  • ToricIdentityMorphism
  • VectorSpace
  • Zlattice
  • Zlattice
  • ^
  • ^
  • ^
  • ^
  • _numpart
  • abelian_closure
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_group
  • abelian_groups
  • abs
  • abs
  • abs2
  • absolute_basis
  • absolute_basis
  • absolute_basis_matrix
  • absolute_charpoly
  • absolute_coordinates
  • absolute_degree
  • absolute_discriminant
  • absolute_minpoly
  • absolute_norm
  • absolute_norm
  • absolute_primary_decomposition
  • absolute_primitive_element
  • absolute_simple_field
  • absolute_tr
  • absolute_tr
  • accuracy_bits
  • accuracy_bits
  • acos
  • acospi
  • acting_domain
  • acting_group
  • acting_subgroup
  • acting_subgroup
  • action_homomorphism
  • add_column
  • add_column!
  • add_edge!
  • add_error!
  • add_glueing!
  • add_row
  • add_row!
  • add_scaled_col!
  • add_scaled_row
  • add_scaled_row
  • add_scaled_row!
  • add_vertex!
  • add_vertices!
  • adjoint_ideal
  • affine_algebra
  • affine_charts
  • affine_charts
  • affine_geometry
  • affine_hull
  • affine_open_covering
  • affine_space
  • affine_space
  • affine_space
  • agm
  • agm
  • agm
  • airy_ai
  • airy_ai
  • airy_ai_prime
  • airy_ai_prime
  • airy_bi
  • airy_bi
  • airy_bi_prime
  • airy_bi_prime
  • alexander_dual
  • algebraic_split
  • all_atlas_group_infos
  • all_blocks
  • all_character_table_names
  • all_cohomologies
  • all_neighbors
  • all_primitive_groups
  • all_small_groups
  • all_subsets_matroid
  • all_transitive_groups
  • all_triangulations
  • alternating_form
  • alternating_group
  • ambient_dim
  • ambient_dim
  • ambient_dim
  • ambient_dim
  • ambient_dim
  • ambient_embedding
  • ambient_space
  • ambient_space
  • ambient_space
  • angle
  • anti_symmetric_parts
  • anticanonical_bundle
  • anticanonical_divisor
  • anticanonical_divisor_class
  • any_order
  • archimedean_solid
  • aretransverse
  • aretransverse
  • arithmetic_genus
  • arithmetic_genus
  • as_perm_group
  • as_polycyclic_group
  • asin
  • asinpi
  • assure_has_basis_mat_inv
  • atan
  • atan2
  • atanpi
  • atlas_group
  • atlas_subgroup
  • augmented_chow_ring
  • 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
  • ball
  • barnes_g
  • base
  • base_field
  • base_field
  • base_field
  • base_field
  • base_field
  • base_field
  • base_field
  • base_ring
  • base_ring
  • base_ring
  • base_ring
  • base_ring
  • base_ring
  • base_ring
  • base_ring
  • base_ring
  • bases
  • basis
  • basis
  • basis
  • basis
  • basis
  • basis
  • basis
  • basis_mat_inv
  • basis_mat_inv
  • basis_mat_inv
  • 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_pmatrix
  • bell
  • bell
  • bell
  • bell
  • bernoulli
  • bernoulli
  • bernoulli_cache
  • bessel_i
  • bessel_j
  • bessel_k
  • bessel_y
  • betti_number
  • betti_numbers
  • bin
  • binomial
  • binomial
  • binomial
  • binomial
  • binomial_exponents_to_ideal
  • binomial_primary_decomposition
  • bipyramid
  • birkhoff
  • block_diagonal_matrix
  • block_diagonal_matrix
  • blocks
  • blowup_on_ith_minimal_torus_orbit
  • bond_matroid
  • bound_inf_norm
  • bound_inf_norm
  • boundary_lattice_points
  • brown_invariant
  • build_doc
  • can_scale_totally_positive
  • can_solve
  • can_solve_left_reduced_triu
  • can_solve_with_solution
  • canonical_bundle
  • canonical_divisor
  • canonical_divisor_class
  • canonical_injection
  • canonical_matrix
  • canonical_projection
  • cansolve
  • cartesian_power
  • catalan_solid
  • cauchy_ideal
  • ceil
  • ceil
  • ceil
  • cellular_associated_primes
  • cellular_decomposition
  • cellular_hull
  • cellular_minimal_associated_primes
  • cellular_primary_decomposition
  • center
  • centralizer
  • centralizer
  • centralizer
  • chain_complex
  • change_base_ring
  • change_base_ring
  • change_base_ring
  • change_base_ring
  • change_base_ring
  • change_base_ring
  • change_coefficient_ring
  • change_coefficient_ring
  • character
  • character
  • character
  • character_field
  • character_lattice
  • character_parameters
  • character_table
  • character_to_rational_function
  • character_to_rational_function
  • characteristic
  • characteristic
  • characteristic_polynomial
  • characteristic_subgroups
  • charpoly
  • charpoly
  • charpoly
  • chebyshev_t
  • chebyshev_t
  • chebyshev_t2
  • chebyshev_u
  • chebyshev_u
  • chebyshev_u2
  • chip_firing_move
  • chow_ring
  • chow_ring
  • circuits
  • cispi
  • class_group
  • class_group
  • class_group
  • class_group_ideal_relation
  • class_lengths
  • class_multiplication_coefficient
  • class_number
  • class_parameters
  • class_positions_of_kernel
  • class_positions_of_pcore
  • clog
  • clog
  • close_vectors
  • closure
  • closure
  • clrbit!
