Index _ | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Z _ __classcall__() (sage.categories.category.Category static method) (sage.categories.category_with_axiom.CategoryWithAxiom static method) __classget__() (sage.categories.category_with_axiom.CategoryWithAxiom static method) __init__() (sage.categories.category.Category method) (sage.categories.category_with_axiom.CategoryWithAxiom method) _all_super_categories() (sage.categories.category.Category method) _all_super_categories_proper() (sage.categories.category.Category method) _make_named_class() (sage.categories.category.Category method) (sage.categories.category.CategoryWithParameters.Category method) _repr_() (sage.categories.category.Category method) (sage.categories.category.JoinCategory.Category method) _repr_object_names() (sage.categories.category.Category method) (sage.categories.category.JoinCategory.Category method) (sage.categories.category_with_axiom.CategoryWithAxiom method) _repr_object_names_static() (sage.categories.category_with_axiom.CategoryWithAxiom static method) _set_of_super_categories() (sage.categories.category.Category method) _sort() (sage.categories.category.Category static method) _sort_uniq() (sage.categories.category.Category static method) _super_categories() (sage.categories.category.Category method) _super_categories_for_classes() (sage.categories.category.Category method) _test_category() (sage.categories.category.Category method) _test_category_with_axiom() (sage.categories.category_with_axiom.CategoryWithAxiom method) _with_axiom() (sage.categories.category.Category method) _with_axiom_as_tuple() (sage.categories.category.Category method) _without_axioms() (sage.categories.category.Category method) (sage.categories.category.JoinCategory.Category method) (sage.categories.category_with_axiom.CategoryWithAxiom method) A a_realization() (sage.categories.examples.with_realizations.SubsetAlgebra method) (sage.categories.sets_cat.Sets.WithRealizations.ParentMethods method) AbelianCategory (class in sage.categories.category_types) AbelianLieAlgebra (class in sage.categories.examples.finite_dimensional_lie_algebras_with_basis) (class in sage.categories.examples.lie_algebras_with_basis) AbelianLieAlgebra.Element (class in sage.categories.examples.finite_dimensional_lie_algebras_with_basis) (class in sage.categories.examples.lie_algebras_with_basis) abs() (sage.categories.metric_spaces.MetricSpaces.ElementMethods method) absolute_covers() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) absolute_le() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) absolute_length() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) absolute_order_ideal() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.Irreducible.ParentMethods method) absolute_poset() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.Irreducible.ParentMethods method) act() (sage.categories.action.Action method) Action (class in sage.categories.action) ActionEndomorphism (class in sage.categories.action) actor() (sage.categories.action.Action method) adams_operator() (sage.categories.bialgebras_with_basis.BialgebrasWithBasis.ElementMethods method) add() (sage.categories.category_cy_helper.AxiomContainer method) addition_table() (sage.categories.additive_magmas.AdditiveMagmas.ParentMethods method) additional_structure() (sage.categories.additive_magmas.AdditiveMagmas.AdditiveUnital method) (sage.categories.affine_weyl_groups.AffineWeylGroups method) (sage.categories.bialgebras.Bialgebras method) (sage.categories.bimodules.Bimodules method) (sage.categories.category.Category method) (sage.categories.category.JoinCategory method) (sage.categories.category_with_axiom.CategoryWithAxiom method) (sage.categories.classical_crystals.ClassicalCrystals method) (sage.categories.complex_reflection_groups.ComplexReflectionGroups method) (sage.categories.covariant_functorial_construction.CovariantConstructionCategory method) (sage.categories.coxeter_groups.CoxeterGroups method) (sage.categories.enumerated_sets.EnumeratedSets method) (sage.categories.gcd_domains.GcdDomains method) (sage.categories.generalized_coxeter_groups.GeneralizedCoxeterGroups method) (sage.categories.highest_weight_crystals.HighestWeightCrystals method) (sage.categories.lie_groups.LieGroups method) (sage.categories.magmas.Magmas.Unital method) (sage.categories.magmas_and_additive_magmas.MagmasAndAdditiveMagmas method) (sage.categories.magmatic_algebras.MagmaticAlgebras method) (sage.categories.manifolds.Manifolds method) (sage.categories.modules.Modules method) (sage.categories.objects.Objects method) (sage.categories.principal_ideal_domains.PrincipalIdealDomains method) (sage.categories.regular_crystals.RegularCrystals method) (sage.categories.unique_factorization_domains.UniqueFactorizationDomains method) (sage.categories.vector_spaces.VectorSpaces method) (sage.categories.weyl_groups.WeylGroups method) additive_order() (sage.categories.commutative_additive_groups.CommutativeAdditiveGroups.CartesianProducts.ElementMethods method) additive_semigroup_generators() (sage.categories.examples.commutative_additive_semigroups.FreeCommutativeAdditiveSemigroup method) AdditiveAssociative (sage.categories.additive_magmas.AdditiveMagmas attribute) AdditiveAssociative() (sage.categories.additive_magmas.AdditiveMagmas.SubcategoryMethods method) AdditiveCommutative (sage.categories.additive_groups.AdditiveGroups attribute) (sage.categories.additive_monoids.AdditiveMonoids attribute) (sage.categories.additive_semigroups.AdditiveSemigroups attribute) AdditiveCommutative() (sage.categories.additive_magmas.AdditiveMagmas.SubcategoryMethods method) AdditiveGroups (class in sage.categories.additive_groups) AdditiveGroups.Algebras (class in sage.categories.additive_groups) AdditiveGroups.Algebras.ParentMethods (class in sage.categories.additive_groups) AdditiveGroups.Finite (class in sage.categories.additive_groups) AdditiveGroups.Finite.Algebras (class in sage.categories.additive_groups) AdditiveGroups.Finite.Algebras.ParentMethods (class in sage.categories.additive_groups) AdditiveInverse (sage.categories.additive_monoids.AdditiveMonoids attribute) (sage.categories.distributive_magmas_and_additive_magmas.DistributiveMagmasAndAdditiveMagmas.AdditiveAssociative.AdditiveCommutative.AdditiveUnital.Associative attribute) AdditiveInverse() (sage.categories.additive_magmas.AdditiveMagmas.AdditiveUnital.SubcategoryMethods method) AdditiveMagmas (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveCommutative (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveCommutative.Algebras (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveCommutative.CartesianProducts (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.AdditiveInverse (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.AdditiveInverse.CartesianProducts (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.AdditiveInverse.CartesianProducts.ElementMethods (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.Algebras (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.Algebras.ParentMethods (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.CartesianProducts (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.CartesianProducts.ParentMethods (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.ElementMethods (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.Homsets (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.Homsets.ParentMethods (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.ParentMethods (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.SubcategoryMethods (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.WithRealizations (class in sage.categories.additive_magmas) AdditiveMagmas.AdditiveUnital.WithRealizations.ParentMethods (class in sage.categories.additive_magmas) AdditiveMagmas.Algebras (class in sage.categories.additive_magmas) AdditiveMagmas.Algebras.ParentMethods (class in sage.categories.additive_magmas) AdditiveMagmas.CartesianProducts (class in sage.categories.additive_magmas) AdditiveMagmas.CartesianProducts.ElementMethods (class in sage.categories.additive_magmas) AdditiveMagmas.ElementMethods (class in sage.categories.additive_magmas) AdditiveMagmas.Homsets (class in sage.categories.additive_magmas) AdditiveMagmas.ParentMethods (class in sage.categories.additive_magmas) AdditiveMagmas.SubcategoryMethods (class in sage.categories.additive_magmas) AdditiveMonoids (class in sage.categories.additive_monoids) AdditiveMonoids.Homsets (class in sage.categories.additive_monoids) AdditiveMonoids.ParentMethods (class in sage.categories.additive_monoids) AdditiveSemigroups (class in sage.categories.additive_semigroups) AdditiveSemigroups.Algebras (class in sage.categories.additive_semigroups) AdditiveSemigroups.Algebras.ParentMethods (class in sage.categories.additive_semigroups) AdditiveSemigroups.CartesianProducts (class in sage.categories.additive_semigroups) AdditiveSemigroups.Homsets (class in sage.categories.additive_semigroups) AdditiveSemigroups.ParentMethods (class in sage.categories.additive_semigroups) AdditiveUnital (sage.categories.additive_semigroups.AdditiveSemigroups attribute) AdditiveUnital() (sage.categories.additive_magmas.AdditiveMagmas.SubcategoryMethods method) adjoint_matrix() (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ElementMethods method) affine_grading() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.TensorProducts.ElementMethods method) affine_grassmannian_elements_of_given_length() (sage.categories.affine_weyl_groups.AffineWeylGroups.ParentMethods method) affine_grassmannian_to_core() (sage.categories.affine_weyl_groups.AffineWeylGroups.ElementMethods method) affine_grassmannian_to_partition() (sage.categories.affine_weyl_groups.AffineWeylGroups.ElementMethods method) AffineWeylGroups (class in sage.categories.affine_weyl_groups) AffineWeylGroups.ElementMethods (class in sage.categories.affine_weyl_groups) AffineWeylGroups.ParentMethods (class in sage.categories.affine_weyl_groups) affinization() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) algebra() (sage.categories.algebra_ideals.AlgebraIdeals method) (sage.categories.algebra_modules.AlgebraModules method) (sage.categories.commutative_algebra_ideals.CommutativeAlgebraIdeals method) (sage.categories.sets_cat.Sets.ParentMethods method) algebra_generators() (sage.categories.additive_magmas.AdditiveMagmas.Algebras.ParentMethods method) (sage.categories.additive_semigroups.AdditiveSemigroups.Algebras.ParentMethods method) (sage.categories.algebras.Algebras.Quotients.ParentMethods method) (sage.categories.examples.algebras_with_basis.FreeAlgebra method) (sage.categories.examples.finite_dimensional_algebras_with_basis.KroneckerQuiverPathAlgebra method) (sage.categories.examples.hopf_algebras_with_basis.MyGroupAlgebra method) (sage.categories.examples.lie_algebras_with_basis.IndexedPolynomialRing method) (sage.categories.magmatic_algebras.MagmaticAlgebras.ParentMethods method) (sage.categories.magmatic_algebras.MagmaticAlgebras.WithBasis.ParentMethods method) (sage.categories.monoids.Monoids.Algebras.ParentMethods method) (sage.categories.semigroups.Semigroups.Algebras.ParentMethods method) AlgebraFunctor (class in sage.categories.algebra_functor) AlgebraicClosureFunctor (class in sage.categories.pushout) AlgebraicExtensionFunctor (class in sage.categories.pushout) AlgebraIdeals (class in sage.categories.algebra_ideals) AlgebraModules (class in sage.categories.algebra_modules) Algebras (class in sage.categories.algebras) (sage.categories.coxeter_groups.CoxeterGroups attribute) (sage.categories.groups.Groups attribute) Algebras() (sage.categories.sets_cat.Sets.SubcategoryMethods method) Algebras.CartesianProducts (class in sage.categories.algebras) Algebras.DualObjects (class in sage.categories.algebras) Algebras.ElementMethods (class in sage.categories.algebras) Algebras.Quotients (class in sage.categories.algebras) Algebras.Quotients.ParentMethods (class in sage.categories.algebras) Algebras.SubcategoryMethods (class in sage.categories.algebras) Algebras.TensorProducts (class in sage.categories.algebras) Algebras.TensorProducts.ElementMethods (class in sage.categories.algebras) Algebras.TensorProducts.ParentMethods (class in sage.categories.algebras) AlgebrasCategory (class in sage.categories.algebra_functor) AlgebrasCategory.ParentMethods (class in sage.categories.algebra_functor) AlgebrasWithBasis (class in sage.categories.algebras_with_basis) AlgebrasWithBasis.CartesianProducts (class in sage.categories.algebras_with_basis) AlgebrasWithBasis.CartesianProducts.ParentMethods (class in sage.categories.algebras_with_basis) AlgebrasWithBasis.ElementMethods (class in sage.categories.algebras_with_basis) AlgebrasWithBasis.ParentMethods (class in sage.categories.algebras_with_basis) AlgebrasWithBasis.TensorProducts (class in sage.categories.algebras_with_basis) AlgebrasWithBasis.TensorProducts.ElementMethods (class in sage.categories.algebras_with_basis) AlgebrasWithBasis.TensorProducts.ParentMethods (class in sage.categories.algebras_with_basis) all_paths_to_highest_weight() (sage.categories.crystals.Crystals.ElementMethods method) all_super_categories() (sage.categories.category.Category method) AlmostComplex() (sage.categories.manifolds.Manifolds.SubcategoryMethods method) ambient() (sage.categories.category_types.Category_in_ambient method) (sage.categories.examples.finite_dimensional_lie_algebras_with_basis.AbelianLieAlgebra method) (sage.categories.examples.finite_enumerated_sets.IsomorphicObjectOfFiniteEnumeratedSet method) (sage.categories.examples.semigroups.IncompleteSubquotientSemigroup method) (sage.categories.examples.semigroups.QuotientOfLeftZeroSemigroup method) (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.Subobjects.ParentMethods method) (sage.categories.sets_cat.Sets.Subquotients.ParentMethods method) an_element() (sage.categories.crystals.Crystals.ParentMethods method) (sage.categories.examples.commutative_additive_semigroups.FreeCommutativeAdditiveSemigroup method) (sage.categories.examples.cw_complexes.Surface method) (sage.categories.examples.finite_monoids.IntegerModMonoid method) (sage.categories.examples.finite_semigroups.LeftRegularBand method) (sage.categories.examples.graphs.Cycle method) (sage.categories.examples.infinite_enumerated_sets.NonNegativeIntegers method) (sage.categories.examples.magmas.FreeMagma method) (sage.categories.examples.manifolds.Plane method) (sage.categories.examples.posets.FiniteSetsOrderedByInclusion method) (sage.categories.examples.semigroups.FreeSemigroup method) (sage.categories.examples.semigroups.LeftZeroSemigroup method) (sage.categories.examples.semigroups.QuotientOfLeftZeroSemigroup method) (sage.categories.examples.sets_cat.PrimeNumbers method) (sage.categories.examples.sets_cat.PrimeNumbers_Abstract method) (sage.categories.examples.sets_with_grading.NonNegativeIntegers method) (sage.categories.sets_cat.Sets.CartesianProducts.ParentMethods method) (sage.categories.sets_cat.Sets.ParentMethods method) an_instance() (sage.categories.algebra_modules.AlgebraModules class method) (sage.categories.bimodules.Bimodules class method) (sage.categories.category.Category class method) (sage.categories.category_types.Category_ideal class method) (sage.categories.category_types.Category_over_base class method) (sage.categories.category_types.Elements class method) (sage.categories.g_sets.GSets class method) (sage.categories.groupoid.Groupoid class method) Analytic() (sage.categories.manifolds.Manifolds.SubcategoryMethods method) annihilator() (sage.categories.finite_dimensional_modules_with_basis.FiniteDimensionalModulesWithBasis.ParentMethods method) annihilator_basis() (sage.categories.finite_dimensional_modules_with_basis.FiniteDimensionalModulesWithBasis.ParentMethods method) antichains() (sage.categories.finite_posets.FinitePosets.ParentMethods method) antipode() (sage.categories.hopf_algebras.HopfAlgebras.ElementMethods method) (sage.categories.hopf_algebras.HopfAlgebras.Super.ElementMethods method) (sage.categories.hopf_algebras_with_basis.HopfAlgebrasWithBasis.ParentMethods method) (sage.categories.super_hopf_algebras_with_basis.SuperHopfAlgebrasWithBasis.ParentMethods method) antipode_by_coercion() (sage.categories.hopf_algebras.HopfAlgebras.Realizations.ParentMethods