• AffineCurveDivisor
• AffineNormalToricVariety
• AffineNormalToricVariety
• AffinePlaneCurve
• Array
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• BasicGAPGroupElem
• CohomologyClass
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• FPGroup
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• Fac
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• FlintPadicField
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• GAPGroup
• GAPGroupCharacterTable
• Graph
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• GrpAbFinGen
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• LaurentPolynomialRing
• LinearProgram
• MPolyBuildCtx
• MapFromFunc
• Matrix
• MatrixGroup
• MatrixGroupElem
• Matroid
• NfAbsOrd
• NormalToricVariety
• NormalToricVariety
• NormalToricVariety
• NormalToricVariety
• Partition
• PcGroup
• PcGroupElem
• Perm
• PermGroup
• PermGroupElem
• Point
• Point_EllCurve
• PolyhedralComplex
• PolyhedralFan
• Polyhedron
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• Polyhedron
• ProjCurve
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• Scheme
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• SimplicialComplex
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• Spec
• SubdivisionOfPoints
• SubdivisionOfPoints
• SymmetricGroup
• ToricDivisor
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• ToricLineBundle
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• TropicalCurve
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• TropicalHypersurface
• TropicalLinearSpace
• TropicalSemiring
• TropicalSemiringMap
• Vector
• WreathProductGroup
• YoungTableau
• fmpz_mat
• fmpz_mat
• *
• *
• *
• *
• *
• *
• *
• *
• *
• *
• *
• *
• *
• +
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• +
• +
• +
• <<
• <<
• <<
• ==
• ==
• ==
• ==
• ==
• ==
• ==
• ==
• ==
• ==
• >>
• >>
• >>
• CyclotomicField
• CyclotomicRealSubfield
• DirectSum
• DivisorOfCharacter
• ECM
• ECPP
• EquationOrder
• FlintFiniteField
• FreeModule
• GF
• GradedPolynomialRing
• IntMult_Point_EllCurveZnZ
• Localization
• 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
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• PseudoMatrix
• PseudoMatrix
• PseudoMatrix
• ResidueField
• ResidueRing
• VectorSpace
• ^
• ^
• ^
• _numpart
• abelian_closure
• 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
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• accuracy_bits
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• acos
• acospi
• acting_domain
• acting_group
• acting_subgroup
• acting_subgroup
• action_homomorphism
• add_column
• add_column!
• add_edge!
• add_error!
• 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_geometry
• affine_hull
• affine_open_covering
• 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
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• all_triangulations
• alternating_form
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• ambient_dim
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• ambient_dim
• ambient_dim
• ambient_space
• angle
• anticanonical_bundle
• anticanonical_divisor
• anticanonical_divisor_class
• any_order
• archimedean_solid
• aretransverse
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• arithmetic_genus
• arithmetic_genus
• as_perm_group
• as_polycyclic_group
• asin
• asinpi
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• atan
• atan2
• atanpi
• atlas_group
• augmented_chow_ring
• automorphism_group
• automorphism_group
• automorphism_group_generators
• automorphism_group_order
• automorphisms
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• ball
• barnes_g
• base
• 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
• 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_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
• 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_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
• 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
• closure
• closure
• clrbit!
• cobases
• cocircuits
• cocycle_matroid
• codifferent
• codim
• codim
• codim
• codim
• coeff
• coeff
• coeff
• coeff
• coeff
• coeff
• coeff
• coeff
• coefficient_ideals
• coefficient_ideals
• coefficients
• coefficients
• coefficients
• coefficients
• coefficients
• cohomology
• cohomology
• cohomology_index
• cohomology_ring
• cohyperplanes
• cokernel
• cokernel
• collength
• colon
• coloops
• combit!