  • cmp
  • cobases
  • cochain_complex
  • cocircuits
  • cocycle_matroid
  • codifferent
  • codim
  • codim
  • codim
  • codim
  • codim
  • codomain
  • codomain
  • coeff
  • coeff
  • coeff
  • coeff
  • coeff
  • coeff
  • coeff
  • coeff
  • coefficient_ideals
  • coefficient_ideals
  • coefficients
  • coefficients
  • coefficients
  • coefficients
  • coefficients
  • coefficients
  • cohomology
  • cohomology
  • cohomology_class
  • cohomology_index
  • cohomology_ring
  • cohyperplanes
  • cokernel
  • cokernel
  • collength
  • colon
  • coloops
  • combinatorial_symmetries
  • combit!
  • comm
  • common_components
  • common_components
  • compact_presentation
  • complement
  • complement_class_reps
  • complement_of_ideal
  • complement_system
  • complete_bipartite_graph
  • complete_graph
  • complex_conjugation
  • complex_embeddings
  • complex_normal_form
  • complex_places
  • complex_projective_plane
  • component
  • components
  • compose
  • compose
  • compose
  • compose
  • compositum
  • compositum
  • conductor
  • cone
  • cones
  • conj
  • conj
  • conj
  • conj
  • conj
  • conj
  • conj
  • conjugacy_class
  • conjugacy_class
  • conjugacy_classes
  • conjugacy_classes_maximal_subgroups
  • conjugacy_classes_subgroups
  • conjugate_transpose
  • conjugates
  • conjugates
  • conjugates
  • conjugates_arb
  • conjugates_arb_log
  • conjugates_arb_log_normalise
  • conjugates_complex
  • conjugates_log
  • conjugates_real
  • connected_components
  • connectivity_function
  • const_catalan
  • const_e
  • const_euler
  • const_euler
  • const_glaisher
  • const_khinchin
  • const_log10
  • const_log2
  • 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_negative
  • contains_nonnegative
  • contains_nonpositive
  • contains_positive
  • contains_zero
  • contains_zero
  • content
  • content
  • continued_fraction_hirzebruch_jung
  • continued_fraction_hirzebruch_jung_to_rational
  • contraction
  • convex_hull
  • convex_hull
  • coordinate_names
  • coordinate_names_of_torus
  • coordinate_ring_of_torus
  • coordinate_ring_of_torus
  • coordinates
  • coordinates
  • coprime_base
  • corank
  • core
  • cornacchia_algorithm
  • corresponding_bilinear_form
  • corresponding_quadratic_form
  • cos
  • cos_integral
  • cos_minpoly
  • cosh_integral
  • cospi
  • cover
  • covered_scheme
  • coverings
  • cox_ring
  • cox_ring
  • cperm
  • cross
  • crt
  • crt
  • crt
  • crt
  • crt_with_lcm
  • crt_with_lcm
  • csgn
  • csgn
  • cube
  • curve
  • curve
  • curve_components
  • curve_components
  • curve_intersect
  • curve_intersect
  • curve_singular_locus
  • curve_singular_locus
  • curve_zero_divisor
  • curve_zero_divisor
  • cycle_matroid
  • cycle_structure
  • cycles
  • cyclic_flats
  • cyclic_group
  • cyclic_polytope
  • cyclotomic
  • cyclotomic_field
  • data
  • dec
  • decomposition_group
  • decomposition_matrix
  • dedekind_eta
  • dedekind_sum
  • default_covering
  • defining_ideal
  • defining_ideal
  • defining_modulus
  • defining_polynomial
  • defining_polynomial
  • defining_polynomial
  • defining_polynomials
  • deflate
  • deflate
  • deflate
  • deflate
  • deflate
  • deflate
  • deflate
  • deflate
  • deflation
  • deflation
  • 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
  • degrees
  • degrevlex
  • dehomogenization
  • del_pezzo_polytope
  • del_pezzo_surface
  • deletion
  • denominator
  • denominator
  • denominator
  • denominator
  • denominator
  • dense_matrix_type
  • density
  • derivative
  • derivative
  • derivative
  • derivative
  • derivative
  • derived_series
  • derived_subgroup
  • describe
  • 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_form
  • diagonal_matrix
  • diagonal_of_rational_span
  • dickman_rho
  • different
  • digamma
  • digamma
  • dihedral_group
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim
  • dim_of_torusfactor
  • dimension_global_sections
  • direct_product
  • direct_product
  • direct_product
  • direct_sum
  • direct_sum
  • direct_sum_components
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant
  • discriminant_group
  • disjoint_union
  • div
  • divexact
  • divides
  • divisible
  • divisible
  • divisor
  • divisor
  • divisor
  • divisor
  • divisor_class
  • divisor_class
  • divisor_lenstra
  • divisor_sigma
  • divisor_sigma
  • divisor_sigma
  • divisors
  • divrem
  • domain
  • domain
  • double_coset
  • double_cosets
  • dst
  • dual
  • dual
  • dual_continued_fraction_hirzebruch_jung
  • dual_matroid
  • dual_subdivision
  • dualgraph
  • echelon_with_transform
  • edgegraph
  • edges
  • ehrhart_polynomial
  • ehrhart_polynomial
  • eigenvalues
  • eigenvalues
  • eigvals
  • eigvals_simple
  • eisenstein_g
  • elem_in_nf
  • elem_type
  • elem_type
  • element_to_homomorphism
  • elementary_divisors
  • elementary_divisors
  • elementary_divisors
  • elements!
  • eliminate
  • eliminate
  • elliptic_e
  • elliptic_k
  • emb
  • emb!