method) antipode_on_basis() (sage.categories.examples.hopf_algebras_with_basis.MyGroupAlgebra method) (sage.categories.graded_hopf_algebras_with_basis.GradedHopfAlgebrasWithBasis.Connected.ParentMethods method) (sage.categories.group_algebras.GroupAlgebras.ParentMethods method) (sage.categories.hopf_algebras_with_basis.HopfAlgebrasWithBasis.ParentMethods method) Aperiodic (sage.categories.semigroups.Semigroups attribute) Aperiodic() (sage.categories.semigroups.Semigroups.SubcategoryMethods method) AperiodicSemigroups (class in sage.categories.aperiodic_semigroups) apply_conjugation_by_simple_reflection() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ElementMethods method) apply_demazure_product() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) apply_multilinear_morphism() (sage.categories.modules_with_basis.ModulesWithBasis.TensorProducts.ElementMethods method) apply_reflections() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ElementMethods method) apply_simple_projection() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) apply_simple_reflection() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ElementMethods method) apply_simple_reflection_left() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ElementMethods method) apply_simple_reflection_right() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ElementMethods method) (sage.categories.examples.finite_coxeter_groups.DihedralGroup.Element method) apply_simple_reflections() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ElementMethods method) as_finite_dimensional_algebra() (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ParentMethods method) Associative (sage.categories.magmas.Magmas attribute) (sage.categories.magmatic_algebras.MagmaticAlgebras attribute) Associative() (sage.categories.magmas.Magmas.SubcategoryMethods method) AssociativeAlgebras (class in sage.categories.associative_algebras) axiom() (in module sage.categories.category_with_axiom) axiom_of_nested_class() (in module sage.categories.category_with_axiom) AxiomContainer (class in sage.categories.category_cy_helper) axioms() (sage.categories.category.Category method) (sage.categories.category_with_axiom.CategoryWithAxiom method) B b_sharp() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) baker_campbell_hausdorff() (sage.categories.lie_algebras.LieAlgebras.ParentMethods method) Bars (class in sage.categories.category_with_axiom) base() (sage.categories.category_types.Category_over_base method) (sage.categories.homsets.HomsetsCategory method) (sage.categories.signed_tensor.SignedTensorProductsCategory method) (sage.categories.tensor.TensorProductsCategory method) base_category() (sage.categories.category_with_axiom.CategoryWithAxiom method) (sage.categories.covariant_functorial_construction.FunctorialConstructionCategory method) base_category_class_and_axiom() (in module sage.categories.category_with_axiom) base_change_matrix() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.ParentMethods method) base_field() (sage.categories.modular_abelian_varieties.ModularAbelianVarieties method) (sage.categories.vector_spaces.VectorSpaces method) base_point() (sage.categories.simplicial_sets.SimplicialSets.Pointed.ParentMethods method) base_point_map() (sage.categories.simplicial_sets.SimplicialSets.Pointed.ParentMethods method) base_ring() (sage.categories.algebra_functor.AlgebraFunctor method) (sage.categories.cartesian_product.CartesianProductsCategory method) (sage.categories.category_types.Category_over_base_ring method) (sage.categories.modules.Modules.Homsets method) (sage.categories.modules.Modules.Homsets.ParentMethods method) (sage.categories.modules.Modules.SubcategoryMethods method) base_scheme() (sage.categories.schemes.Schemes_over_base method) base_set() (sage.categories.examples.with_realizations.SubsetAlgebra method) base_space() (sage.categories.vector_bundles.VectorBundles method) basis() (sage.categories.examples.finite_dimensional_lie_algebras_with_basis.AbelianLieAlgebra method) (sage.categories.examples.graded_modules_with_basis.GradedPartitionModule method) (sage.categories.filtered_modules_with_basis.FilteredModulesWithBasis.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) basis_matrix() (sage.categories.examples.finite_dimensional_lie_algebras_with_basis.AbelianLieAlgebra method) (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.Subobjects.ParentMethods method) bch() (sage.categories.lie_algebras.LieAlgebras.ParentMethods method) bhz_poset() (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods method) Bialgebras (class in sage.categories.bialgebras) Bialgebras.ElementMethods (class in sage.categories.bialgebras) Bialgebras.Super (class in sage.categories.bialgebras) BialgebrasWithBasis (class in sage.categories.bialgebras_with_basis) BialgebrasWithBasis.ElementMethods (class in sage.categories.bialgebras_with_basis) BialgebrasWithBasis.ParentMethods (class in sage.categories.bialgebras_with_basis) Bimodules (class in sage.categories.bimodules) Bimodules.ElementMethods (class in sage.categories.bimodules) Bimodules.ParentMethods (class in sage.categories.bimodules) binary_factorizations() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) birational_free_labelling() (sage.categories.finite_posets.FinitePosets.ParentMethods method) birational_rowmotion() (sage.categories.finite_posets.FinitePosets.ParentMethods method) birational_toggle() (sage.categories.finite_posets.FinitePosets.ParentMethods method) birational_toggles() (sage.categories.finite_posets.FinitePosets.ParentMethods method) BlackBoxConstructionFunctor (class in sage.categories.pushout) Blahs (class in sage.categories.category_with_axiom) Blahs.Commutative (class in sage.categories.category_with_axiom) Blahs.Connected (class in sage.categories.category_with_axiom) Blahs.FiniteDimensional (class in sage.categories.category_with_axiom) Blahs.Flying (class in sage.categories.category_with_axiom) Blahs.SubcategoryMethods (class in sage.categories.category_with_axiom) Blahs.Unital (class in sage.categories.category_with_axiom) Blahs.Unital.Blue (class in sage.categories.category_with_axiom) Blue() (sage.categories.category_with_axiom.Blahs.SubcategoryMethods method) Blue_extra_super_categories() (sage.categories.category_with_axiom.Blahs method) bracket() (sage.categories.lambda_bracket_algebras.LambdaBracketAlgebras.ElementMethods method) (sage.categories.lie_algebras.LieAlgebras.ElementMethods method) (sage.categories.lie_algebras.LieAlgebras.ParentMethods method) (sage.categories.rings.Rings.ParentMethods method) bracket_on_basis() (sage.categories.examples.lie_algebras_with_basis.AbelianLieAlgebra method) (sage.categories.lie_algebras_with_basis.LieAlgebrasWithBasis.ParentMethods method) braid_group_as_finitely_presented_group() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) braid_orbit() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) braid_relations() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) bruhat_cone() (sage.categories.weyl_groups.WeylGroups.ParentMethods method) bruhat_graph() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) bruhat_interval() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) bruhat_interval_poset() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) bruhat_le() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) bruhat_lower_covers() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) bruhat_lower_covers_coroots() (sage.categories.weyl_groups.WeylGroups.ElementMethods method) bruhat_lower_covers_reflections() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) bruhat_poset() (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods method) bruhat_upper_covers() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ElementMethods method) bruhat_upper_covers_coroots() (sage.categories.weyl_groups.WeylGroups.ElementMethods method) bruhat_upper_covers_reflections() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) C CallMorphism (class in sage.categories.morphism) cambrian_lattice() (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods method) canonical_matrix() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) canonical_representation() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) canonicalize_axioms() (in module sage.categories.category_cy_helper) cardinality() (sage.categories.classical_crystals.ClassicalCrystals.ParentMethods method) (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.ParentMethods method) (sage.categories.finite_enumerated_sets.FiniteEnumeratedSets.CartesianProducts.ParentMethods method) (sage.categories.finite_enumerated_sets.FiniteEnumeratedSets.IsomorphicObjects.ParentMethods method) (sage.categories.finite_enumerated_sets.FiniteEnumeratedSets.ParentMethods method) (sage.categories.finite_groups.FiniteGroups.ParentMethods method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals.TensorProducts.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) (sage.categories.sets_cat.Sets.CartesianProducts.ParentMethods method) (sage.categories.sets_cat.Sets.Infinite.ParentMethods method) cartan_invariants_matrix() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ParentMethods method) cartan_type() (sage.categories.crystals.CrystalMorphism method) (sage.categories.crystals.Crystals.ElementMethods method) (sage.categories.crystals.Crystals.ParentMethods method) (sage.categories.examples.finite_weyl_groups.SymmetricGroup method) (sage.categories.kac_moody_algebras.KacMoodyAlgebras.ParentMethods method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations.ParentMethods method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations.TensorProducts.ParentMethods method) cartesian_factors() (sage.categories.sets_cat.Sets.CartesianProducts.ElementMethods method) (sage.categories.sets_cat.Sets.CartesianProducts.ParentMethods method) cartesian_product() (sage.categories.sets_cat.Sets.ElementMethods method) (sage.categories.sets_cat.Sets.ParentMethods method) cartesian_projection() (sage.categories.sets_cat.Sets.CartesianProducts.ElementMethods method) (sage.categories.sets_cat.Sets.CartesianProducts.ParentMethods method) CartesianProduct 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(sage.categories.cw_complexes.CWComplexes.ParentMethods method) (sage.categories.examples.cw_complexes.Surface.Element method) (sage.categories.examples.graphs.Cycle.Element method) (sage.categories.examples.manifolds.Plane method) (sage.categories.graphs.Graphs.ParentMethods method) (sage.categories.lie_algebras_with_basis.LieAlgebrasWithBasis.ParentMethods method) (sage.categories.manifolds.Manifolds.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) (sage.categories.simplicial_complexes.SimplicialComplexes.Finite.ParentMethods method) (sage.categories.vector_spaces.VectorSpaces.ParentMethods method) direct_sum() (sage.categories.crystals.Crystals.ParentMethods method) directed_subset() (sage.categories.posets.Posets.ParentMethods method) directed_subsets() (sage.categories.finite_posets.FinitePosets.ParentMethods method) DiscreteValuationFields (class in sage.categories.discrete_valuation) DiscreteValuationFields.ElementMethods (class in sage.categories.discrete_valuation) DiscreteValuationFields.ParentMethods (class in sage.categories.discrete_valuation) DiscreteValuationRings (class in sage.categories.discrete_valuation) DiscreteValuationRings.ElementMethods (class in sage.categories.discrete_valuation) DiscreteValuationRings.ParentMethods (class in sage.categories.discrete_valuation) dist() (sage.categories.metric_spaces.MetricSpaces.CartesianProducts.ParentMethods method) (sage.categories.metric_spaces.MetricSpaces.ElementMethods method) (sage.categories.metric_spaces.MetricSpaces.ParentMethods method) (sage.categories.metric_spaces.MetricSpaces.WithRealizations.ParentMethods method) distinguished_reflection() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) distinguished_reflections() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) Distributive (sage.categories.magmas_and_additive_magmas.MagmasAndAdditiveMagmas attribute) Distributive() (sage.categories.magmas.Magmas.SubcategoryMethods method) (sage.categories.magmas_and_additive_magmas.MagmasAndAdditiveMagmas.SubcategoryMethods method) DistributiveMagmasAndAdditiveMagmas (class in sage.categories.distributive_magmas_and_additive_magmas) DistributiveMagmasAndAdditiveMagmas.AdditiveAssociative (class in sage.categories.distributive_magmas_and_additive_magmas) DistributiveMagmasAndAdditiveMagmas.AdditiveAssociative.AdditiveCommutative (class in sage.categories.distributive_magmas_and_additive_magmas) DistributiveMagmasAndAdditiveMagmas.AdditiveAssociative.AdditiveCommutative.AdditiveUnital (class in sage.categories.distributive_magmas_and_additive_magmas) DistributiveMagmasAndAdditiveMagmas.AdditiveAssociative.AdditiveCommutative.AdditiveUnital.Associative (class in sage.categories.distributive_magmas_and_additive_magmas) DistributiveMagmasAndAdditiveMagmas.CartesianProducts (class in sage.categories.distributive_magmas_and_additive_magmas) DistributiveMagmasAndAdditiveMagmas.ParentMethods (class in sage.categories.distributive_magmas_and_additive_magmas) Division (sage.categories.rings.Rings attribute) Division() (sage.categories.rings.Rings.SubcategoryMethods method) DivisionRings (class in sage.categories.division_rings) DivisionRings.ElementMethods (class in sage.categories.division_rings) DivisionRings.ParentMethods (class in sage.categories.division_rings) domain (sage.categories.map.Map attribute) domain() (sage.categories.action.Action method) (sage.categories.action.PrecomposedAction method) (sage.categories.functor.Functor method) (sage.categories.homset.Homset method) (sage.categories.poor_man_map.PoorManMap method) Domains (class in sage.categories.domains) domains() (sage.categories.map.FormalCompositeMap method) (sage.categories.map.Map method) Domains.ElementMethods (class in sage.categories.domains) Domains.ParentMethods (class in sage.categories.domains) dot_tex() (sage.categories.crystals.Crystals.ParentMethods method) dual() (sage.categories.hopf_algebras.HopfAlgebras method) (sage.categories.hopf_algebras.HopfAlgebras.Super method) (sage.categories.modules.Modules.SubcategoryMethods method) dual_equivalence_class() (sage.categories.regular_crystals.RegularCrystals.ElementMethods method) dual_equivalence_graph() (sage.categories.regular_crystals.RegularCrystals.ParentMethods method) DualFunctor (class in sage.categories.dual) DualObjects() (sage.categories.modules.Modules.SubcategoryMethods method) DualObjectsCategory (class in sage.categories.dual) E e() (sage.categories.crystals.Crystals.ElementMethods method) (sage.categories.examples.crystals.HighestWeightCrystalOfTypeA.Element method) (sage.categories.examples.crystals.NaiveCrystal.Element method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations.WithBasis.ElementMethods method) (sage.categories.triangular_kac_moody_algebras.TriangularKacMoodyAlgebras.ParentMethods method) e_on_basis() (sage.categories.quantum_group_representations.QuantumGroupRepresentations.WithBasis.TensorProducts.ParentMethods method) e_string() (sage.categories.crystals.Crystals.ElementMethods method) e_string_to_ground_state() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.TensorProducts.ElementMethods method) echelon_form() (sage.categories.finite_dimensional_modules_with_basis.FiniteDimensionalModulesWithBasis.