• comm
• common_components
• common_components
• compact_presentation
• complement
• complement_of_ideal
• complement_system
• complete_bipartite_graph
• complete_graph
• complex_conjugation
• complex_embeddings
• complex_normal_form
• complex_places
• complex_projective_plane
• component
• 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
• 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
• 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
• deletion
• delpezzo
• 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_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_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
• div
• divexact
• divides
• divisible
• divisible
• divisor
• divisor
• divisor
• divisor
• divisor_class
• divisor_class
• divisor_lenstra
• divisor_sigma
• divisor_sigma
• divisor_sigma
• divisors
• divrem
• double_coset
• double_cosets
• dst
• 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
• elementary_divisors
• elementary_divisors
• elementary_divisors
• elements!
• eliminate
• elliptic_e
• elliptic_k
• emb
• emb!
• embed
• embedding
• embedding
• embedding
• embedding
• embedding
• 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
• 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
• extend
• 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
• 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_hermitian
• general_linear_group
• generalized_jordan_block
• generalized_jordan_form
• generators
• gens
• gens
• gens
• gens
• gens
• genus_field
• 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
• grade
• grade
• grade
• grading_group
• grading_group
• gram
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix
• gram_matrix_of_generators
• gram_matrix_of_rational_span
• graph
• 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
• 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_product
• hom_tensor
• homogeneous_component
• homogeneous_component
• homogeneous_component
• homogeneous_components
• homogeneous_components
• homogenization
• homogenization
• homology
• homomorphism_of_semidirect_product
• homomorphism_of_wreath_product
• hooklength
• howell_form
• howell_form
• hypergeometric_1f1
• hypergeometric_1f1_regularized
• hypergeometric_2f1
• hypergeometric_u
• hyperplanes
• hypersurface_complement
• id_hom
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal
• ideal_membership
• ideal_membership
• ideal_of_linear_relations
• ideal_of_linear_relations
• ideal_point
• idempotents
• idempotents
• identifier
• identity_matrix
• identity_matrix
• identity_matrix
• identity_matrix
• imag
• imag
• image
• image
• image
• image
• image
• image
• in
• in
• in
• in
• in
• in
• in
• in
• in
• in
• independent_sets
• index
• index
• indicator
• induce_crt
• induce_rational_reconstruction
• induced_automorphism
• induced_class_function
• induced_cyclic
• inertia_subgroup
• infinite_places
• infinite_places_uniformizers
• infinity
• infinity
• inflate
• inflate
• inflate
• inflate
• inflate
• inflate
• inneighbors
• inner_automorphism
• inner_automorphisms_group
• inner_cartesian_power
• inner_direct_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
• 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_quadratic_form
• invariant_quadratic_forms
• invariant_ring
• invariant_sesquilinear_form
• invariant_sesquilinear_forms
• invariant_symmetric_forms
• invariants
• 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_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_degenerate
• is_diagonal
• is_divisible_by
• is_duplicate_table
• is_dyadic
• is_effective
• is_effective
• is_effective
• is_embedded
• 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_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_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_invariant
• is_invariant
• 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_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_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_norm
• is_local_norm
• is_local_norm
• is_locally_hyperbolic
• is_locally_isometric
• is_locally_represented_by
• is_loopless
• is_maximal
• is_maximal
• is_maximal_integral
• is_maximal_integral
• is_minor
• 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_nilpotent
• 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_pointed
• is_pointed
• is_positive
• is_positive
• is_positive
• is_positive_definite
• is_positive_definite
• is_positively_graded
• is_power
• is_power
• is_power
• is_power_with_root
• is_primary
• 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_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_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_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
• isequal
• isequal
• 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
• isqrt
• isqrtrem
• isreal
• isreal
• isreal
• isreal
• issubset
• issubset
• issubset
• issubset
• istrivial
• isupper_triangular
• 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
• klein_bottle
• known_class_fusion
• kronecker_symbol
• kummer_failure
• largest_elementary_divisor
• 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_kernel
• left_transversal
• leglength
• length
• length
• length
• length
• length
• length
• length
• lex
• lgamma
• lgamma
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lift
• lindep
• lindep
• lindep
• lineality_dim
• lineality_dim
• lineality_dim
• lineality_space
• lineality_space
• lineality_space
• link_subcomplex
• list_rand
• 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
• log
• log
• log
• log
• log
• log_barnes_g
• log_integral
• log_integral_offset
• log_pi_i
• log_sinpi
• loops
• lorenz_module
• 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_word
• mass
• 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_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
• 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
• moebius_mu
• moebius_mu
• molien_series
• monomial_ordering
• monomial_ordering
• monomial_ordering
• monomial_to_newton!