  • embed
  • embedding
  • embedding
  • embedding
  • embedding
  • embedding
  • epimorphism_from_free_group
  • equidimensional_decomposition_radical
  • equidimensional_decomposition_weak
  • equidimensional_hull
  • equidimensional_hull_radical
  • erf
  • erf
  • erfc
  • erfi
  • erfi
  • eta_qexp
  • eta_qexp
  • euler_characteristic
  • euler_characteristic
  • euler_phi
  • euler_phi
  • euler_phi
  • euler_phi_inv
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate2
  • evaluate_mod
  • evaluate_naive
  • evaluation_function
  • excess
  • exp
  • exp
  • exp
  • exp
  • exp
  • exp
  • exp
  • exp_integral_e
  • exp_integral_ei
  • exp_pi_i
  • exponent
  • exponent
  • exponent_vectors
  • exponent_word
  • exponent_words
  • exponents
  • ext
  • extend
  • exterior_power
  • f4
  • f_vector
  • f_vector
  • f_vector
  • f_vector
  • f_vector
  • face_fan
  • facets
  • 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
  • fan
  • fano_matroid
  • fano_simplex
  • feasible_region
  • fflu
  • fglm
  • fiber_product
  • fibonacci
  • fibonacci
  • fibonacci
  • fibonacci
  • fill!
  • find_isomorphism
  • find_row_starting_with
  • finish
  • fits
  • fits
  • fitting_subgroup
  • fixed_field
  • fixed_field
  • fixed_field
  • fixed_field
  • fixed_field
  • fixed_ring
  • flat
  • flats
  • flog
  • flog
  • floor
  • floor
  • floor
  • fractional_cut_polytope
  • fractional_ideal
  • fractional_ideal
  • fractional_ideal
  • fractional_ideal
  • fractional_ideal
  • fractional_ideal
  • fractional_ideal
  • fractional_matching_polytope
  • frattini_subgroup
  • free_abelian_group
  • free_extension
  • free_group
  • free_module
  • free_resolution
  • frobenius
  • frobenius
  • from_roots
  • from_roots
  • fundamental_circuit
  • fundamental_cocircuit
  • fundamental_group
  • fundamental_invariants
  • g_vector
  • galois_group
  • galois_group
  • galois_ideal
  • galois_quotient
  • galois_quotient
  • galois_quotient
  • galois_quotient
  • gamma
  • gamma
  • gamma
  • gamma
  • gamma
  • gamma
  • gamma
  • gamma_lower
  • gamma_lower
  • gamma_lower_regularized
  • gamma_lower_regularized
  • gamma_regularized
  • gamma_regularized
  • gcd
  • gcd
  • gcd
  • gcd
  • gcd
  • gcd
  • gcd
  • gcdinv
  • gcdx
  • gcdx
  • gcdx
  • gelfand_tsetlin
  • gen
  • gen
  • gen
  • gen
  • gen
  • gen
  • gen
  • gen
  • gen
  • gen
  • gen
  • gen_index
  • genera
  • genera_hermitian
  • general_linear_group
  • generalized_jordan_block
  • generalized_jordan_form
  • generators
  • gens
  • gens
  • gens
  • gens
  • gens
  • gens_of_rational_equivalence_classes
  • genus
  • genus
  • genus
  • genus
  • genus
  • genus_field
  • genus_representatives
  • genus_representatives
  • geometric_genus
  • geometric_genus
  • geometric_genus
  • get_attribute
  • get_attribute!
  • get_html_as_latex
  • get_variable
  • getindex
  • getindex
  • getindex
  • getindex
  • getindex
  • getindex
  • getindex
  • getindex
  • getindex
  • getindex
  • getindex
  • girth
  • global_sections
  • glue_map
  • glueing_domains
  • glueing_morphisms
  • glueings
  • grade
  • grade
  • grade
  • grading_group
  • grading_group
  • gram
  • 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
  • graph
  • graph
  • grassmann_pluecker_ideal
  • grid_morphism
  • groebner_basis
  • groebner_basis
  • groebner_basis_with_transformation_matrix
  • gset
  • gso
  • guess
  • guess
  • h_star_polynomial
  • h_star_polynomial
  • h_vector
  • h_vector
  • hadamard
  • hadamard_bound2
  • hall_subgroup_reps
  • hall_system
  • harmonic
  • has_2_elem
  • has_2_elem_normal
  • has_attribute
  • has_basis
  • has_basis_matrix
  • has_complement
  • has_edge
  • has_gens
  • has_minimum
  • has_nonempty_intersection
  • has_norm
  • has_number_perfect_groups
  • has_number_primitive_groups
  • has_number_small_groups
  • has_number_transitive_groups
  • has_perfect_group_identification
  • has_perfect_groups
  • has_primitive_group_identification
  • has_primitive_groups
  • has_princ_gen_special
  • has_quotient
  • has_small_group_identification
  • has_small_groups
  • has_torusfactor
  • has_transitive_group_identification
  • has_transitive_groups
  • has_vertex
  • has_weakly_normal
  • haspreimage
  • hasse_invariant
  • hasse_invariant
  • hasse_invariant
  • hcat
  • hcat!