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) edges() (sage.categories.examples.graphs.Cycle method) (sage.categories.graphs.Graphs.ParentMethods method) Element (sage.categories.crystals.CrystalHomset attribute) (sage.categories.examples.infinite_enumerated_sets.NonNegativeIntegers attribute) (sage.categories.examples.manifolds.Plane attribute) (sage.categories.examples.semigroups_cython.LeftZeroSemigroup attribute) (sage.categories.highest_weight_crystals.HighestWeightCrystalHomset attribute) element_class (sage.categories.examples.sets_cat.PrimeNumbers attribute) (sage.categories.examples.sets_cat.PrimeNumbers_Facade attribute) element_class() (sage.categories.category.Category method) element_class_set_morphism() (sage.categories.homset.Homset method) Elements (class in sage.categories.category_types) elements_below_coxeter_element() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.Irreducible.ParentMethods method) elements_of_length() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) ElementWrapper (sage.categories.examples.sets_cat.PrimeNumbers_Wrapper attribute) EmptySetError End() (in module sage.categories.homset) end() (in module sage.categories.homset) Endset() (sage.categories.homsets.Homsets.SubcategoryMethods method) Endsets() (sage.categories.objects.Objects.SubcategoryMethods method) energy_function() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ElementMethods method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals.TensorProducts.ElementMethods method) Enumerated (sage.categories.sets_cat.Sets attribute) Enumerated() (sage.categories.sets_cat.Sets.SubcategoryMethods method) EnumeratedSets (class in sage.categories.enumerated_sets) EnumeratedSets.CartesianProducts (class in sage.categories.enumerated_sets) EnumeratedSets.CartesianProducts.ParentMethods (class in sage.categories.enumerated_sets) EnumeratedSets.ElementMethods (class in sage.categories.enumerated_sets) EnumeratedSets.ParentMethods (class in sage.categories.enumerated_sets) Epsilon() (sage.categories.crystals.Crystals.ElementMethods method) epsilon() (sage.categories.crystals.Crystals.ElementMethods method) (sage.categories.regular_crystals.RegularCrystals.ElementMethods method) (sage.categories.regular_supercrystals.RegularSuperCrystals.ElementMethods method) EquivariantSubobjectConstructionFunctor (class in sage.categories.pushout) euclidean_degree() (sage.categories.discrete_valuation.DiscreteValuationRings.ElementMethods method) (sage.categories.euclidean_domains.EuclideanDomains.ElementMethods method) (sage.categories.fields.Fields.ElementMethods method) EuclideanDomains (class in sage.categories.euclidean_domains) EuclideanDomains.ElementMethods (class in sage.categories.euclidean_domains) EuclideanDomains.ParentMethods (class in sage.categories.euclidean_domains) even_component() (sage.categories.super_modules_with_basis.SuperModulesWithBasis.ElementMethods method) Example (class in sage.categories.examples.finite_enumerated_sets) (in module sage.categories.examples.algebras_with_basis) (in module sage.categories.examples.commutative_additive_monoids) (in module sage.categories.examples.commutative_additive_semigroups) (in module sage.categories.examples.cw_complexes) (in module sage.categories.examples.finite_coxeter_groups) (in module sage.categories.examples.finite_dimensional_algebras_with_basis) (in module sage.categories.examples.finite_dimensional_lie_algebras_with_basis) (in module sage.categories.examples.finite_monoids) (in module sage.categories.examples.finite_semigroups) (in module sage.categories.examples.finite_weyl_groups) (in module sage.categories.examples.graded_connected_hopf_algebras_with_basis) (in module sage.categories.examples.graded_modules_with_basis) (in module sage.categories.examples.graphs) (in module sage.categories.examples.infinite_enumerated_sets) (in module sage.categories.examples.lie_algebras) (in module sage.categories.examples.lie_algebras_with_basis) (in module sage.categories.examples.magmas) (in module sage.categories.examples.manifolds) (in module sage.categories.examples.monoids) (in module sage.categories.examples.sets_with_grading) example() (sage.categories.algebras_with_basis.AlgebrasWithBasis method) (sage.categories.category.Category method) (sage.categories.classical_crystals.ClassicalCrystals method) (sage.categories.complex_reflection_groups.ComplexReflectionGroups method) (sage.categories.crystals.Crystals method) (sage.categories.facade_sets.FacadeSets method) (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups method) (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.Irreducible method) (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.WellGenerated method) (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.WellGenerated.Irreducible method) (sage.categories.finite_crystals.FiniteCrystals method) (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis method) (sage.categories.finite_enumerated_sets.FiniteEnumeratedSets.IsomorphicObjects method) (sage.categories.finite_groups.FiniteGroups method) (sage.categories.finite_permutation_groups.FinitePermutationGroups method) (sage.categories.finitely_generated_semigroups.FinitelyGeneratedSemigroups method) (sage.categories.graded_hopf_algebras_with_basis.GradedHopfAlgebrasWithBasis method) (sage.categories.graded_hopf_algebras_with_basis.GradedHopfAlgebrasWithBasis.Connected method) (sage.categories.group_algebras.GroupAlgebras method) (sage.categories.groups.Groups method) (sage.categories.highest_weight_crystals.HighestWeightCrystals method) (sage.categories.hopf_algebras_with_basis.HopfAlgebrasWithBasis method) (sage.categories.kac_moody_algebras.KacMoodyAlgebras method) (sage.categories.lie_algebras.LieAlgebras method) (sage.categories.lie_algebras_with_basis.LieAlgebrasWithBasis method) (sage.categories.lie_conformal_algebras.LieConformalAlgebras method) (sage.categories.loop_crystals.LoopCrystals method) (sage.categories.magmas.Magmas.CartesianProducts method) (sage.categories.posets.Posets method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations method) (sage.categories.regular_crystals.RegularCrystals method) (sage.categories.semigroups.Semigroups method) (sage.categories.semigroups.Semigroups.Quotients method) (sage.categories.semigroups.Semigroups.Subquotients method) (sage.categories.sets_cat.Sets method) (sage.categories.sets_cat.Sets.CartesianProducts method) (sage.categories.sets_cat.Sets.WithRealizations method) (sage.categories.super_lie_conformal_algebras.SuperLieConformalAlgebras method) (sage.categories.vector_spaces.VectorSpaces.WithBasis.Filtered method) (sage.categories.vector_spaces.VectorSpaces.WithBasis.Graded method) exp() (sage.categories.lie_algebras.LieAlgebras.ElementMethods method) expand() (sage.categories.pushout.AlgebraicExtensionFunctor method) (sage.categories.pushout.CompositeConstructionFunctor method) (sage.categories.pushout.ConstructionFunctor method) (sage.categories.pushout.InfinitePolynomialFunctor method) (sage.categories.pushout.MultiPolynomialFunctor method) expand_tower() (in module sage.categories.pushout) extend_codomain() (sage.categories.map.Map method) extend_domain() (sage.categories.map.Map method) extend_to_fraction_field() (sage.categories.rings.Rings.MorphismMethods method) extra_super_categories() (sage.categories.additive_groups.AdditiveGroups.Finite.Algebras method) (sage.categories.additive_magmas.AdditiveMagmas.AdditiveCommutative.Algebras method) (sage.categories.additive_magmas.AdditiveMagmas.AdditiveCommutative.CartesianProducts method) (sage.categories.additive_magmas.AdditiveMagmas.AdditiveUnital.AdditiveInverse.CartesianProducts method) (sage.categories.additive_magmas.AdditiveMagmas.AdditiveUnital.Algebras method) (sage.categories.additive_magmas.AdditiveMagmas.AdditiveUnital.CartesianProducts method) (sage.categories.additive_magmas.AdditiveMagmas.AdditiveUnital.Homsets method) (sage.categories.additive_magmas.AdditiveMagmas.Algebras method) (sage.categories.additive_magmas.AdditiveMagmas.CartesianProducts method) (sage.categories.additive_magmas.AdditiveMagmas.Homsets method) (sage.categories.additive_monoids.AdditiveMonoids.Homsets method) (sage.categories.additive_semigroups.AdditiveSemigroups.Algebras method) (sage.categories.additive_semigroups.AdditiveSemigroups.CartesianProducts method) (sage.categories.additive_semigroups.AdditiveSemigroups.Homsets method) (sage.categories.algebras.Algebras.CartesianProducts method) (sage.categories.algebras.Algebras.DualObjects method) (sage.categories.algebras.Algebras.TensorProducts method) (sage.categories.algebras_with_basis.AlgebrasWithBasis.CartesianProducts method) (sage.categories.algebras_with_basis.AlgebrasWithBasis.TensorProducts method) (sage.categories.aperiodic_semigroups.AperiodicSemigroups method) (sage.categories.category_with_axiom.Blahs.Flying method) (sage.categories.category_with_axiom.CategoryWithAxiom method) (sage.categories.classical_crystals.ClassicalCrystals.TensorProducts method) (sage.categories.coalgebras.Coalgebras.DualObjects method) (sage.categories.coalgebras.Coalgebras.Super method) (sage.categories.coalgebras.Coalgebras.TensorProducts method) (sage.categories.coalgebras_with_basis.CoalgebrasWithBasis.Super method) (sage.categories.commutative_algebras.CommutativeAlgebras.TensorProducts method) (sage.categories.commutative_rings.CommutativeRings.CartesianProducts method) (sage.categories.covariant_functorial_construction.FunctorialConstructionCategory method) (sage.categories.crystals.Crystals.TensorProducts method) (sage.categories.cw_complexes.CWComplexes.Finite method) (sage.categories.distributive_magmas_and_additive_magmas.DistributiveMagmasAndAdditiveMagmas.CartesianProducts method) (sage.categories.division_rings.DivisionRings method) (sage.categories.fields.Fields method) (sage.categories.filtered_modules.FilteredModules method) (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups method) (sage.categories.finite_crystals.FiniteCrystals method) (sage.categories.finite_crystals.FiniteCrystals.TensorProducts method) (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.Cellular.TensorProducts method) (sage.categories.finite_dimensional_modules_with_basis.FiniteDimensionalModulesWithBasis.TensorProducts method) (sage.categories.finite_enumerated_sets.FiniteEnumeratedSets.CartesianProducts method) (sage.categories.finite_fields.FiniteFields method) (sage.categories.finite_groups.FiniteGroups.Algebras method) (sage.categories.finite_permutation_groups.FinitePermutationGroups method) (sage.categories.finite_sets.FiniteSets.Algebras method) (sage.categories.finite_sets.FiniteSets.Subquotients method) (sage.categories.finitely_generated_semigroups.FinitelyGeneratedSemigroups method) (sage.categories.generalized_coxeter_groups.GeneralizedCoxeterGroups.Finite method) (sage.categories.graded_algebras.GradedAlgebras.SignedTensorProducts method) (sage.categories.graded_algebras_with_basis.GradedAlgebrasWithBasis.SignedTensorProducts method) (sage.categories.graded_coalgebras.GradedCoalgebras.SignedTensorProducts method) (sage.categories.graded_coalgebras_with_basis.GradedCoalgebrasWithBasis.SignedTensorProducts method) (sage.categories.graded_lie_algebras.GradedLieAlgebras.Stratified.FiniteDimensional method) (sage.categories.graphs.Graphs.Connected method) (sage.categories.group_algebras.GroupAlgebras method) (sage.categories.groups.Groups.CartesianProducts method) (sage.categories.hecke_modules.HeckeModules.Homsets method) (sage.categories.highest_weight_crystals.HighestWeightCrystals.TensorProducts method) (sage.categories.homsets.Homsets.Endset method) (sage.categories.hopf_algebras.HopfAlgebras.TensorProducts method) (sage.categories.hopf_algebras_with_basis.HopfAlgebrasWithBasis.TensorProducts method) (sage.categories.j_trivial_semigroups.JTrivialSemigroups method) (sage.categories.l_trivial_semigroups.LTrivialSemigroups method) (sage.categories.lie_algebras.LieAlgebras.FiniteDimensional method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals.TensorProducts method) (sage.categories.magmas.Magmas.Algebras method) (sage.categories.magmas.Magmas.CartesianProducts method) (sage.categories.magmas.Magmas.Commutative.Algebras method) (sage.categories.magmas.Magmas.Commutative.CartesianProducts method) (sage.categories.magmas.Magmas.Unital.Algebras method) (sage.categories.magmas.Magmas.Unital.CartesianProducts method) (sage.categories.magmas.Magmas.Unital.Inverse.CartesianProducts method) (sage.categories.magmas_and_additive_magmas.MagmasAndAdditiveMagmas.CartesianProducts method) (sage.categories.manifolds.Manifolds.AlmostComplex method) (sage.categories.manifolds.Manifolds.Analytic method) (sage.categories.manifolds.Manifolds.Smooth method) (sage.categories.metric_spaces.MetricSpaces.CartesianProducts method) (sage.categories.metric_spaces.MetricSpaces.Complete.CartesianProducts method) (sage.categories.modular_abelian_varieties.ModularAbelianVarieties.Homsets.Endset method) (sage.categories.modules.Modules.CartesianProducts method) (sage.categories.modules.Modules.FiniteDimensional method) (sage.categories.modules.Modules.FiniteDimensional.TensorProducts method) (sage.categories.modules.Modules.FinitelyPresented method) (sage.categories.modules.Modules.Homsets method) (sage.categories.modules.Modules.Homsets.Endset method) (sage.categories.modules.Modules.TensorProducts method) (sage.categories.modules_with_basis.ModulesWithBasis.CartesianProducts method) (sage.categories.modules_with_basis.ModulesWithBasis.DualObjects method) (sage.categories.modules_with_basis.ModulesWithBasis.TensorProducts method) (sage.categories.monoids.Monoids.Algebras method) (sage.categories.monoids.Monoids.CartesianProducts method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations.TensorProducts method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations.WithBasis.TensorProducts method) (sage.categories.r_trivial_semigroups.RTrivialSemigroups method) (sage.categories.regular_crystals.RegularCrystals.TensorProducts method) (sage.categories.regular_supercrystals.RegularSuperCrystals.TensorProducts method) (sage.categories.semigroups.Semigroups.Algebras method) (sage.categories.semigroups.Semigroups.CartesianProducts method) (sage.categories.sets_cat.Sets.Algebras method) (sage.categories.sets_cat.Sets.CartesianProducts method) (sage.categories.sets_cat.Sets.WithRealizations method) (sage.categories.super_algebras.SuperAlgebras method) (sage.categories.super_algebras.SuperAlgebras.SignedTensorProducts method) (sage.categories.super_algebras_with_basis.SuperAlgebrasWithBasis method) (sage.categories.super_algebras_with_basis.SuperAlgebrasWithBasis.SignedTensorProducts method) (sage.categories.super_lie_conformal_algebras.SuperLieConformalAlgebras method) (sage.categories.super_modules.SuperModules method) (sage.categories.supercommutative_algebras.SupercommutativeAlgebras.SignedTensorProducts method) (sage.categories.supercrystals.SuperCrystals.TensorProducts method) (sage.categories.topological_spaces.TopologicalSpaces.CartesianProducts method) (sage.categories.topological_spaces.TopologicalSpaces.Compact.CartesianProducts method) (sage.categories.topological_spaces.TopologicalSpaces.Connected.CartesianProducts method) (sage.categories.vector_spaces.VectorSpaces.CartesianProducts method) (sage.categories.vector_spaces.VectorSpaces.DualObjects method) (sage.categories.vector_spaces.VectorSpaces.FiniteDimensional.TensorProducts method) (sage.categories.vector_spaces.VectorSpaces.TensorProducts method) (sage.categories.vector_spaces.VectorSpaces.WithBasis.CartesianProducts method) (sage.categories.vector_spaces.VectorSpaces.WithBasis.FiniteDimensional.TensorProducts method) (sage.categories.vector_spaces.VectorSpaces.WithBasis.TensorProducts method) F F (sage.categories.examples.with_realizations.SubsetAlgebra attribute) f() (sage.categories.crystals.Crystals.ElementMethods method) (sage.categories.examples.crystals.HighestWeightCrystalOfTypeA.Element method) (sage.categories.examples.crystals.NaiveCrystal.Element method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations.WithBasis.ElementMethods method) (sage.categories.triangular_kac_moody_algebras.TriangularKacMoodyAlgebras.ParentMethods method) f_on_basis() (sage.categories.quantum_group_representations.QuantumGroupRepresentations.WithBasis.TensorProducts.ParentMethods method) f_string() (sage.categories.crystals.Crystals.ElementMethods method) Facade (sage.categories.sets_cat.Sets attribute) Facade() (sage.categories.sets_cat.Sets.SubcategoryMethods method) facade_for() (sage.categories.facade_sets.FacadeSets.ParentMethods method) (sage.categories.sets_cat.Sets.WithRealizations.ParentMethods method) FacadeSets (class in sage.categories.facade_sets) FacadeSets.ParentMethods (class in sage.categories.facade_sets) faces() (sage.categories.graphs.Graphs.ParentMethods method) (sage.categories.simplicial_complexes.SimplicialComplexes.ParentMethods method) facets() (sage.categories.graphs.Graphs.ParentMethods method) (sage.categories.simplicial_complexes.SimplicialComplexes.ParentMethods method) factor() (sage.categories.fields.Fields.ElementMethods method) (sage.categories.quotient_fields.QuotientFields.ElementMethods