• mori_cone
• 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
• 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
• 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
• omega_group
• on_indeterminates
• on_sets
• on_tuples
• one
• one
• one
• one
• one
• onei
• onei
• 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_group
• orthogonal_sign
• orthogonal_sum
• orthogonal_sum
• orthogonal_sum
• outneighbors
• overlaps
• overlaps
• overlaps
• overlaps
• overlaps
• overlaps
• pappus_matroid
• parallel_extension
• parametrization_plane_curve
• parent
• parent
• parent
• parent
• parent_type
• parity
• partitions
• partitionseq
• 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_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
• preserved_quadratic_forms
• preserved_sesquilinear_forms
• prevpow2
• primary_decomposition
• primary_invariants
• prime
• prime
• prime
• prime_decomposition_type
• prime_ideals_up_to
• primes
• primes_up_to
• 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
• push!
• push_term!
• pyramid
• quadratic_defect
• quadratic_field
• quadratic_form
• quadratic_form
• quadratic_lattice
• quadratic_lattice
• quadratic_lattice
• quadratic_lattice
• quadratic_space
• quadratic_space
• quaternion_group
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quo
• quotient
• quotient
• radical
• radical
• radical_extension
• radical_membership
• 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_action
• ranks
• rational_point_conic
• 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_full
• reduce_ideal
• reduce_mod
• reduce_mod
• reduced_characteristic_polynomial
• reduced_discriminant
• reduction
• reduction
• regular_triangulation
• regular_triangulations
• regulator
• 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_action
• representative_action
• representatives
• rescale
• resolvent
• restrict
• restrict
• restrict_automorphism
• restrict_homomorphism
• 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_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_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_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
• shortest_path_dijkstra
• sign
• sign
• sign
• sign
• sign
• sign
• sign
• sign_imag
• sign_real
• signature
• signature
• signature
• signature
• signatures
• signs
• signs
• similarity!
• simple_extension
• simplest_between
• simplest_rational_inside
• simplex
• simplified_fp_group
• simplified_simple_extension
• 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_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
• stanley_reisner_ideal
• stanley_reisner_ideal
• stanley_reisner_ideal
• stanley_reisner_ideal
• stanley_reisner_ring
• stanley_reisner_ring
• star_subcomplex
• starsubdivision
• std_basis
• strong_echelon_form
• strong_echelon_form
• structure_sheaf
• structure_tropical_jacobian
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• sub
• subalgebra_membership
• subfields
• subfields
• subfields
• subgroups
• subgroups
• subquotient
• 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
• symbols
• symmetric_form
• symmetric_group
• symplectic_group
• syzygy_generators
• t2
• tail
• tail
• tan
• tangent
• tangent
• tangent_lines
• tangent_lines
• tanpi
• teichmuller
• teichmuller
• tensor_product
• theta_qexp
• to_univariate
• toric_divisor
• toric_divisor
• toric_ideal
• toric_ideal
• toric_ideal
• toric_variety
• toric_variety
• toric_variety
• toric_variety
• toric_variety
• torsion_points_division_poly
• torsion_points_lutz_nagell
• 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
• 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
• v_reduced
• valence_mc
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• valuation
• vamos_matroid
• vanishing_sets
• var
• var
• var_index
• vars
• vcat
• vcat!
• versioninfo
• vertical_connectivity
• vertices
• vertices
• visualize
• visualize
• visualize
• volume
• volume
• volume_form
• wdeglex
• wdegrevlex
• weak_popov
• weak_popov_with_transform
• weierstrass_form
• weierstrass_p
• weighted_ordering
• 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