  • height
  • height
  • height_bits
  • height_bits
  • hermitian_form
  • hermitian_lattice
  • hermitian_lattice
  • hermitian_lattice
  • hermitian_lattice
  • hermitian_space
  • hermitian_space
  • hessenberg
  • hex
  • hilbert
  • hilbert_basis
  • hilbert_class_field
  • hilbert_class_polynomial
  • hilbert_function
  • 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
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom
  • hom_product
  • hom_tensor
  • hom_without_reversing_direction
  • homogeneous_component
  • homogeneous_component
  • homogeneous_component
  • homogeneous_components
  • homogeneous_components
  • homogenization
  • homogenization
  • homology
  • homology
  • homology
  • homomorphism_of_semidirect_product
  • homomorphism_of_wreath_product
  • homomorphism_to_element
  • hooklength
  • howell_form
  • howell_form
  • hyperbolic_plane_lattice
  • hypergeometric_1f1
  • hypergeometric_1f1_regularized
  • hypergeometric_2f1
  • hypergeometric_u
  • hyperplanes
  • hypersurface_complement
  • hypersurface_complement
  • id_hom
  • ideal
  • ideal
  • ideal
  • ideal
  • ideal
  • ideal
  • ideal
  • ideal
  • ideal
  • ideal
  • ideal_membership
  • ideal_membership
  • ideal_membership
  • ideal_of_linear_relations
  • ideal_of_linear_relations
  • ideal_point
  • idempotents
  • idempotents
  • identifier
  • identity_map
  • identity_matrix
  • identity_matrix
  • identity_matrix
  • identity_matrix
  • imag
  • imag
  • image
  • image
  • image
  • image
  • image
  • image
  • image_ideal
  • in
  • in
  • in
  • in
  • in
  • in
  • in
  • in
  • in
  • in
  • in
  • in
  • inclusion_morphism
  • independent_sets
  • index
  • index
  • indicator
  • induce_crt
  • induce_rational_reconstruction
  • induced_automorphism
  • induced_class_function
  • induced_cyclic
  • induced_ring_ordering
  • inertia_subgroup
  • infinite_places
  • infinite_places_uniformizers
  • infinity
  • infinity
  • inflate
  • inflate
  • inflate
  • inflate
  • inflate
  • inflate
  • inneighbors
  • inner_automorphism
  • inner_automorphism_group
  • inner_cartesian_power
  • inner_direct_product
  • inner_product
  • inner_product
  • integral
  • integral
  • integral
  • integral_basis
  • integral_split
  • integrate
  • interior_lattice_points
  • interpolate
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersect
  • intersection
  • intersection_form
  • intersection_multiplicity
  • intersection_multiplicity
  • inv
  • inv
  • inv
  • inv
  • inv
  • inv
  • inv
  • inv
  • inv_coeff_ideals
  • invariant_alternating_forms
  • invariant_bilinear_form
  • invariant_bilinear_forms
  • invariant_factors
  • invariant_hermitian_forms
  • invariant_lattice
  • invariant_quadratic_form
  • invariant_quadratic_forms
  • invariant_ring
  • invariant_sesquilinear_form
  • invariant_sesquilinear_forms
  • invariant_symmetric_forms
  • invariants
  • inverse
  • inverse
  • invert_birational_map
  • invmod
  • involution
  • involution
  • iroot
  • iroot
  • irreducible_secondary_invariants
  • irrelevant_ideal
  • irrelevant_ideal
  • is_GLZ_conjugate
  • is_abelian
  • is_abelian
  • is_absolute
  • is_affine
  • is_algebraic
  • is_algebraic_integer
  • is_almostsimple
  • is_alternating_form
  • is_ample
  • is_ample
  • is_anti_isometric_with_anti_isometry
  • is_basepoint_free
  • is_basepoint_free
  • is_bass
  • is_bicoset
  • is_bijective
  • is_bijective
  • is_binary
  • is_binomial
  • is_binomial
  • is_bounded
  • is_cartier
  • is_cellular
  • is_central
  • is_characteristic
  • is_closed_embedding
  • is_clutter
  • is_cm_field
  • is_coloopless
  • is_compatible
  • is_complete
  • is_complete
  • is_complex
  • is_conductor
  • is_congruent
  • is_conjugate
  • is_conjugate
  • is_connected
  • is_constant
  • is_constant
  • is_contained
  • is_cyclic
  • is_cyclic
  • is_defining_polynomial_nice
  • is_definite
  • is_definite
  • is_definite
  • is_definite
  • is_degenerate
  • is_degenerate
  • is_diagonal
  • is_divisible_by
  • is_duplicate_table
  • is_dyadic
  • is_effective
  • is_effective
  • is_effective
  • is_elementary
  • is_elementary_abelian
  • 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_exact
  • is_exact
  • is_fano
  • is_feasible
  • is_finalized
  • is_finitelygenerated
  • is_finiteorder
  • is_full_direct_product
  • is_full_semidirect_product
  • is_full_wreath_product
  • is_fulldimensional
  • is_fulldimensional
  • 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_hadamard
  • is_hermitian_form
  • is_hermitian_matrix
  • is_hessenberg
  • is_hnf
  • is_hnf
  • is_homogeneous
  • is_homogeneous
  • is_homogeneous
  • is_identity_map
  • is_imaginary
  • is_imaginary
  • is_independent
  • is_index_divisor
  • is_inert
  • is_infinite
  • is_injective
  • is_injective
  • is_inner_automorphism
  • 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_involution
  • is_irreducible
  • 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_with_alternating_group
  • is_isomorphic_with_map
  • is_isomorphic_with_map
  • is_isomorphic_with_symmetric_group
  • is_isomorphism
  • is_isotropic
  • is_isotropic
  • is_k_separation
  • is_kummer_extension
  • 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_equivalent
  • is_linearly_equivalent
  • 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_maximal