method) fat_wedge() (sage.categories.simplicial_sets.SimplicialSets.Pointed.Finite.ParentMethods method) Fields (class in sage.categories.fields) Fields.ElementMethods (class in sage.categories.fields) Fields.ParentMethods (class in sage.categories.fields) Filtered (sage.categories.algebras.Algebras attribute) (sage.categories.algebras_with_basis.AlgebrasWithBasis attribute) (sage.categories.hopf_algebras_with_basis.HopfAlgebrasWithBasis attribute) (sage.categories.modules.Modules attribute) (sage.categories.modules_with_basis.ModulesWithBasis attribute) Filtered() (sage.categories.modules.Modules.SubcategoryMethods method) FilteredAlgebras (class in sage.categories.filtered_algebras) FilteredAlgebras.ParentMethods (class in sage.categories.filtered_algebras) FilteredAlgebrasWithBasis (class in sage.categories.filtered_algebras_with_basis) FilteredAlgebrasWithBasis.ElementMethods (class in sage.categories.filtered_algebras_with_basis) FilteredAlgebrasWithBasis.ParentMethods (class in sage.categories.filtered_algebras_with_basis) FilteredModules (class in sage.categories.filtered_modules) FilteredModules.Connected (class in sage.categories.filtered_modules) FilteredModules.SubcategoryMethods (class in sage.categories.filtered_modules) FilteredModulesCategory (class in sage.categories.filtered_modules) FilteredModulesWithBasis (class in sage.categories.filtered_modules_with_basis) FilteredModulesWithBasis.ElementMethods (class in sage.categories.filtered_modules_with_basis) FilteredModulesWithBasis.ParentMethods (class in sage.categories.filtered_modules_with_basis) FilteredModulesWithBasis.Subobjects (class in sage.categories.filtered_modules_with_basis) FilteredModulesWithBasis.Subobjects.ElementMethods (class in sage.categories.filtered_modules_with_basis) FilteredModulesWithBasis.Subobjects.ParentMethods (class in sage.categories.filtered_modules_with_basis) Finite (sage.categories.complex_reflection_groups.ComplexReflectionGroups attribute) (sage.categories.coxeter_groups.CoxeterGroups attribute) (sage.categories.crystals.Crystals attribute) (sage.categories.enumerated_sets.EnumeratedSets attribute) (sage.categories.fields.Fields attribute) (sage.categories.groups.Groups attribute) (sage.categories.lattice_posets.LatticePosets attribute) (sage.categories.monoids.Monoids attribute) (sage.categories.permutation_groups.PermutationGroups attribute) (sage.categories.posets.Posets attribute) (sage.categories.semigroups.Semigroups attribute) (sage.categories.sets_cat.Sets attribute) (sage.categories.weyl_groups.WeylGroups attribute) Finite() (sage.categories.sets_cat.Sets.SubcategoryMethods method) Finite_extra_super_categories() (sage.categories.division_rings.DivisionRings method) (sage.categories.h_trivial_semigroups.HTrivialSemigroups method) FiniteComplexReflectionGroups (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.ElementMethods (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.Irreducible (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.Irreducible.ParentMethods (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.ParentMethods (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.SubcategoryMethods (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.WellGenerated (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.WellGenerated.Irreducible (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.WellGenerated.Irreducible.ParentMethods (class in sage.categories.finite_complex_reflection_groups) FiniteComplexReflectionGroups.WellGenerated.ParentMethods (class in sage.categories.finite_complex_reflection_groups) FiniteCoxeterGroups (class in sage.categories.finite_coxeter_groups) FiniteCoxeterGroups.ElementMethods (class in sage.categories.finite_coxeter_groups) FiniteCoxeterGroups.ParentMethods (class in sage.categories.finite_coxeter_groups) FiniteCrystals (class in sage.categories.finite_crystals) FiniteCrystals.TensorProducts (class in sage.categories.finite_crystals) FiniteDimensional (sage.categories.algebras_with_basis.AlgebrasWithBasis attribute) (sage.categories.graded_lie_algebras_with_basis.GradedLieAlgebrasWithBasis attribute) (sage.categories.hopf_algebras_with_basis.HopfAlgebrasWithBasis attribute) (sage.categories.modules_with_basis.ModulesWithBasis attribute) FiniteDimensional() (sage.categories.category_with_axiom.Blahs.SubcategoryMethods method) (sage.categories.cw_complexes.CWComplexes.SubcategoryMethods method) (sage.categories.manifolds.Manifolds.SubcategoryMethods method) (sage.categories.modules.Modules.SubcategoryMethods method) FiniteDimensionalAlgebrasWithBasis (class in sage.categories.finite_dimensional_algebras_with_basis) FiniteDimensionalAlgebrasWithBasis.Cellular (class in sage.categories.finite_dimensional_algebras_with_basis) FiniteDimensionalAlgebrasWithBasis.Cellular.ElementMethods (class in sage.categories.finite_dimensional_algebras_with_basis) FiniteDimensionalAlgebrasWithBasis.Cellular.ParentMethods (class in 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sage.categories.loop_crystals) lower_central_series() (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ParentMethods method) lower_cover_reflections() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) lower_covers() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) (sage.categories.posets.Posets.ParentMethods method) lowest_weight_vectors() (sage.categories.highest_weight_crystals.HighestWeightCrystals.ParentMethods method) (sage.categories.supercrystals.SuperCrystals.Finite.ParentMethods method) lt() (sage.categories.posets.Posets.ParentMethods method) LTrivial (sage.categories.semigroups.Semigroups attribute) LTrivial() (sage.categories.semigroups.Semigroups.SubcategoryMethods method) LTrivialSemigroups (class in sage.categories.l_trivial_semigroups) lusztig_involution() (sage.categories.classical_crystals.ClassicalCrystals.ElementMethods method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ElementMethods method) M m_cambrian_lattice() (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods method) magma_generators() (sage.categories.examples.magmas.FreeMagma method) (sage.categories.finitely_generated_magmas.FinitelyGeneratedMagmas.ParentMethods method) (sage.categories.semigroups.Semigroups.ParentMethods method) Magmas (class in sage.categories.magmas) Magmas.Algebras (class in sage.categories.magmas) Magmas.Algebras.ParentMethods (class in sage.categories.magmas) Magmas.CartesianProducts (class in sage.categories.magmas) Magmas.CartesianProducts.ParentMethods (class in sage.categories.magmas) Magmas.Commutative (class in sage.categories.magmas) Magmas.Commutative.Algebras (class in sage.categories.magmas) Magmas.Commutative.CartesianProducts (class in sage.categories.magmas) Magmas.Commutative.ParentMethods (class in sage.categories.magmas) Magmas.ElementMethods (class in sage.categories.magmas) Magmas.JTrivial (class in sage.categories.magmas) Magmas.ParentMethods (class in sage.categories.magmas) Magmas.Realizations (class in sage.categories.magmas) Magmas.Realizations.ParentMethods (class in sage.categories.magmas) Magmas.SubcategoryMethods (class in sage.categories.magmas) Magmas.Subquotients (class in sage.categories.magmas) Magmas.Subquotients.ParentMethods (class in sage.categories.magmas) Magmas.Unital (class in sage.categories.magmas) Magmas.Unital.Algebras (class in sage.categories.magmas) Magmas.Unital.CartesianProducts (class in sage.categories.magmas) Magmas.Unital.CartesianProducts.ElementMethods (class in sage.categories.magmas) Magmas.Unital.CartesianProducts.ParentMethods (class in sage.categories.magmas) Magmas.Unital.ElementMethods (class in sage.categories.magmas) Magmas.Unital.Inverse (class in sage.categories.magmas) Magmas.Unital.Inverse.CartesianProducts (class in sage.categories.magmas) Magmas.Unital.ParentMethods (class in sage.categories.magmas) Magmas.Unital.Realizations (class in sage.categories.magmas) Magmas.Unital.Realizations.ParentMethods (class in sage.categories.magmas) Magmas.Unital.SubcategoryMethods (class in sage.categories.magmas) MagmasAndAdditiveMagmas (class in sage.categories.magmas_and_additive_magmas) MagmasAndAdditiveMagmas.CartesianProducts (class in sage.categories.magmas_and_additive_magmas) MagmasAndAdditiveMagmas.SubcategoryMethods (class in sage.categories.magmas_and_additive_magmas) MagmaticAlgebras (class in sage.categories.magmatic_algebras) MagmaticAlgebras.ParentMethods (class in sage.categories.magmatic_algebras) MagmaticAlgebras.WithBasis (class in sage.categories.magmatic_algebras) MagmaticAlgebras.WithBasis.FiniteDimensional (class in sage.categories.magmatic_algebras) MagmaticAlgebras.WithBasis.FiniteDimensional.ParentMethods (class in sage.categories.magmatic_algebras) MagmaticAlgebras.WithBasis.ParentMethods (class in sage.categories.magmatic_algebras) Manifolds (class in sage.categories.manifolds) Manifolds.AlmostComplex (class in sage.categories.manifolds) Manifolds.Analytic (class in sage.categories.manifolds) Manifolds.Connected (class in sage.categories.manifolds) Manifolds.Differentiable (class in sage.categories.manifolds) Manifolds.FiniteDimensional (class in sage.categories.manifolds) Manifolds.ParentMethods (class in sage.categories.manifolds) Manifolds.Smooth (class in sage.categories.manifolds) Manifolds.SubcategoryMethods (class in sage.categories.manifolds) Map (class in sage.categories.map) map() (sage.categories.enumerated_sets.EnumeratedSets.ParentMethods method) map_coefficients() (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) map_item() (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) map_support() (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) map_support_skip_none() (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) matrix() (sage.categories.finite_dimensional_modules_with_basis.FiniteDimensionalModulesWithBasis.MorphismMethods method) MatrixAlgebras (class in sage.categories.matrix_algebras) MatrixFunctor (class in sage.categories.pushout) maximal_degree() (sage.categories.filtered_modules_with_basis.FilteredModulesWithBasis.ElementMethods method) (sage.categories.filtered_modules_with_basis.FilteredModulesWithBasis.Subobjects.ElementMethods method) maximal_vector() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals.TensorProducts.ParentMethods method) meet() (sage.categories.category.Category static method) (sage.categories.lattice_posets.LatticePosets.ParentMethods method) meet_irreducibles() (sage.categories.finite_lattice_posets.FiniteLatticePosets.ParentMethods method) meet_irreducibles_poset() (sage.categories.finite_lattice_posets.FiniteLatticePosets.ParentMethods method) merge() 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(sage.categories.metric_spaces.MetricSpaces.ParentMethods method) MetricSpaces (class in sage.categories.metric_spaces) MetricSpaces.CartesianProducts (class in sage.categories.metric_spaces) MetricSpaces.CartesianProducts.ParentMethods (class in sage.categories.metric_spaces) MetricSpaces.Complete (class in sage.categories.metric_spaces) MetricSpaces.Complete.CartesianProducts (class in sage.categories.metric_spaces) MetricSpaces.ElementMethods (class in sage.categories.metric_spaces) MetricSpaces.Homsets (class in sage.categories.metric_spaces) MetricSpaces.Homsets.ElementMethods (class in sage.categories.metric_spaces) MetricSpaces.ParentMethods (class in sage.categories.metric_spaces) MetricSpaces.SubcategoryMethods (class in sage.categories.metric_spaces) MetricSpaces.WithRealizations (class in sage.categories.metric_spaces) MetricSpaces.WithRealizations.ParentMethods (class in sage.categories.metric_spaces) MetricSpacesCategory (class in sage.categories.metric_spaces) min_demazure_product_greater() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) ModularAbelianVarieties (class in sage.categories.modular_abelian_varieties) ModularAbelianVarieties.Homsets (class in sage.categories.modular_abelian_varieties) ModularAbelianVarieties.Homsets.Endset (class in sage.categories.modular_abelian_varieties) module sage.categories.action sage.categories.additive_groups sage.categories.additive_magmas sage.categories.additive_monoids sage.categories.additive_semigroups sage.categories.affine_weyl_groups sage.categories.algebra_functor sage.categories.algebra_ideals sage.categories.algebra_modules sage.categories.algebras sage.categories.algebras_with_basis sage.categories.all sage.categories.aperiodic_semigroups sage.categories.associative_algebras sage.categories.bialgebras sage.categories.bialgebras_with_basis sage.categories.bimodules sage.categories.cartesian_product sage.categories.category sage.categories.category_cy_helper sage.categories.category_singleton sage.categories.category_types sage.categories.category_with_axiom sage.categories.classical_crystals sage.categories.coalgebras sage.categories.coalgebras_with_basis sage.categories.coercion_methods sage.categories.commutative_additive_groups sage.categories.commutative_additive_monoids sage.categories.commutative_additive_semigroups sage.categories.commutative_algebra_ideals sage.categories.commutative_algebras sage.categories.commutative_ring_ideals sage.categories.commutative_rings sage.categories.complete_discrete_valuation sage.categories.complex_reflection_groups sage.categories.complex_reflection_or_generalized_coxeter_groups sage.categories.covariant_functorial_construction sage.categories.coxeter_group_algebras sage.categories.coxeter_groups sage.categories.crystals sage.categories.cw_complexes sage.categories.discrete_valuation sage.categories.distributive_magmas_and_additive_magmas sage.categories.division_rings sage.categories.domains sage.categories.dual sage.categories.enumerated_sets sage.categories.euclidean_domains sage.categories.examples.algebras_with_basis sage.categories.examples.commutative_additive_monoids sage.categories.examples.commutative_additive_semigroups sage.categories.examples.coxeter_groups sage.categories.examples.crystals sage.categories.examples.cw_complexes sage.categories.examples.facade_sets sage.categories.examples.finite_coxeter_groups sage.categories.examples.finite_dimensional_algebras_with_basis sage.categories.examples.finite_dimensional_lie_algebras_with_basis sage.categories.examples.finite_enumerated_sets sage.categories.examples.finite_monoids sage.categories.examples.finite_semigroups sage.categories.examples.finite_weyl_groups sage.categories.examples.graded_connected_hopf_algebras_with_basis sage.categories.examples.graded_modules_with_basis sage.categories.examples.graphs sage.categories.examples.hopf_algebras_with_basis sage.categories.examples.infinite_enumerated_sets sage.categories.examples.lie_algebras sage.categories.examples.lie_algebras_with_basis sage.categories.examples.magmas sage.categories.examples.manifolds sage.categories.examples.monoids sage.categories.examples.posets sage.categories.examples.semigroups sage.categories.examples.semigroups_cython sage.categories.examples.sets_cat sage.categories.examples.sets_with_grading sage.categories.examples.with_realizations sage.categories.facade_sets sage.categories.fields sage.categories.filtered_algebras sage.categories.filtered_algebras_with_basis sage.categories.filtered_modules sage.categories.filtered_modules_with_basis sage.categories.finite_complex_reflection_groups sage.categories.finite_coxeter_groups sage.categories.finite_crystals sage.categories.finite_dimensional_algebras_with_basis sage.categories.finite_dimensional_bialgebras_with_basis sage.categories.finite_dimensional_coalgebras_with_basis sage.categories.finite_dimensional_graded_lie_algebras_with_basis sage.categories.finite_dimensional_hopf_algebras_with_basis sage.categories.finite_dimensional_lie_algebras_with_basis sage.categories.finite_dimensional_modules_with_basis sage.categories.finite_dimensional_nilpotent_lie_algebras_with_basis sage.categories.finite_dimensional_semisimple_algebras_with_basis sage.categories.finite_enumerated_sets sage.categories.finite_fields sage.categories.finite_groups sage.categories.finite_lattice_posets sage.categories.finite_monoids sage.categories.finite_permutation_groups sage.categories.finite_posets sage.categories.finite_semigroups sage.categories.finite_sets sage.categories.finite_weyl_groups sage.categories.finitely_generated_lambda_bracket_algebras sage.categories.finitely_generated_lie_conformal_algebras