  • is_maximal
  • is_maximal_integral
  • is_maximal_integral
  • 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_nef
  • is_negative
  • is_negative
  • is_negative_definite
  • is_negative_definite
  • is_negative_definite
  • is_nilpotent
  • is_non_zero_divisor
  • is_nonnegative
  • is_nonpositive
  • is_nonzero
  • is_norm
  • is_norm_divisible
  • is_normal
  • is_normal
  • is_normal
  • is_normal
  • is_normal
  • is_number
  • is_open_embedding
  • is_orbifold
  • is_perfect
  • is_perfect_power
  • is_pgroup
  • is_pgroup_with_prime
  • is_pointed
  • is_pointed
  • is_positive
  • is_positive
  • is_positive
  • is_positive_definite
  • is_positive_definite
  • is_positive_definite
  • is_positively_graded
  • is_power
  • is_power
  • is_power
  • is_power_with_root
  • is_primary
  • is_primary
  • is_primary_with_prime
  • is_prime
  • is_prime
  • is_prime
  • is_prime
  • is_prime_known
  • is_prime_power
  • is_prime_power
  • is_prime_power_with_data
  • is_primitive
  • is_primitive
  • is_principal
  • is_principal
  • is_principal
  • is_principal_fac_elem
  • is_probable_prime
  • is_projective
  • is_projective_space
  • is_q_cartier
  • is_q_gorenstein
  • is_quadratic
  • is_quadratic_form
  • is_quasisimple
  • is_radical_extension
  • is_ramified
  • is_ramified
  • is_rational
  • is_rational
  • is_rationally_isometric
  • is_rationally_isometric
  • is_reduced
  • is_reduced
  • is_regular
  • is_regular
  • is_regular
  • is_regular
  • is_regular
  • is_represented_by
  • is_right
  • is_rimhook
  • is_rimhook
  • is_root_of_unity
  • is_rref
  • is_rref
  • is_semi_regular
  • is_semiregular
  • is_semisimple
  • is_signed_inf
  • is_simple
  • is_simple
  • is_simple
  • is_simple
  • is_simplicial
  • is_simplicial
  • is_singular
  • is_skew_symmetric
  • is_skewsymmetric_matrix
  • is_smooth
  • is_smooth
  • is_smooth
  • is_smooth
  • is_smooth
  • is_smooth_curve
  • is_smooth_curve
  • is_snf
  • is_snf
  • is_snf
  • is_solvable
  • is_split
  • is_sporadic_simple
  • is_square
  • is_square
  • is_square
  • is_square
  • is_square
  • is_square
  • is_square_with_sqrt
  • is_standard_graded
  • is_subfield
  • is_subfield
  • is_subfield_normal
  • is_subgroup
  • is_sublattice
  • is_sublattice_with_relations
  • is_submodule
  • is_supersolvable
  • is_surjective
  • is_surjective
  • is_symmetric
  • is_symmetric_form
  • is_tamely_ramified
  • is_tamely_ramified
  • is_term
  • is_term
  • is_term
  • is_term_recursive
  • is_ternary
  • is_torsion
  • is_torsion_point
  • is_torsion_unit
  • is_totally_complex
  • is_totally_positive
  • is_totally_real
  • is_transitive
  • is_uinf
  • is_undefined
  • is_unipotent
  • is_unit
  • is_unit
  • is_unital
  • is_univariate
  • is_univariate
  • is_unknown
  • is_upper_triangular
  • is_vertical_k_separation
  • is_very_ample
  • is_very_ample
  • is_very_ample
  • is_weak_popov
  • is_weakly_ramified
  • is_z_graded
  • is_zm_graded
  • isempty
  • isempty
  • isequal
  • isequal
  • iseven
  • iseven
  • iseven
  • iseven
  • isfinite
  • isfinite
  • isfinite
  • isfinite
  • isfinite
  • ishermitian
  • isinf
  • isinteger
  • isinteger
  • isinteger
  • isinteger
  • isinteger
  • isodd
  • isometry_group
  • isomorphism
  • isomorphism
  • isomorphism
  • isone
  • isone
  • isone
  • isone
  • isone
  • isone
  • isone
  • isone
  • isqrt
  • isqrtrem
  • isreal
  • isreal
  • isreal
  • isreal
  • issubset
  • issubset
  • issubset
  • issubset
  • issubset
  • istrivial
  • isupper_triangular
  • iszero
  • iszero
  • iszero
  • iszero
  • iszero
  • iszero
  • iszero
  • iszero
  • iszero
  • iszero
  • iszero
  • iterate_basis
  • j_invariant
  • j_invariant
  • jacobi_ideal
  • jacobi_ideal
  • jacobi_symbol
  • jacobi_symbol
  • jacobi_theta
  • jordan_decomposition
  • jordan_normal_form
  • katsura
  • katsura
  • kernel
  • kernel
  • kernel
  • kernel
  • kernel
  • kernel_lattice
  • kissing_number
  • klein_bottle
  • known_class_fusion
  • kronecker_symbol
  • kummer_failure
  • largest_elementary_divisor
  • lattice
  • lattice
  • lattice
  • lattice
  • lattice
  • lattice_points
  • lattice_volume
  • lcm
  • lcm
  • lcm
  • lcm
  • leading_coefficient
  • leading_coefficient
  • leading_coefficient
  • leading_ideal
  • leading_ideal
  • leading_monomial
  • leading_term
  • left_acting_group
  • left_coset
  • left_cosets
  • left_ideal
  • left_kernel
  • left_transversal
  • leglength
  • length
  • length
  • length
  • length
  • length
  • length
  • length
  • length
  • level
  • level
  • lex
  • lgamma
  • lgamma
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift
  • lift_homomorphism_contravariant
  • lift_homomorphism_covariant
  • lindep
  • lindep
  • lindep
  • lineality_dim
  • lineality_dim
  • lineality_dim
  • lineality_space
  • lineality_space
  • lineality_space
  • linear_symmetries
  • link_subcomplex
  • list_rand
  • 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
  • local_basis_matrix
  • local_genera_hermitian
  • local_modification
  • local_symbol
  • localization
  • log
  • log
  • log
  • log
  • log
  • log_barnes_g
  • log_integral
  • log_integral_offset
  • log_pi_i
  • log_sinpi
  • loops
  • lorenz_module
  • lower_triangular_matrix
  • lower_triangular_matrix
  • lu
  • map
  • map!
  • map_coefficients
  • map_coefficients
  • map_coefficients
  • map_entries
  • map_from_character_lattice_to_torusinvariant_weil_divisor_group
  • 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_word
  • mass
  • mass
  • mass
  • matrix
  • matrix
  • matrix
  • matrix
  • matrix
  • matrix
  • matrix_group
  • matrix_ordering
  • matrix_repr
  • matrix_repr
  • matrix_repr
  • matroid_from_bases
  • matroid_from_circuits
  • matroid_from_hyperplanes
  • matroid_from_matrix_columns
  • matroid_from_matrix_rows
  • matroid_from_nonbases
  • matroid_from_revlex_basis_encoding
  • matroid_groundset
  • max_exp
  • max_precision
  • maxabs_exp
  • maxes
  • maximal_abelian_quotient
  • maximal_abelian_subfield
  • maximal_abelian_subfield
  • maximal_blocks
  • maximal_cells
  • maximal_cones
  • maximal_elementary_divisor
  • maximal_extension
  • maximal_integral_lattice
  • maximal_integral_lattice
  • maximal_integral_lattice
  • maximal_integral_lattice
  • maximal_normal_subgroups
  • maximal_polyhedra
  • maximal_subgroups
  • maximum
  • maximum
  • maximum
  • maximum
  • maximum
  • midpoint
  • min_exp
  • min_weights
  • minimal_block_reps
  • minimal_generating_set
  • minimal_generating_set
  • minimal_nonfaces
  • minimal_normal_subgroups
  • minimal_primes
  • minimal_subalgebra_generators
  • minimum
  • minimum
  • minimum
  • minimum
  • minimum
  • minimum
  • minimum
  • minkowski_map
  • minkowski_map
  • minkowski_matrix
  • minor
  • minors
  • minpoly
  • minpoly
  • minpoly
  • minpoly
  • minpoly
  • minpoly
  • mod
  • mod
  • mod
  • mod
  • mod
  • mod!
  • mod!
  • mod_sym
  • mod_sym!
  • mod_sym!
  • mod_sym!
  • mod_sym!
  • modord
  • modular_delta
  • modular_lambda
  • modular_proj
  • modular_weber_f
  • modular_weber_f1
  • modular_weber_f2
  • modulus
  • modulus
  • modulus
  • modulus
  • modulus
  • modulus_bilinear_form
  • modulus_quadratic_form
  • moebius_mu
  • moebius_mu
  • molien_series
  • monomial_to_newton!
  • mori_cone
  • morphism_from_cox_variety
  • morphism_on_torusinvariant_cartier_divisor_group
  • morphism_on_torusinvariant_weil_divisor_group
  • mul
  • mul
  • mul
  • mul
  • mul_red!
  • mullow
  • mullow
  • mulmod
  • multi_hilbert_function
  • multi_hilbert_series
  • multi_hilbert_series_reduced
  • multiplicative_group
  • multiplicative_group_generators
  • multiplicative_jordan_decomposition
  • multiplicity
  • multiplicity
  • multiplicity
  • multiplicity
  • multiply_column
  • multiply_column!
  • multiply_row
  • multiply_row!
  • n_connected_components
  • n_maximal_cells
  • n_maximal_cones
  • n_maximal_polyhedra
  • n_nodes
  • name
  • names_of_fusion_sources
  • narrow_class_group
  • natural_character
  • natural_character
  • nbits
  • ncols
  • ncols
  • ncols
  • ndigits
  • ne
  • nef_cone
  • negdeglex
  • negdegrevlex
  • neglex
  • negrevlex
  • negwdeglex
  • negwdegrevlex
  • neighbors
  • newton_polytope
  • newton_to_monomial!
  • next_calkin_wilf
  • next_minimal
  • next_signed_calkin_wilf
  • next_signed_minimal
  • nextpow2
  • nf
  • nf
  • nfacets
  • nfacets
  • ngens
  • ngens
  • nilpotency_class
  • nnz
  • noether_normalization
  • non_fano_matroid
  • non_pappus_matroid
  • nonbases
  • 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_subgroup
  • normal_subgroup
  • normal_subgroups
  • normalization
  • normalization_with_delta
  • normalized_volume
  • normalizer
  • normalizer
  • norms
  • npolyhedra
  • nrays
  • nrays
  • nrays
  • nrels
  • nrows
  • nrows
  • nrows
  • nrows
  • nullity
  • nullspace
  • nullspace_right_rational
  • num_coeff
  • number_atlas_groups
  • number_conjugacy_classes
  • number_field
  • number_field
  • number_of_factors
  • number_of_partitions
  • number_of_partitions
  • number_perfect_groups
  • number_primitive_groups
  • number_small_groups
  • number_transitive_groups
  • numerator
  • numerator
  • numerator
  • numerator
  • numerator
  • numpart
  • numpart
  • nv
  • nvars
  • nvertices
  • nvertices
  • nvertices
  • objective_function
  • oct
  • oddity
  • omega_group
  • on_indeterminates
  • on_sets
  • on_tuples
  • one
  • one
  • one
  • one
  • one
  • onei
  • onei
  • 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
  • orders_centralizers
  • orders_class_representatives
  • orders_perfect_groups
  • orthogonal_basis
  • orthogonal_complement
  • orthogonal_components
  • orthogonal_group
  • orthogonal_sign
  • orthogonal_submodule
  • orthogonal_submodule
  • orthogonal_submodule
  • orthogonal_sum
  • orthogonal_sum
  • orthogonal_sum
  • orthogonal_sum
  • orthogonal_sum
  • orthogonal_sum
  • outneighbors
  • overlaps
  • overlaps
  • overlaps
  • overlaps
  • overlaps
  • overlaps
  • overlattice
  • pappus_matroid
  • parallel_extension
  • parametrization_plane_curve
  • parent
  • parent
  • parent
  • parent
  • parent_type
  • parity
  • partitions
  • partitionseq
  • patches
  • pbw_algebra
  • pcore
  • perfect_group
  • perfect_group_identification
  • perm
  • permtype
  • permutation
  • permutation_matrix
  • permuted
  • pfaffian
  • pfaffians
  • picard_group
  • picard_group
  • pmaximal_overorder
  • points
  • pol_elementary_divisors
  • polarize
  • polarize
  • polygamma
  • polyhedra
  • polyhedra_of_dim
  • polyhedron
  • polylog
  • polylog
  • polynomial
  • polynomial
  • polynomial
  • polynomial
  • polynomial_to_power_sums
  • popcount
  • popov
  • popov_with_transform
  • positive_hull
  • possible_class_fusions
  • poverorder
  • poverorders
  • pow
  • power_class
  • power_product_class
  • power_reduce
  • power_sums_to_polynomial
  • powermod
  • powers
  • powers_of_element
  • ppio
  • pradical
  • pradical
  • precision
  • precision
  • precision
  • preimage
  • preimage
  • preimage
  • preimage
  • preimage_map
  • preimage_map
  • presentation
  • preserved_quadratic_forms
  • preserved_sesquilinear_forms
  • prevpow2
  • primary_decomposition
  • primary_invariants
  • prime
  • prime
  • prime
  • prime
  • prime_decomposition_type
  • prime_ideals_up_to
  • prime_of_pgroup
  • primes
  • primes
  • primes_up_to
  • primitive_closure
  • primitive_closure
  • primitive_collections
  • primitive_group
  • primitive_group_identification
  • primorial
  • primorial
  • primpart
  • principal_divisor
  • principal_extension
  • principal_generator
  • principal_generator_fac_elem
  • principal_subfields
  • print_constraints
  • print_constraints
  • product
  • product
  • proj_space
  • proj_space
  • project_full
  • projection
  • projection
  • projection
  • projective_geometry
  • projective_plane
  • projective_space
  • pseudo_basis
  • pseudo_basis
  • pseudo_hnf
  • pseudo_hnf_with_transform
  • pseudo_inv
  • pseudo_matrix
  • pseudodivrem
  • pseudorem
  • psi_guess
  • psi_lower
  • psubgroups
  • psylow_subgroup
  • pth_root
  • pullback
  • push!