sage.categories.finitely_generated_magmas sage.categories.finitely_generated_semigroups sage.categories.function_fields sage.categories.functor sage.categories.g_sets sage.categories.gcd_domains sage.categories.generalized_coxeter_groups sage.categories.graded_algebras sage.categories.graded_algebras_with_basis sage.categories.graded_bialgebras sage.categories.graded_bialgebras_with_basis sage.categories.graded_coalgebras sage.categories.graded_coalgebras_with_basis sage.categories.graded_hopf_algebras sage.categories.graded_hopf_algebras_with_basis sage.categories.graded_lie_algebras sage.categories.graded_lie_algebras_with_basis sage.categories.graded_lie_conformal_algebras sage.categories.graded_modules sage.categories.graded_modules_with_basis sage.categories.graphs sage.categories.group_algebras sage.categories.groupoid sage.categories.groups sage.categories.h_trivial_semigroups sage.categories.hecke_modules sage.categories.highest_weight_crystals sage.categories.homset sage.categories.homsets sage.categories.hopf_algebras sage.categories.hopf_algebras_with_basis sage.categories.infinite_enumerated_sets sage.categories.integral_domains sage.categories.isomorphic_objects sage.categories.j_trivial_semigroups sage.categories.kac_moody_algebras sage.categories.l_trivial_semigroups sage.categories.lambda_bracket_algebras sage.categories.lambda_bracket_algebras_with_basis sage.categories.lattice_posets sage.categories.left_modules sage.categories.lie_algebras sage.categories.lie_algebras_with_basis sage.categories.lie_conformal_algebras sage.categories.lie_conformal_algebras_with_basis sage.categories.lie_groups sage.categories.loop_crystals sage.categories.magmas sage.categories.magmas_and_additive_magmas sage.categories.magmatic_algebras sage.categories.manifolds sage.categories.map sage.categories.matrix_algebras sage.categories.metric_spaces sage.categories.modular_abelian_varieties sage.categories.modules sage.categories.modules_with_basis sage.categories.monoid_algebras sage.categories.monoids sage.categories.morphism sage.categories.number_fields sage.categories.objects sage.categories.partially_ordered_monoids sage.categories.permutation_groups sage.categories.pointed_sets sage.categories.polyhedra sage.categories.poor_man_map sage.categories.posets sage.categories.primer sage.categories.principal_ideal_domains sage.categories.pushout sage.categories.quantum_group_representations sage.categories.quotient_fields sage.categories.quotients sage.categories.r_trivial_semigroups sage.categories.realizations sage.categories.regular_crystals sage.categories.regular_supercrystals sage.categories.right_modules sage.categories.ring_ideals sage.categories.rings sage.categories.rngs sage.categories.schemes sage.categories.semigroups sage.categories.semirings sage.categories.semisimple_algebras sage.categories.sets_cat sage.categories.sets_with_grading sage.categories.sets_with_partial_maps sage.categories.shephard_groups sage.categories.signed_tensor sage.categories.simplicial_complexes sage.categories.simplicial_sets sage.categories.subobjects sage.categories.subquotients sage.categories.super_algebras sage.categories.super_algebras_with_basis sage.categories.super_hopf_algebras_with_basis sage.categories.super_lie_conformal_algebras sage.categories.super_modules sage.categories.super_modules_with_basis sage.categories.supercommutative_algebras sage.categories.supercrystals sage.categories.tensor sage.categories.topological_spaces sage.categories.triangular_kac_moody_algebras sage.categories.tutorial sage.categories.unique_factorization_domains sage.categories.unital_algebras sage.categories.vector_bundles sage.categories.vector_spaces sage.categories.weyl_groups sage.categories.with_realizations module() (sage.categories.examples.finite_dimensional_lie_algebras_with_basis.AbelianLieAlgebra method) (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ParentMethods method) (sage.categories.lie_algebras.LieAlgebras.ParentMethods method) (sage.categories.lie_algebras_with_basis.LieAlgebrasWithBasis.ParentMethods method) module_generator() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) module_morphism() (sage.categories.modules.Modules.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) Modules (class in sage.categories.modules) Modules.CartesianProducts (class in sage.categories.modules) Modules.CartesianProducts.ElementMethods (class in sage.categories.modules) Modules.CartesianProducts.ParentMethods (class in sage.categories.modules) Modules.ElementMethods (class in sage.categories.modules) Modules.FiniteDimensional (class in sage.categories.modules) Modules.FiniteDimensional.TensorProducts (class in sage.categories.modules) Modules.FinitelyPresented (class in sage.categories.modules) Modules.Homsets (class in sage.categories.modules) Modules.Homsets.Endset (class in sage.categories.modules) Modules.Homsets.ParentMethods (class in sage.categories.modules) Modules.ParentMethods (class in sage.categories.modules) Modules.SubcategoryMethods (class in sage.categories.modules) Modules.TensorProducts (class in sage.categories.modules) Modules.TensorProducts.ParentMethods (class in sage.categories.modules) ModulesWithBasis (class in sage.categories.modules_with_basis) ModulesWithBasis.CartesianProducts (class in sage.categories.modules_with_basis) ModulesWithBasis.CartesianProducts.ParentMethods (class in sage.categories.modules_with_basis) ModulesWithBasis.DualObjects (class in sage.categories.modules_with_basis) ModulesWithBasis.ElementMethods (class in sage.categories.modules_with_basis) ModulesWithBasis.Homsets (class in sage.categories.modules_with_basis) ModulesWithBasis.Homsets.ParentMethods (class in sage.categories.modules_with_basis) ModulesWithBasis.MorphismMethods (class in sage.categories.modules_with_basis) ModulesWithBasis.ParentMethods (class in sage.categories.modules_with_basis) ModulesWithBasis.TensorProducts (class in sage.categories.modules_with_basis) ModulesWithBasis.TensorProducts.ElementMethods (class in sage.categories.modules_with_basis) ModulesWithBasis.TensorProducts.ParentMethods (class in sage.categories.modules_with_basis) monoid_generators() (sage.categories.examples.monoids.FreeMonoid method) (sage.categories.finite_groups.FiniteGroups.ParentMethods method) (sage.categories.groups.Groups.ParentMethods method) (sage.categories.monoids.Monoids.CartesianProducts.ParentMethods method) MonoidAlgebras() (in module sage.categories.monoid_algebras) Monoids (class in sage.categories.monoids) Monoids.Algebras (class in sage.categories.monoids) Monoids.Algebras.ElementMethods (class in sage.categories.monoids) Monoids.Algebras.ParentMethods (class in sage.categories.monoids) Monoids.CartesianProducts (class in sage.categories.monoids) Monoids.CartesianProducts.ElementMethods (class in sage.categories.monoids) Monoids.CartesianProducts.ParentMethods (class in sage.categories.monoids) Monoids.Commutative (class in sage.categories.monoids) Monoids.ElementMethods (class in sage.categories.monoids) Monoids.ParentMethods (class in sage.categories.monoids) Monoids.Subquotients (class in sage.categories.monoids) Monoids.Subquotients.ParentMethods (class in sage.categories.monoids) Monoids.WithRealizations (class in sage.categories.monoids) Monoids.WithRealizations.ParentMethods (class in sage.categories.monoids) monomial() (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) monomial_coefficients() (sage.categories.examples.finite_dimensional_lie_algebras_with_basis.AbelianLieAlgebra.Element method) (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) monomial_or_zero_if_none() (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) monomials() (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) Morphism (class in sage.categories.morphism) morphism() (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ParentMethods method) morphism_class() (sage.categories.category.Category method) multiplication_table() (sage.categories.magmas.Magmas.ParentMethods method) multiplicative_order() (sage.categories.monoids.Monoids.CartesianProducts.ElementMethods method) MultiPolynomialFunctor (class in sage.categories.pushout) MultivariateConstructionFunctor (class in sage.categories.pushout) MyGroupAlgebra (class in sage.categories.examples.hopf_algebras_with_basis) N NaiveCrystal (class in sage.categories.examples.crystals) NaiveCrystal.Element (class in sage.categories.examples.crystals) natural_map() (sage.categories.homset.Homset method) nerve() (sage.categories.finite_monoids.FiniteMonoids.ParentMethods method) next() (sage.categories.enumerated_sets.EnumeratedSets.ParentMethods method) (sage.categories.examples.infinite_enumerated_sets.NonNegativeIntegers method) (sage.categories.examples.sets_cat.PrimeNumbers_Abstract method) (sage.categories.examples.sets_cat.PrimeNumbers_Abstract.Element method) ngens() (sage.categories.finitely_generated_lambda_bracket_algebras.FinitelyGeneratedLambdaBracketAlgebras.ParentMethods method) (sage.categories.semigroups.Semigroups.Algebras.ParentMethods method) Nilpotent (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis attribute) Nilpotent() (sage.categories.lie_algebras.LieAlgebras.SubcategoryMethods method) noncrossing_partition_lattice() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.Irreducible.ParentMethods method) NonNegativeIntegers (class in sage.categories.examples.infinite_enumerated_sets) (class in sage.categories.examples.sets_with_grading) NoZeroDivisors (sage.categories.rings.Rings attribute) NoZeroDivisors() (sage.categories.rings.Rings.SubcategoryMethods method) nproduct() (sage.categories.lambda_bracket_algebras.LambdaBracketAlgebras.ElementMethods method) number_of_connected_components() (sage.categories.crystals.Crystals.ParentMethods method) number_of_irreducible_components() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) number_of_reflection_hyperplanes() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.ParentMethods method) number_of_reflections() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.ParentMethods method) number_of_reflections_of_full_support() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.WellGenerated.Irreducible.ParentMethods method) number_of_simple_reflections() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) NumberFields (class in sage.categories.number_fields) NumberFields.ElementMethods (class in sage.categories.number_fields) NumberFields.ParentMethods (class in sage.categories.number_fields) numerator() (sage.categories.complete_discrete_valuation.CompleteDiscreteValuationFields.ElementMethods method) (sage.categories.complete_discrete_valuation.CompleteDiscreteValuationRings.ElementMethods method) (sage.categories.quotient_fields.QuotientFields.ElementMethods method) O object() (sage.categories.category_types.Elements method) Objects (class in sage.categories.objects) Objects.ParentMethods (class in sage.categories.objects) Objects.SubcategoryMethods (class in sage.categories.objects) odd_component() (sage.categories.super_modules_with_basis.SuperModulesWithBasis.ElementMethods method) on_basis() (sage.categories.modules_with_basis.ModulesWithBasis.MorphismMethods method) on_left_matrix() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ElementMethods method) one() (sage.categories.algebras_with_basis.AlgebrasWithBasis.CartesianProducts.ParentMethods method) (sage.categories.algebras_with_basis.AlgebrasWithBasis.ParentMethods method) (sage.categories.examples.finite_coxeter_groups.DihedralGroup method) (sage.categories.examples.finite_dimensional_algebras_with_basis.KroneckerQuiverPathAlgebra method) (sage.categories.examples.finite_monoids.IntegerModMonoid method) (sage.categories.examples.finite_weyl_groups.SymmetricGroup method) (sage.categories.examples.monoids.FreeMonoid method) (sage.categories.examples.with_realizations.SubsetAlgebra.Bases.ParentMethods method) (sage.categories.examples.with_realizations.SubsetAlgebra.Fundamental method) (sage.categories.homset.Homset method) (sage.categories.magmas.Magmas.Unital.CartesianProducts.ParentMethods method) (sage.categories.magmas.Magmas.Unital.ParentMethods method) (sage.categories.magmas.Magmas.Unital.Realizations.ParentMethods method) (sage.categories.monoids.Monoids.Subquotients.ParentMethods method) (sage.categories.monoids.Monoids.WithRealizations.ParentMethods method) (sage.categories.simplicial_sets.SimplicialSets.Homsets.Endset.ParentMethods method) (sage.categories.unital_algebras.UnitalAlgebras.WithBasis.ParentMethods method) one_basis() (sage.categories.additive_magmas.AdditiveMagmas.AdditiveUnital.Algebras.ParentMethods method) (sage.categories.algebras_with_basis.AlgebrasWithBasis.TensorProducts.ParentMethods method) (sage.categories.examples.algebras_with_basis.FreeAlgebra method) (sage.categories.examples.graded_connected_hopf_algebras_with_basis.GradedConnectedCombinatorialHopfAlgebraWithPrimitiveGenerator method) (sage.categories.examples.hopf_algebras_with_basis.MyGroupAlgebra method) (sage.categories.examples.lie_algebras_with_basis.IndexedPolynomialRing method) (sage.categories.examples.with_realizations.SubsetAlgebra.Fundamental method) (sage.categories.graded_algebras_with_basis.GradedAlgebrasWithBasis.SignedTensorProducts.ParentMethods method) (sage.categories.monoids.Monoids.Algebras.ParentMethods method) (sage.categories.unital_algebras.UnitalAlgebras.WithBasis.ParentMethods method) one_dimensional_configuration_sum() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.TensorProducts.ParentMethods method) one_from_cartesian_product_of_one_basis() (sage.categories.algebras_with_basis.AlgebrasWithBasis.CartesianProducts.ParentMethods method) one_from_one_basis() (sage.categories.unital_algebras.UnitalAlgebras.WithBasis.ParentMethods method) op (sage.categories.action.Action attribute) operation() (sage.categories.action.Action method) or_subcategory() (sage.categories.category.Category method) order() (sage.categories.groups.Groups.CartesianProducts.ParentMethods method) order_filter() (sage.categories.posets.Posets.ParentMethods method) order_filter_generators() (sage.categories.finite_posets.FinitePosets.ParentMethods method) order_ideal() (sage.categories.posets.Posets.ParentMethods method) order_ideal_complement_generators() (sage.categories.finite_posets.FinitePosets.ParentMethods method) order_ideal_generators() (sage.categories.finite_posets.FinitePosets.ParentMethods method) order_ideal_toggle() (sage.categories.posets.Posets.ParentMethods method) order_ideal_toggles() (sage.categories.posets.Posets.ParentMethods method) order_ideals_lattice() (sage.categories.finite_posets.FinitePosets.ParentMethods method) orthogonal_idempotents_central_mod_radical() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ParentMethods method) over() (sage.categories.commutative_rings.CommutativeRings.ParentMethods method) P panyushev_complement() (sage.categories.finite_posets.FinitePosets.ParentMethods method) panyushev_orbit_iter() (sage.categories.finite_posets.FinitePosets.ParentMethods method) panyushev_orbits() (sage.categories.finite_posets.FinitePosets.ParentMethods method) parent() (sage.categories.map.Map method) parent_class() (sage.categories.category.Category method) part() (sage.categories.triangular_kac_moody_algebras.TriangularKacMoodyAlgebras.ElementMethods method) partial_fraction_decomposition() (sage.categories.quotient_fields.QuotientFields.ElementMethods method) PartiallyOrderedMonoids (class in sage.categories.partially_ordered_monoids) PartiallyOrderedMonoids.ElementMethods (class in sage.categories.partially_ordered_monoids) PartiallyOrderedMonoids.ParentMethods (class in sage.categories.partially_ordered_monoids) pbw_basis() (sage.categories.lie_algebras_with_basis.LieAlgebrasWithBasis.ParentMethods method) peirce_decomposition() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ParentMethods method) peirce_summand() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ParentMethods method) permutahedron() (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods method) PermutationGroupFunctor (class in sage.categories.pushout) PermutationGroups (class in sage.categories.permutation_groups) Phi() (sage.categories.crystals.Crystals.ElementMethods method) phi() (sage.categories.crystals.Crystals.ElementMethods