  • push_term!
  • pyramid
  • quadratic_defect
  • quadratic_field
  • quadratic_form
  • quadratic_form
  • quadratic_lattice
  • quadratic_lattice
  • quadratic_lattice
  • quadratic_lattice
  • quadratic_product
  • quadratic_space
  • quadratic_space
  • quadratic_space
  • quaternion_group
  • quo
  • quo
  • quo
  • quo
  • quo
  • quo
  • quo
  • quo
  • quo
  • quo
  • quo
  • quo
  • quo
  • quotient
  • quotient
  • radical
  • radical
  • radical
  • radical_bilinear
  • radical_extension
  • radical_membership
  • radical_quadratic
  • radical_subgroup
  • radius
  • ramification_group
  • ramification_index
  • ramified_primes
  • rand
  • rand
  • rand
  • rand
  • rand
  • rand
  • rand
  • rand
  • rand
  • rand
  • rand_bits
  • rand_bits
  • rand_bits_prime
  • rand_pair_EllCurve_Point
  • rand_pseudo
  • rand_row
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank
  • rank_action
  • ranks
  • rational_point_conic
  • rational_representative
  • rational_span
  • rational_span
  • 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
  • rays
  • rays
  • rays
  • rays
  • real
  • real
  • real_embeddings
  • real_places
  • real_projective_plane
  • recession_cone
  • reconstruct
  • reconstruct
  • reconstruct
  • reconstruct
  • 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
  • reduction
  • reduction
  • regular_triangulation
  • regular_triangulations
  • regulator
  • relations
  • relative_class_number
  • relative_interior_point
  • relative_simple_extension
  • relators
  • rels
  • rem_edge!
  • rem_vertex!
  • remove
  • remove
  • representation_matrix
  • representation_matrix
  • representation_matrix
  • representative
  • representative
  • representative
  • representative
  • representative
  • representative
  • representative
  • representative
  • representative
  • representative_action
  • representative_action
  • representatives
  • representatives
  • represents
  • represents
  • rescale
  • rescale
  • rescale
  • rescale
  • rescale
  • resolvent
  • restrict
  • restrict
  • restrict
  • restrict
  • restrict_automorphism
  • restrict_homomorphism
  • restrict_scalars
  • restricted_map
  • restriction
  • resultant
  • resx
  • reverse
  • reverse
  • reverse
  • reverse
  • reverse
  • reverse_rows!
  • revlex
  • revlex_basis_encoding
  • reynolds_operator
  • rgamma
  • rgamma
  • right_acting_group
  • right_coset
  • right_cosets
  • right_ideal
  • right_kernel
  • right_transversal
  • ring
  • ring_class_field
  • ring_class_group
  • ring_of_multipliers
  • rising_factorial
  • rising_factorial
  • rising_factorial
  • rising_factorial
  • rising_factorial
  • rising_factorial
  • rising_factorial2
  • rising_factorial2
  • root
  • root
  • root
  • root
  • root_lattice
  • root_lattice_recognition
  • root_lattice_recognition_fundamental
  • root_of_unity
  • root_of_unity
  • root_of_unity
  • root_of_unity_as_args
  • roots
  • roots
  • roots
  • roots
  • roots
  • roots
  • roots_upper_bound
  • roots_upper_bound
  • rowlength
  • rref
  • rref_rational
  • rsqrt
  • rsqrt
  • saturate
  • saturate
  • saturated_ideal
  • saturation
  • saturation_with_index
  • save
  • scalar_product
  • scale
  • scale
  • scale
  • scale
  • scale
  • scale_row!
  • scales
  • schur_index
  • secondary_cone
  • secondary_cone
  • secondary_invariants
  • secondary_polytope
  • semidirect_product
  • series_extension
  • set_attribute!
  • set_coefficient!
  • set_coordinate_names
  • set_coordinate_names_of_torus
  • set_html_as_latex
  • set_variable!
  • setbit!
  • setindex!
  • setindex!
  • setpermstyle
  • setunion
  • setyoungtabstyle
  • shift_left
  • shift_left
  • shift_left
  • shift_right
  • shift_right
  • shift_right
  • short_vectors
  • short_vectors_iterator
  • shortest_path_dijkstra
  • shortest_vectors
  • sign
  • sign
  • sign
  • sign
  • sign
  • sign
  • sign
  • sign_imag
  • sign_real
  • signature
  • signature
  • signature
  • signature
  • signature
  • signature
  • signature_tuple
  • signatures
  • signs
  • signs
  • similarity!