method) (sage.categories.regular_crystals.RegularCrystals.ElementMethods method) (sage.categories.regular_supercrystals.RegularSuperCrystals.ElementMethods method) phi_minus_epsilon() (sage.categories.crystals.Crystals.ElementMethods method) pieri_factors() (sage.categories.weyl_groups.WeylGroups.ParentMethods method) Plane (class in sage.categories.examples.manifolds) plot() (sage.categories.crystals.Crystals.ParentMethods method) plot3d() (sage.categories.crystals.Crystals.ParentMethods method) poincare_birkhoff_witt_basis() (sage.categories.lie_algebras_with_basis.LieAlgebrasWithBasis.ParentMethods method) Pointed() (sage.categories.simplicial_sets.SimplicialSets.SubcategoryMethods method) PointedSets (class in sage.categories.pointed_sets) PolyhedralSets (class in sage.categories.polyhedra) PolynomialFunctor (class in sage.categories.pushout) PoorManMap (class in sage.categories.poor_man_map) Posets (class in sage.categories.posets) Posets.ElementMethods (class in sage.categories.posets) Posets.ParentMethods (class in sage.categories.posets) PositiveIntegerMonoid (class in sage.categories.examples.facade_sets) PositiveIntegersOrderedByDivisibilityFacade (class in sage.categories.examples.posets) PositiveIntegersOrderedByDivisibilityFacade.element_class (class in sage.categories.examples.posets) post_compose() (sage.categories.map.Map method) powers() (sage.categories.monoids.Monoids.ElementMethods method) pre_compose() (sage.categories.map.Map method) PrecomposedAction (class in sage.categories.action) PrimeNumbers (class in sage.categories.examples.sets_cat) PrimeNumbers_Abstract (class in sage.categories.examples.sets_cat) PrimeNumbers_Abstract.Element (class in sage.categories.examples.sets_cat) PrimeNumbers_Facade (class in sage.categories.examples.sets_cat) PrimeNumbers_Inherits (class in sage.categories.examples.sets_cat) PrimeNumbers_Inherits.Element (class in sage.categories.examples.sets_cat) PrimeNumbers_Wrapper (class in sage.categories.examples.sets_cat) PrimeNumbers_Wrapper.Element (class in sage.categories.examples.sets_cat) principal_ideal() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ParentMethods method) principal_lower_set() (sage.categories.posets.Posets.ParentMethods method) principal_order_filter() (sage.categories.posets.Posets.ParentMethods method) principal_order_ideal() (sage.categories.posets.Posets.ParentMethods method) principal_upper_set() (sage.categories.posets.Posets.ParentMethods method) PrincipalIdealDomains (class in sage.categories.principal_ideal_domains) PrincipalIdealDomains.ElementMethods (class in sage.categories.principal_ideal_domains) PrincipalIdealDomains.ParentMethods (class in sage.categories.principal_ideal_domains) print_compare() (in module sage.categories.sets_cat) prod() (sage.categories.monoids.Monoids.ParentMethods method) (sage.categories.semigroups.Semigroups.ParentMethods method) product() (sage.categories.examples.finite_monoids.IntegerModMonoid method) (sage.categories.examples.finite_semigroups.LeftRegularBand method) (sage.categories.examples.finite_weyl_groups.SymmetricGroup method) (sage.categories.examples.magmas.FreeMagma method) (sage.categories.examples.semigroups.FreeSemigroup method) (sage.categories.examples.semigroups.LeftZeroSemigroup method) (sage.categories.magmas.Magmas.CartesianProducts.ParentMethods method) (sage.categories.magmas.Magmas.ParentMethods method) (sage.categories.magmas.Magmas.Subquotients.ParentMethods method) (sage.categories.magmatic_algebras.MagmaticAlgebras.WithBasis.ParentMethods method) product_by_coercion() (sage.categories.magmas.Magmas.Realizations.ParentMethods method) product_from_element_class_mul() (sage.categories.magmas.Magmas.ParentMethods method) product_on_basis() (sage.categories.additive_magmas.AdditiveMagmas.Algebras.ParentMethods method) (sage.categories.additive_semigroups.AdditiveSemigroups.Algebras.ParentMethods method) (sage.categories.algebras_with_basis.AlgebrasWithBasis.TensorProducts.ParentMethods method) (sage.categories.examples.algebras_with_basis.FreeAlgebra method) (sage.categories.examples.finite_dimensional_algebras_with_basis.KroneckerQuiverPathAlgebra method) (sage.categories.examples.graded_connected_hopf_algebras_with_basis.GradedConnectedCombinatorialHopfAlgebraWithPrimitiveGenerator method) (sage.categories.examples.hopf_algebras_with_basis.MyGroupAlgebra method) (sage.categories.examples.lie_algebras_with_basis.IndexedPolynomialRing method) (sage.categories.examples.with_realizations.SubsetAlgebra.Fundamental method) (sage.categories.graded_algebras_with_basis.GradedAlgebrasWithBasis.SignedTensorProducts.ParentMethods method) (sage.categories.magmatic_algebras.MagmaticAlgebras.WithBasis.ParentMethods method) (sage.categories.semigroups.Semigroups.Algebras.ParentMethods method) product_space() (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ParentMethods method) profile() (sage.categories.finite_permutation_groups.FinitePermutationGroups.ParentMethods method) profile_polynomial() (sage.categories.finite_permutation_groups.FinitePermutationGroups.ParentMethods method) profile_series() (sage.categories.finite_permutation_groups.FinitePermutationGroups.ParentMethods method) projection() (sage.categories.filtered_algebras_with_basis.FilteredAlgebrasWithBasis.ParentMethods method) (sage.categories.filtered_modules_with_basis.FilteredModulesWithBasis.ParentMethods method) pseudo_order() (sage.categories.finite_monoids.FiniteMonoids.ElementMethods method) pushforward() (sage.categories.morphism.Morphism method) pushout() (in module sage.categories.pushout) (sage.categories.pushout.ConstructionFunctor method) pushout_lattice() (in module sage.categories.pushout) Q q() (sage.categories.quantum_group_representations.QuantumGroupRepresentations.ParentMethods method) q_dimension() (sage.categories.highest_weight_crystals.HighestWeightCrystals.ParentMethods method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) quantum_bruhat_graph() (sage.categories.weyl_groups.WeylGroups.ParentMethods method) quantum_bruhat_successors() (sage.categories.weyl_groups.WeylGroups.ElementMethods method) QuantumGroupRepresentations (class in sage.categories.quantum_group_representations) QuantumGroupRepresentations.ParentMethods (class in sage.categories.quantum_group_representations) QuantumGroupRepresentations.TensorProducts (class in sage.categories.quantum_group_representations) QuantumGroupRepresentations.TensorProducts.ParentMethods (class in sage.categories.quantum_group_representations) QuantumGroupRepresentations.WithBasis (class in sage.categories.quantum_group_representations) QuantumGroupRepresentations.WithBasis.ElementMethods (class in sage.categories.quantum_group_representations) QuantumGroupRepresentations.WithBasis.ParentMethods (class in sage.categories.quantum_group_representations) QuantumGroupRepresentations.WithBasis.TensorProducts (class in sage.categories.quantum_group_representations) QuantumGroupRepresentations.WithBasis.TensorProducts.ParentMethods (class in sage.categories.quantum_group_representations) quo() (sage.categories.rings.Rings.ParentMethods method) quo_rem() (sage.categories.discrete_valuation.DiscreteValuationRings.ElementMethods method) (sage.categories.euclidean_domains.EuclideanDomains.ElementMethods method) (sage.categories.fields.Fields.ElementMethods method) quotient() (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ParentMethods method) (sage.categories.modules.Modules.ParentMethods method) (sage.categories.rings.Rings.ParentMethods method) quotient_module() (sage.categories.graded_modules_with_basis.GradedModulesWithBasis.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) quotient_ring() (sage.categories.rings.Rings.ParentMethods method) QuotientFields (class in sage.categories.quotient_fields) QuotientFields.ElementMethods (class in sage.categories.quotient_fields) QuotientFields.ParentMethods (class in sage.categories.quotient_fields) QuotientFunctor (class in sage.categories.pushout) QuotientOfLeftZeroSemigroup (class in sage.categories.examples.semigroups) QuotientOfLeftZeroSemigroup.Element (class in sage.categories.examples.semigroups) Quotients() (sage.categories.sets_cat.Sets.SubcategoryMethods method) QuotientsCategory (class in sage.categories.quotients) R r() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) R_matrix() (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) radical() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ParentMethods method) (sage.categories.unique_factorization_domains.UniqueFactorizationDomains.ElementMethods method) radical_basis() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ParentMethods method) (sage.categories.finite_dimensional_semisimple_algebras_with_basis.FiniteDimensionalSemisimpleAlgebrasWithBasis.ParentMethods method) (sage.categories.semisimple_algebras.SemisimpleAlgebras.ParentMethods method) random_element() (sage.categories.enumerated_sets.EnumeratedSets.ParentMethods method) (sage.categories.finite_enumerated_sets.FiniteEnumeratedSets.CartesianProducts.ParentMethods method) (sage.categories.finite_enumerated_sets.FiniteEnumeratedSets.ParentMethods method) (sage.categories.infinite_enumerated_sets.InfiniteEnumeratedSets.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) (sage.categories.sets_cat.Sets.CartesianProducts.ParentMethods method) random_element_of_length() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) rank (sage.categories.pushout.AlgebraicClosureFunctor attribute) (sage.categories.pushout.AlgebraicExtensionFunctor attribute) (sage.categories.pushout.BlackBoxConstructionFunctor attribute) (sage.categories.pushout.CompletionFunctor attribute) (sage.categories.pushout.FractionField attribute) (sage.categories.pushout.IdentityConstructionFunctor attribute) (sage.categories.pushout.InfinitePolynomialFunctor attribute) (sage.categories.pushout.LaurentPolynomialFunctor attribute) (sage.categories.pushout.MatrixFunctor attribute) (sage.categories.pushout.MultiPolynomialFunctor attribute) (sage.categories.pushout.PermutationGroupFunctor attribute) (sage.categories.pushout.PolynomialFunctor attribute) (sage.categories.pushout.QuotientFunctor attribute) (sage.categories.pushout.SubspaceFunctor attribute) (sage.categories.pushout.VectorFunctor attribute) rank() (sage.categories.complex_reflection_groups.ComplexReflectionGroups.ParentMethods method) (sage.categories.enumerated_sets.EnumeratedSets.ElementMethods method) (sage.categories.enumerated_sets.EnumeratedSets.ParentMethods method) (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.ParentMethods method) (sage.categories.finite_enumerated_sets.FiniteEnumeratedSets.CartesianProducts.ParentMethods method) rational_catalan_number() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.WellGenerated.Irreducible.ParentMethods method) realization_of() (sage.categories.sets_cat.Sets.Realizations.ParentMethods method) Realizations() (in module sage.categories.realizations) (sage.categories.category.Category method) realizations() (sage.categories.sets_cat.Sets.WithRealizations.ParentMethods method) RealizationsCategory (class in sage.categories.realizations) reduced_word() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) reduced_word_graph() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) reduced_word_reverse_iterator() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) reduced_words() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) reflection() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) reflection_index_set() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) reflection_length() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ElementMethods method) (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.ElementMethods method) reflection_to_coroot() (sage.categories.weyl_groups.WeylGroups.ElementMethods method) reflection_to_root() (sage.categories.weyl_groups.WeylGroups.ElementMethods method) reflections() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) reflections_from_w0() (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods method) register_as_coercion() (sage.categories.morphism.Morphism method) register_as_conversion() (sage.categories.morphism.Morphism method) RegressiveCovariantConstructionCategory (class in sage.categories.covariant_functorial_construction) regular_representation() (sage.categories.semigroups.Semigroups.Algebras.ParentMethods method) (sage.categories.semigroups.Semigroups.ParentMethods method) RegularCrystals (class in sage.categories.regular_crystals) RegularCrystals.ElementMethods (class in sage.categories.regular_crystals) RegularCrystals.MorphismMethods (class in sage.categories.regular_crystals) RegularCrystals.ParentMethods (class in sage.categories.regular_crystals) RegularCrystals.TensorProducts (class in sage.categories.regular_crystals) RegularLoopCrystals (class in sage.categories.loop_crystals) RegularLoopCrystals.ElementMethods (class in sage.categories.loop_crystals) RegularSuperCrystals (class in sage.categories.regular_supercrystals) RegularSuperCrystals.ElementMethods (class in sage.categories.regular_supercrystals) RegularSuperCrystals.TensorProducts (class in sage.categories.regular_supercrystals) required_methods() (sage.categories.category.Category method) residue_field() (sage.categories.discrete_valuation.DiscreteValuationFields.ParentMethods method) (sage.categories.discrete_valuation.DiscreteValuationRings.ParentMethods method) retract() (sage.categories.examples.finite_enumerated_sets.IsomorphicObjectOfFiniteEnumeratedSet method) (sage.categories.examples.semigroups.QuotientOfLeftZeroSemigroup method) (sage.categories.sets_cat.Sets.Subquotients.ParentMethods method) reversed() (sage.categories.homset.Homset method) rhodes_radical_congruence() (sage.categories.finite_monoids.FiniteMonoids.ParentMethods method) right_base_ring() (sage.categories.bimodules.Bimodules method) right_domain() (sage.categories.action.Action method) right_precomposition (sage.categories.action.PrecomposedAction attribute) RightModules (class in sage.categories.right_modules) RightModules.ElementMethods (class in sage.categories.right_modules) RightModules.ParentMethods (class in sage.categories.right_modules) ring() (sage.categories.category_types.Category_ideal method) RingIdeals (class in sage.categories.ring_ideals) Rings (class in sage.categories.rings) Rings.ElementMethods (class in sage.categories.rings) Rings.MorphismMethods (class in sage.categories.rings) Rings.ParentMethods (class in sage.categories.rings) Rings.SubcategoryMethods (class in sage.categories.rings) Rngs (class in sage.categories.rngs) rowmotion() (sage.categories.finite_posets.FinitePosets.ParentMethods method) rowmotion_orbit_iter() (sage.categories.finite_posets.FinitePosets.ParentMethods method) rowmotion_orbits() (sage.categories.finite_posets.FinitePosets.ParentMethods method) rowmotion_orbits_plots() (sage.categories.finite_posets.FinitePosets.ParentMethods method) RTrivial (sage.categories.semigroups.Semigroups attribute) RTrivial() (sage.categories.semigroups.Semigroups.SubcategoryMethods method) RTrivial_extra_super_categories() (sage.categories.l_trivial_semigroups.LTrivialSemigroups method) RTrivialSemigroups (class in sage.categories.r_trivial_semigroups) S s() (sage.categories.crystals.Crystals.ElementMethods method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals.ParentMethods method) sage.categories.action module sage.categories.additive_groups module sage.categories.additive_magmas module sage.categories.additive_monoids module sage.categories.additive_semigroups module sage.categories.affine_weyl_groups module sage.categories.algebra_functor module sage.categories.algebra_ideals module sage.categories.algebra_modules module sage.categories.algebras module sage.categories.algebras_with_basis module sage.categories.all module sage.categories.aperiodic_semigroups module sage.categories.associative_algebras module sage.categories.bialgebras module sage.categories.bialgebras_with_basis module sage.categories.bimodules module sage.categories.cartesian_product module sage.categories.category module sage.categories.category_cy_helper module sage.categories.category_singleton module sage.categories.category_types module sage.categories.category_with_axiom module sage.categories.classical_crystals