  • simple_extension
  • simplest_between
  • simplest_rational_inside
  • simplex
  • simplified_fp_group
  • simplified_simple_extension
  • simplify
  • simplify
  • simplify
  • simplify
  • simplify
  • simplify
  • sin
  • sin_integral
  • sinh_integral
  • sinpi
  • size
  • size
  • size
  • size
  • small_group
  • small_group_identification
  • snf
  • snf
  • snf
  • snf
  • snf
  • snf_diagonal
  • snf_with_transform
  • snf_with_transform
  • socle
  • solve
  • solve
  • solve_dixon
  • solve_dixon
  • solve_dixon_sf
  • solve_ineq
  • solve_left
  • solve_lp
  • solve_milp
  • solve_mixed
  • solve_mixed
  • solve_non_negative
  • solve_rational
  • solve_triu
  • spanning_sets
  • sparse
  • sparse_matrix
  • sparse_matrix
  • sparse_matrix
  • sparse_matrix
  • sparse_row
  • sparse_row
  • sparse_row
  • sparsity
  • special_linear_group
  • special_orthogonal_group
  • special_unitary_group
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt
  • sqrt1pm1
  • sqrtmod
  • sqrtpos
  • src
  • stabilizer
  • stably_intersect
  • standard_basis
  • standard_basis_with_transformation_matrix
  • stanley_reisner_ideal
  • stanley_reisner_ideal
  • stanley_reisner_ideal
  • stanley_reisner_ideal
  • stanley_reisner_ring
  • stanley_reisner_ring
  • star_subcomplex
  • starsubdivision
  • strictly_lower_triangular_matrix
  • strictly_upper_triangular_matrix
  • strong_echelon_form
  • strong_echelon_form
  • structure_sheaf
  • structure_tropical_jacobian
  • sub
  • sub
  • sub
  • sub
  • sub
  • sub
  • sub
  • sub
  • sub
  • sub
  • subalgebra_membership
  • subfields
  • subfields
  • subgroups
  • subgroups
  • subquotient
  • subscheme
  • subscheme
  • subst
  • sum
  • sum_Point_EllCurveZnZ
  • summands
  • sunit_group
  • sunit_group_fac_elem
  • sunit_mod_units_group_fac_elem
  • supermodule
  • supermodule
  • support_function
  • swap_cols
  • swap_cols!
  • swap_cols!
  • swap_rows
  • swap_rows!
  • swap_rows!
  • swinnerton_dyer
  • sylow_subgroup
  • sylow_system
  • sylvester_matrix
  • symbol
  • symbols
  • symmetric_form
  • symmetric_group
  • symmetric_parts
  • symmetric_power
  • symmetrizations
  • symplectic_components
  • symplectic_group
  • syzygy_generators
  • t2
  • tail
  • tail
  • tan
  • tangent
  • tangent
  • tangent_lines
  • tangent_lines
  • tanpi
  • teichmuller
  • teichmuller
  • tensor_product
  • tensor_product
  • tensor_product
  • tensor_product
  • test_module
  • theta_qexp
  • to_univariate
  • tor
  • toric_divisor
  • toric_divisor
  • toric_ideal
  • toric_ideal
  • toric_ideal
  • toric_variety
  • toric_variety
  • toric_variety
  • toric_variety
  • toric_variety
  • toric_variety
  • toric_variety
  • torsion_points_division_poly
  • torsion_points_lutz_nagell
  • torsion_quadratic_module
  • torsion_quadratic_module
  • torsion_subgroup
  • torsion_unit_group
  • torsion_unit_order
  • torsion_units
  • torsion_units_gen_order
  • torsion_units_generator
  • torus
  • torusinvariant_cartier_divisor_group
  • torusinvariant_prime_divisors
  • torusinvariant_weil_divisor_group
  • toweierstrass
  • tr
  • tr
  • tr
  • tr
  • tr
  • tr
  • trace_matrix
  • trailing_coefficient
  • trailing_coefficient
  • trailing_coefficient
  • trailing_zeros
  • transform_row
  • transform_row!
  • transitive_group
  • transitive_group_identification
  • transitivity
  • transpose
  • transpose
  • trim
  • trim
  • trivial_character
  • trivial_character
  • trivial_divisor
  • trivial_divisor_class
  • trivial_morphism
  • trivial_subgroup
  • tropical_polynomial
  • truncate
  • truncate
  • truncate
  • truncate
  • truncate
  • tstbit
  • tutte_connectivity
  • tutte_polynomial
  • two_sided_ideal
  • undefined
  • uniform_matroid
  • uniformizer
  • union
  • unique_integer
  • unique_integer
  • unique_integer
  • unique_integer
  • unit
  • unit
  • unit_group
  • unit_group_fac_elem
  • unit_group_rank
  • unitary_group
  • unknown
  • unsigned_infinity
  • upper_bound
  • upper_triangular_matrix
  • upper_triangular_matrix
  • v_reduced
  • valence_mc
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • valuation
  • value_module
  • value_module_quadratic_form
  • vamos_matroid
  • vanishing_sets
  • var
  • var
  • var_index
  • vars
  • vcat
  • vcat!
  • vdim
  • versioninfo
  • vertical_connectivity
  • vertices
  • vertices
  • visualize
  • visualize
  • visualize
  • volume
  • volume
  • volume_form
  • wdeglex
  • wdegrevlex
  • weak_popov
  • weak_popov_with_transform
  • weierstrass_form
  • weierstrass_p
  • weight_ordering
  • weighted_projective_space
  • weyl_algebra
  • wildanger_field
  • witt_index
  • witt_invariant
  • witt_invariant
  • wreath_product
  • write_as_full
  • zero
  • zero
  • zero
  • zero
  • zero
  • zero_matrix
  • zero_matrix
  • zeta
  • zeta
  • zeta
  • zeta
  • zeta
  • zeta_log_residue
  • @attr
  • @attributes
  • @perm
  • @perm_str
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