module sage.categories.coalgebras module sage.categories.coalgebras_with_basis module sage.categories.coercion_methods module sage.categories.commutative_additive_groups module sage.categories.commutative_additive_monoids module sage.categories.commutative_additive_semigroups module sage.categories.commutative_algebra_ideals module sage.categories.commutative_algebras module sage.categories.commutative_ring_ideals module sage.categories.commutative_rings module sage.categories.complete_discrete_valuation module sage.categories.complex_reflection_groups module sage.categories.complex_reflection_or_generalized_coxeter_groups module sage.categories.covariant_functorial_construction module sage.categories.coxeter_group_algebras module sage.categories.coxeter_groups module sage.categories.crystals module sage.categories.cw_complexes module sage.categories.discrete_valuation module sage.categories.distributive_magmas_and_additive_magmas module sage.categories.division_rings module sage.categories.domains module sage.categories.dual module sage.categories.enumerated_sets module sage.categories.euclidean_domains module sage.categories.examples.algebras_with_basis module sage.categories.examples.commutative_additive_monoids module sage.categories.examples.commutative_additive_semigroups module sage.categories.examples.coxeter_groups module sage.categories.examples.crystals module sage.categories.examples.cw_complexes module sage.categories.examples.facade_sets module sage.categories.examples.finite_coxeter_groups module sage.categories.examples.finite_dimensional_algebras_with_basis module sage.categories.examples.finite_dimensional_lie_algebras_with_basis module sage.categories.examples.finite_enumerated_sets module sage.categories.examples.finite_monoids module sage.categories.examples.finite_semigroups module sage.categories.examples.finite_weyl_groups module sage.categories.examples.graded_connected_hopf_algebras_with_basis module sage.categories.examples.graded_modules_with_basis module sage.categories.examples.graphs module sage.categories.examples.hopf_algebras_with_basis module sage.categories.examples.infinite_enumerated_sets module sage.categories.examples.lie_algebras module sage.categories.examples.lie_algebras_with_basis module sage.categories.examples.magmas module sage.categories.examples.manifolds module sage.categories.examples.monoids module sage.categories.examples.posets module sage.categories.examples.semigroups module sage.categories.examples.semigroups_cython module sage.categories.examples.sets_cat module sage.categories.examples.sets_with_grading module sage.categories.examples.with_realizations module sage.categories.facade_sets module sage.categories.fields module sage.categories.filtered_algebras module sage.categories.filtered_algebras_with_basis module sage.categories.filtered_modules module sage.categories.filtered_modules_with_basis module sage.categories.finite_complex_reflection_groups module sage.categories.finite_coxeter_groups module sage.categories.finite_crystals module sage.categories.finite_dimensional_algebras_with_basis module sage.categories.finite_dimensional_bialgebras_with_basis module sage.categories.finite_dimensional_coalgebras_with_basis module sage.categories.finite_dimensional_graded_lie_algebras_with_basis module sage.categories.finite_dimensional_hopf_algebras_with_basis module sage.categories.finite_dimensional_lie_algebras_with_basis module sage.categories.finite_dimensional_modules_with_basis module sage.categories.finite_dimensional_nilpotent_lie_algebras_with_basis module sage.categories.finite_dimensional_semisimple_algebras_with_basis module sage.categories.finite_enumerated_sets module sage.categories.finite_fields module sage.categories.finite_groups module sage.categories.finite_lattice_posets module sage.categories.finite_monoids module sage.categories.finite_permutation_groups module sage.categories.finite_posets module sage.categories.finite_semigroups module sage.categories.finite_sets module sage.categories.finite_weyl_groups module sage.categories.finitely_generated_lambda_bracket_algebras module sage.categories.finitely_generated_lie_conformal_algebras module sage.categories.finitely_generated_magmas module sage.categories.finitely_generated_semigroups module sage.categories.function_fields module sage.categories.functor module sage.categories.g_sets module sage.categories.gcd_domains module sage.categories.generalized_coxeter_groups module sage.categories.graded_algebras module sage.categories.graded_algebras_with_basis module sage.categories.graded_bialgebras module sage.categories.graded_bialgebras_with_basis module sage.categories.graded_coalgebras module sage.categories.graded_coalgebras_with_basis module sage.categories.graded_hopf_algebras module sage.categories.graded_hopf_algebras_with_basis module sage.categories.graded_lie_algebras module sage.categories.graded_lie_algebras_with_basis module sage.categories.graded_lie_conformal_algebras module sage.categories.graded_modules module sage.categories.graded_modules_with_basis module sage.categories.graphs module sage.categories.group_algebras module sage.categories.groupoid module sage.categories.groups module sage.categories.h_trivial_semigroups module sage.categories.hecke_modules module sage.categories.highest_weight_crystals module sage.categories.homset module sage.categories.homsets module sage.categories.hopf_algebras module sage.categories.hopf_algebras_with_basis module sage.categories.infinite_enumerated_sets module sage.categories.integral_domains module sage.categories.isomorphic_objects module sage.categories.j_trivial_semigroups module sage.categories.kac_moody_algebras module sage.categories.l_trivial_semigroups module sage.categories.lambda_bracket_algebras module sage.categories.lambda_bracket_algebras_with_basis module sage.categories.lattice_posets module sage.categories.left_modules module sage.categories.lie_algebras module sage.categories.lie_algebras_with_basis module sage.categories.lie_conformal_algebras module sage.categories.lie_conformal_algebras_with_basis module sage.categories.lie_groups module sage.categories.loop_crystals module sage.categories.magmas module sage.categories.magmas_and_additive_magmas module sage.categories.magmatic_algebras module sage.categories.manifolds module sage.categories.map module sage.categories.matrix_algebras module sage.categories.metric_spaces module sage.categories.modular_abelian_varieties module sage.categories.modules module sage.categories.modules_with_basis module sage.categories.monoid_algebras module sage.categories.monoids module sage.categories.morphism module sage.categories.number_fields module sage.categories.objects module sage.categories.partially_ordered_monoids module sage.categories.permutation_groups module sage.categories.pointed_sets module sage.categories.polyhedra module sage.categories.poor_man_map module sage.categories.posets module sage.categories.primer module sage.categories.principal_ideal_domains module sage.categories.pushout module sage.categories.quantum_group_representations module sage.categories.quotient_fields module sage.categories.quotients module sage.categories.r_trivial_semigroups module sage.categories.realizations module sage.categories.regular_crystals module sage.categories.regular_supercrystals module sage.categories.right_modules module sage.categories.ring_ideals module sage.categories.rings module sage.categories.rngs module sage.categories.schemes module sage.categories.semigroups module sage.categories.semirings module sage.categories.semisimple_algebras module sage.categories.sets_cat module sage.categories.sets_with_grading module sage.categories.sets_with_partial_maps module sage.categories.shephard_groups module sage.categories.signed_tensor module sage.categories.simplicial_complexes module sage.categories.simplicial_sets module sage.categories.subobjects module sage.categories.subquotients module sage.categories.super_algebras module sage.categories.super_algebras_with_basis module sage.categories.super_hopf_algebras_with_basis module sage.categories.super_lie_conformal_algebras module sage.categories.super_modules module sage.categories.super_modules_with_basis module sage.categories.supercommutative_algebras module sage.categories.supercrystals module sage.categories.tensor module sage.categories.topological_spaces module sage.categories.triangular_kac_moody_algebras module sage.categories.tutorial module sage.categories.unique_factorization_domains module sage.categories.unital_algebras module sage.categories.vector_bundles module sage.categories.vector_spaces module sage.categories.weyl_groups module sage.categories.with_realizations module scaling_factors() (sage.categories.crystals.CrystalMorphism method) Schemes (class in sage.categories.schemes) Schemes_over_base (class in sage.categories.schemes) Section (class in sage.categories.map) section() (sage.categories.map.FormalCompositeMap method) (sage.categories.map.Map method) (sage.categories.morphism.IdentityMorphism method) semidirect_product() (sage.categories.groups.Groups.ParentMethods method) semigroup_generators() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) (sage.categories.examples.finite_monoids.IntegerModMonoid method) (sage.categories.examples.finite_semigroups.LeftRegularBand method) (sage.categories.examples.semigroups.FreeSemigroup method) (sage.categories.finite_groups.FiniteGroups.ParentMethods method) (sage.categories.finitely_generated_semigroups.FinitelyGeneratedSemigroups.ParentMethods method) (sage.categories.monoids.Monoids.ParentMethods method) (sage.categories.semigroups.Semigroups.ParentMethods method) (sage.categories.semigroups.Semigroups.Quotients.ParentMethods method) Semigroups (class in sage.categories.semigroups) Semigroups.Algebras (class in sage.categories.semigroups) Semigroups.Algebras.ParentMethods (class in sage.categories.semigroups) Semigroups.CartesianProducts (class in sage.categories.semigroups) Semigroups.ElementMethods (class in sage.categories.semigroups) Semigroups.ParentMethods (class in sage.categories.semigroups) Semigroups.Quotients (class in sage.categories.semigroups) Semigroups.Quotients.ParentMethods (class in sage.categories.semigroups) Semigroups.SubcategoryMethods (class in sage.categories.semigroups) Semigroups.Subquotients (class in sage.categories.semigroups) Semirings (class in sage.categories.semirings) Semisimple (sage.categories.algebras.Algebras attribute) Semisimple() (sage.categories.algebras.Algebras.SubcategoryMethods method) semisimple_quotient() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.ParentMethods method) SemisimpleAlgebras (class in sage.categories.semisimple_algebras) SemisimpleAlgebras.FiniteDimensional (class in sage.categories.semisimple_algebras) SemisimpleAlgebras.ParentMethods (class in sage.categories.semisimple_algebras) set_base_point() (sage.categories.simplicial_sets.SimplicialSets.ParentMethods method) SetMorphism (class in sage.categories.morphism) Sets (class in sage.categories.sets_cat) Sets.Algebras (class in sage.categories.sets_cat) Sets.Algebras.ParentMethods (class in sage.categories.sets_cat) Sets.CartesianProducts (class in sage.categories.sets_cat) Sets.CartesianProducts.ElementMethods (class in sage.categories.sets_cat) Sets.CartesianProducts.ParentMethods (class in sage.categories.sets_cat) Sets.ElementMethods (class in sage.categories.sets_cat) Sets.Infinite (class in sage.categories.sets_cat) Sets.Infinite.ParentMethods (class in sage.categories.sets_cat) Sets.IsomorphicObjects (class in sage.categories.sets_cat) Sets.IsomorphicObjects.ParentMethods (class in sage.categories.sets_cat) Sets.MorphismMethods (class in sage.categories.sets_cat) Sets.ParentMethods (class in sage.categories.sets_cat) Sets.Quotients (class in sage.categories.sets_cat) Sets.Quotients.ParentMethods (class in sage.categories.sets_cat) Sets.Realizations (class in sage.categories.sets_cat) Sets.Realizations.ParentMethods (class in sage.categories.sets_cat) Sets.SubcategoryMethods (class in sage.categories.sets_cat) Sets.Subobjects (class in sage.categories.sets_cat) Sets.Subobjects.ParentMethods (class in sage.categories.sets_cat) Sets.Subquotients (class in sage.categories.sets_cat) Sets.Subquotients.ElementMethods (class in sage.categories.sets_cat) Sets.Subquotients.ParentMethods (class in sage.categories.sets_cat) Sets.WithRealizations (class in sage.categories.sets_cat) Sets.WithRealizations.ParentMethods (class in sage.categories.sets_cat) Sets.WithRealizations.ParentMethods.Realizations (class in sage.categories.sets_cat) SetsWithGrading (class in sage.categories.sets_with_grading) SetsWithGrading.ParentMethods (class in sage.categories.sets_with_grading) SetsWithPartialMaps (class in sage.categories.sets_with_partial_maps) shard_poset() (sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods method) ShephardGroups (class in sage.categories.shephard_groups) sign_representation() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) SignedTensorProductFunctor (class in sage.categories.signed_tensor) SignedTensorProducts() (sage.categories.graded_algebras.GradedAlgebras.SubcategoryMethods method) (sage.categories.graded_coalgebras.GradedCoalgebras.SubcategoryMethods method) (sage.categories.signed_tensor.SignedTensorProductsCategory method) SignedTensorProductsCategory (class in sage.categories.signed_tensor) simple_module_parameterization() (sage.categories.finite_dimensional_algebras_with_basis.FiniteDimensionalAlgebrasWithBasis.Cellular.ParentMethods method) simple_projection() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) simple_projections() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) simple_reflection() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) (sage.categories.examples.finite_weyl_groups.SymmetricGroup method) simple_reflection_orders() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) simple_reflections() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) SimplicialComplexes (class in sage.categories.simplicial_complexes) SimplicialComplexes.Connected (class in sage.categories.simplicial_complexes) SimplicialComplexes.Finite (class in sage.categories.simplicial_complexes) SimplicialComplexes.Finite.ParentMethods (class in sage.categories.simplicial_complexes) SimplicialComplexes.ParentMethods (class in sage.categories.simplicial_complexes) SimplicialComplexes.SubcategoryMethods (class in sage.categories.simplicial_complexes) SimplicialSets (class in sage.categories.simplicial_sets) SimplicialSets.Finite (class in sage.categories.simplicial_sets) SimplicialSets.Homsets (class in sage.categories.simplicial_sets) SimplicialSets.Homsets.Endset (class in sage.categories.simplicial_sets) SimplicialSets.Homsets.Endset.ParentMethods (class in sage.categories.simplicial_sets) SimplicialSets.ParentMethods (class in sage.categories.simplicial_sets) SimplicialSets.Pointed (class in sage.categories.simplicial_sets) SimplicialSets.Pointed.Finite (class in sage.categories.simplicial_sets) SimplicialSets.Pointed.Finite.ParentMethods (class in sage.categories.simplicial_sets) SimplicialSets.Pointed.ParentMethods (class in sage.categories.simplicial_sets) SimplicialSets.SubcategoryMethods (class in sage.categories.simplicial_sets) smash_product() (sage.categories.simplicial_sets.SimplicialSets.Pointed.Finite.ParentMethods method) Smooth() (sage.categories.manifolds.Manifolds.SubcategoryMethods method) (sage.categories.vector_bundles.VectorBundles.SubcategoryMethods method) some_elements() (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups.ParentMethods method) (sage.categories.enumerated_sets.EnumeratedSets.ParentMethods method) (sage.categories.examples.semigroups.LeftZeroSemigroup method) (sage.categories.examples.semigroups.QuotientOfLeftZeroSemigroup method) (sage.categories.examples.sets_cat.PrimeNumbers_Abstract method) (sage.categories.finite_groups.FiniteGroups.ParentMethods method) (sage.categories.finitely_generated_lambda_bracket_algebras.FinitelyGeneratedLambdaBracketAlgebras.ParentMethods method) (sage.categories.finitely_generated_lie_conformal_algebras.FinitelyGeneratedLieConformalAlgebras.ParentMethods method) (sage.categories.finitely_generated_semigroups.FinitelyGeneratedSemigroups.Finite.ParentMethods method) (sage.categories.sets_cat.Sets.ParentMethods method) special_node() (sage.categories.affine_weyl_groups.AffineWeylGroups.ParentMethods method) squarefree_part() (sage.categories.unique_factorization_domains.UniqueFactorizationDomains.ElementMethods method) standard_coxeter_elements() (sage.categories.coxeter_groups.CoxeterGroups.ParentMethods method) (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.WellGenerated.ParentMethods method) stanley_symmetric_function() (sage.categories.weyl_groups.WeylGroups.ElementMethods method) stanley_symmetric_function_as_polynomial() (sage.categories.weyl_groups.WeylGroups.ElementMethods method) stembridgeDel_depth() (sage.categories.regular_crystals.RegularCrystals.ElementMethods method) stembridgeDel_rise() (sage.categories.regular_crystals.RegularCrystals.ElementMethods method) stembridgeDelta_depth() (sage.categories.regular_crystals.RegularCrystals.ElementMethods method) stembridgeDelta_rise() (sage.categories.regular_crystals.RegularCrystals.ElementMethods method) stembridgeTriple() (sage.categories.regular_crystals.RegularCrystals.ElementMethods method) step() (sage.categories.finite_dimensional_nilpotent_lie_algebras_with_basis.FiniteDimensionalNilpotentLieAlgebrasWithBasis.ParentMethods method) (sage.categories.lie_algebras.LieAlgebras.Nilpotent.ParentMethods method) Stratified() (sage.categories.graded_lie_algebras.GradedLieAlgebras.SubcategoryMethods method) string_parameters() (sage.categories.highest_weight_crystals.HighestWeightCrystals.ElementMethods method) structure() (sage.categories.category.Category method) structure_coefficients() (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ParentMethods method) subalgebra() (sage.categories.examples.finite_dimensional_lie_algebras_with_basis.AbelianLieAlgebra method) (sage.categories.finite_dimensional_lie_algebras_with_basis.FiniteDimensionalLieAlgebrasWithBasis.ParentMethods method) (sage.categories.lie_algebras.LieAlgebras.ParentMethods method) subcategory_class() (sage.categories.category.Category method) subcrystal() (sage.categories.crystals.Crystals.ElementMethods method) (sage.categories.crystals.Crystals.ParentMethods method) submodule() (sage.categories.graded_modules_with_basis.GradedModulesWithBasis.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) submonoid() (sage.categories.monoids.Monoids.ParentMethods method) Subobjects() (sage.categories.sets_cat.Sets.SubcategoryMethods method) SubobjectsCategory (class in sage.categories.subobjects) Subquotients() (sage.categories.sets_cat.Sets.SubcategoryMethods method) SubquotientsCategory (class in sage.categories.subquotients) subsemigroup() (sage.categories.semigroups.Semigroups.ParentMethods method) subset() (sage.categories.sets_with_grading.SetsWithGrading.ParentMethods method) SubsetAlgebra (class in sage.categories.examples.with_realizations) SubsetAlgebra.Bases (class in sage.categories.examples.with_realizations) SubsetAlgebra.Bases.ParentMethods (class in sage.categories.examples.with_realizations) SubsetAlgebra.Fundamental (class in sage.categories.examples.with_realizations) SubsetAlgebra.In (class in sage.categories.examples.with_realizations) SubsetAlgebra.Out (class in sage.categories.examples.with_realizations) SubspaceFunctor (class in sage.categories.pushout) succ_generators() (sage.categories.finitely_generated_semigroups.FinitelyGeneratedSemigroups.ParentMethods method) sum() (sage.categories.additive_monoids.AdditiveMonoids.ParentMethods method) sum_of_monomials() (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) sum_of_terms() (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) summation() (sage.categories.additive_magmas.AdditiveMagmas.ParentMethods method) (sage.categories.examples.commutative_additive_semigroups.FreeCommutativeAdditiveSemigroup method) summation_from_element_class_add() (sage.categories.additive_magmas.AdditiveMagmas.ParentMethods method) Super (sage.categories.algebras.Algebras attribute) (sage.categories.algebras_with_basis.AlgebrasWithBasis attribute) (sage.categories.hopf_algebras_with_basis.HopfAlgebrasWithBasis attribute) (sage.categories.lie_conformal_algebras.LieConformalAlgebras attribute) (sage.categories.modules.Modules attribute) (sage.categories.modules_with_basis.ModulesWithBasis attribute) Super() (sage.categories.graded_lie_conformal_algebras.GradedLieConformalAlgebrasCategory method) (sage.categories.modules.Modules.SubcategoryMethods method) super_categories() (sage.categories.additive_magmas.AdditiveMagmas method) (sage.categories.affine_weyl_groups.AffineWeylGroups method) (sage.categories.algebra_ideals.AlgebraIdeals method) (sage.categories.algebra_modules.AlgebraModules method) (sage.categories.bialgebras.Bialgebras method) (sage.categories.bimodules.Bimodules method) (sage.categories.category.Category method) (sage.categories.category.JoinCategory method) (sage.categories.category_types.Elements method) (sage.categories.category_with_axiom.Bars method) (sage.categories.category_with_axiom.Blahs method) (sage.categories.category_with_axiom.CategoryWithAxiom method) (sage.categories.category_with_axiom.TestObjects method) (sage.categories.category_with_axiom.TestObjectsOverBaseRing method) (sage.categories.classical_crystals.ClassicalCrystals method) (sage.categories.coalgebras.Coalgebras method) (sage.categories.commutative_algebra_ideals.CommutativeAlgebraIdeals method) (sage.categories.commutative_ring_ideals.CommutativeRingIdeals method) (sage.categories.complete_discrete_valuation.CompleteDiscreteValuationFields method) (sage.categories.complete_discrete_valuation.CompleteDiscreteValuationRings method) (sage.categories.complex_reflection_groups.ComplexReflectionGroups method) (sage.categories.complex_reflection_or_generalized_coxeter_groups.ComplexReflectionOrGeneralizedCoxeterGroups method) (sage.categories.covariant_functorial_construction.FunctorialConstructionCategory method) (sage.categories.coxeter_groups.CoxeterGroups method) (sage.categories.crystals.Crystals method) (sage.categories.cw_complexes.CWComplexes method) (sage.categories.discrete_valuation.DiscreteValuationFields method) (sage.categories.discrete_valuation.DiscreteValuationRings method) (sage.categories.domains.Domains method) (sage.categories.enumerated_sets.EnumeratedSets method) (sage.categories.euclidean_domains.EuclideanDomains method) (sage.categories.examples.semigroups_cython.IdempotentSemigroups method) (sage.categories.examples.with_realizations.SubsetAlgebra.Bases method) (sage.categories.function_fields.FunctionFields method) (sage.categories.g_sets.GSets method) (sage.categories.gcd_domains.GcdDomains method) (sage.categories.generalized_coxeter_groups.GeneralizedCoxeterGroups method) (sage.categories.graded_hopf_algebras_with_basis.GradedHopfAlgebrasWithBasis.WithRealizations method) (sage.categories.graphs.Graphs method) (sage.categories.groupoid.Groupoid method) (sage.categories.hecke_modules.HeckeModules method) (sage.categories.highest_weight_crystals.HighestWeightCrystals method) (sage.categories.homsets.Homsets method) (sage.categories.homsets.HomsetsOf method) (sage.categories.hopf_algebras.HopfAlgebras method) (sage.categories.kac_moody_algebras.KacMoodyAlgebras method) (sage.categories.lambda_bracket_algebras.LambdaBracketAlgebras method) (sage.categories.lattice_posets.LatticePosets method) (sage.categories.left_modules.LeftModules method) (sage.categories.lie_algebras.LieAlgebras method) (sage.categories.lie_conformal_algebras.LieConformalAlgebras method) (sage.categories.lie_groups.LieGroups method) (sage.categories.loop_crystals.KirillovReshetikhinCrystals method) (sage.categories.loop_crystals.LoopCrystals method) (sage.categories.loop_crystals.RegularLoopCrystals method) (sage.categories.magmas.Magmas method) (sage.categories.magmas_and_additive_magmas.MagmasAndAdditiveMagmas method) (sage.categories.magmatic_algebras.MagmaticAlgebras method) (sage.categories.manifolds.ComplexManifolds method) (sage.categories.manifolds.Manifolds method) (sage.categories.matrix_algebras.MatrixAlgebras method) (sage.categories.modular_abelian_varieties.ModularAbelianVarieties method) (sage.categories.modules.Modules method) (sage.categories.number_fields.NumberFields method) (sage.categories.objects.Objects method) (sage.categories.partially_ordered_monoids.PartiallyOrderedMonoids method) (sage.categories.permutation_groups.PermutationGroups method) (sage.categories.pointed_sets.PointedSets method) (sage.categories.polyhedra.PolyhedralSets method) (sage.categories.posets.Posets method) (sage.categories.principal_ideal_domains.PrincipalIdealDomains method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations method) (sage.categories.quotient_fields.QuotientFields method) (sage.categories.regular_crystals.RegularCrystals method) (sage.categories.regular_supercrystals.RegularSuperCrystals method) (sage.categories.right_modules.RightModules method) (sage.categories.ring_ideals.RingIdeals method) (sage.categories.schemes.Schemes method) (sage.categories.schemes.Schemes_over_base method) (sage.categories.semisimple_algebras.SemisimpleAlgebras method) (sage.categories.sets_cat.Sets method) (sage.categories.sets_cat.Sets.WithRealizations.ParentMethods.Realizations method) (sage.categories.sets_with_grading.SetsWithGrading method) (sage.categories.sets_with_partial_maps.SetsWithPartialMaps method) (sage.categories.shephard_groups.ShephardGroups method) (sage.categories.simplicial_complexes.SimplicialComplexes method) (sage.categories.simplicial_sets.SimplicialSets method) (sage.categories.super_modules.SuperModules method) (sage.categories.supercrystals.SuperCrystals method) (sage.categories.triangular_kac_moody_algebras.TriangularKacMoodyAlgebras method) (sage.categories.unique_factorization_domains.UniqueFactorizationDomains method) (sage.categories.vector_bundles.VectorBundles method) (sage.categories.vector_spaces.VectorSpaces method) (sage.categories.weyl_groups.WeylGroups method) SuperAlgebras (class in sage.categories.super_algebras) SuperAlgebras.ParentMethods (class in sage.categories.super_algebras) SuperAlgebras.SignedTensorProducts (class in sage.categories.super_algebras) SuperAlgebras.SubcategoryMethods (class in sage.categories.super_algebras) SuperAlgebrasWithBasis (class in sage.categories.super_algebras_with_basis) SuperAlgebrasWithBasis.ElementMethods (class in sage.categories.super_algebras_with_basis) SuperAlgebrasWithBasis.ParentMethods (class in sage.categories.super_algebras_with_basis) SuperAlgebrasWithBasis.SignedTensorProducts (class in sage.categories.super_algebras_with_basis) Supercocommutative() (sage.categories.coalgebras.Coalgebras.Super.SubcategoryMethods method) Supercommutative (sage.categories.super_algebras.SuperAlgebras attribute) Supercommutative() (sage.categories.algebras.Algebras.SubcategoryMethods method) (sage.categories.super_algebras.SuperAlgebras.SubcategoryMethods method) SupercommutativeAlgebras (class in sage.categories.supercommutative_algebras) SupercommutativeAlgebras.SignedTensorProducts (class in sage.categories.supercommutative_algebras) SupercommutativeAlgebras.WithBasis (class in sage.categories.supercommutative_algebras) SupercommutativeAlgebras.WithBasis.ParentMethods (class in sage.categories.supercommutative_algebras) supercommutator() (sage.categories.super_algebras_with_basis.SuperAlgebrasWithBasis.ElementMethods method) SuperCrystals (class in sage.categories.supercrystals) SuperCrystals.Finite (class in sage.categories.supercrystals) SuperCrystals.Finite.ElementMethods (class in sage.categories.supercrystals) SuperCrystals.Finite.ParentMethods (class in sage.categories.supercrystals) SuperCrystals.ParentMethods (class in sage.categories.supercrystals) SuperCrystals.TensorProducts (class in sage.categories.supercrystals) SuperHopfAlgebrasWithBasis (class in sage.categories.super_hopf_algebras_with_basis) SuperHopfAlgebrasWithBasis.ParentMethods (class in sage.categories.super_hopf_algebras_with_basis) SuperLieConformalAlgebras (class in sage.categories.super_lie_conformal_algebras) SuperLieConformalAlgebras.ElementMethods (class in sage.categories.super_lie_conformal_algebras) SuperLieConformalAlgebras.Graded (class in sage.categories.super_lie_conformal_algebras) SuperLieConformalAlgebras.ParentMethods (class in sage.categories.super_lie_conformal_algebras) SuperModules (class in sage.categories.super_modules) SuperModules.ElementMethods (class in sage.categories.super_modules) SuperModules.ParentMethods (class in sage.categories.super_modules) SuperModulesCategory (class in sage.categories.super_modules) SuperModulesWithBasis (class in sage.categories.super_modules_with_basis) SuperModulesWithBasis.ElementMethods (class in sage.categories.super_modules_with_basis) SuperModulesWithBasis.ParentMethods (class in sage.categories.super_modules_with_basis) support() (sage.categories.coxeter_groups.CoxeterGroups.ElementMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) support_of_term() (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) supsets() (sage.categories.examples.with_realizations.SubsetAlgebra method) Surface (class in sage.categories.examples.cw_complexes) Surface.Element (class in sage.categories.examples.cw_complexes) symbol (sage.categories.cartesian_product.CartesianProductFunctor attribute) (sage.categories.dual.DualFunctor attribute) (sage.categories.signed_tensor.SignedTensorProductFunctor attribute) (sage.categories.tensor.TensorProductFunctor attribute) SymmetricGroup (class in sage.categories.examples.finite_weyl_groups) SymmetricGroup.Element (class in sage.categories.examples.finite_weyl_groups) T T() (sage.categories.lambda_bracket_algebras.LambdaBracketAlgebras.ElementMethods method) tensor (in module sage.categories.tensor) tensor() (sage.categories.crystals.Crystals.ElementMethods method) (sage.categories.crystals.Crystals.ParentMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) (sage.categories.quantum_group_representations.QuantumGroupRepresentations.WithBasis.ParentMethods method) (sage.categories.super_algebras.SuperAlgebras.ParentMethods method) (sage.categories.supercrystals.SuperCrystals.ParentMethods method) tensor_factors() (sage.categories.modules.Modules.TensorProducts.ParentMethods method) tensor_square() (sage.categories.modules.Modules.ParentMethods method) TensorProductFunctor (class in sage.categories.tensor) TensorProducts() (sage.categories.crystals.Crystals.SubcategoryMethods method) (sage.categories.modules.Modules.SubcategoryMethods method) (sage.categories.tensor.TensorProductsCategory method) TensorProductsCategory (class in sage.categories.tensor) term() (sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods method) terms() (sage.categories.modules_with_basis.ModulesWithBasis.ElementMethods method) TestObjects (class in sage.categories.category_with_axiom) TestObjects.Commutative (class in sage.categories.category_with_axiom) TestObjects.Commutative.Facade (class in sage.categories.category_with_axiom) TestObjects.Commutative.Finite (class in sage.categories.category_with_axiom) TestObjects.Commutative.FiniteDimensional (class in sage.categories.category_with_axiom) TestObjects.FiniteDimensional (class in sage.categories.category_with_axiom) TestObjects.FiniteDimensional.Finite (class in sage.categories.category_with_axiom) TestObjects.FiniteDimensional.Unital (class in sage.categories.category_with_axiom) TestObjects.FiniteDimensional.Unital.Commutative (class in sage.categories.category_with_axiom) TestObjects.Unital (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.Commutative (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.Commutative.Facade (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.Commutative.Finite (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.Commutative.FiniteDimensional (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.FiniteDimensional (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.FiniteDimensional.Finite (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.FiniteDimensional.Unital (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.FiniteDimensional.Unital.Commutative (class in sage.categories.category_with_axiom) TestObjectsOverBaseRing.Unital (class in sage.categories.category_with_axiom) the_answer() (sage.categories.examples.semigroups.QuotientOfLeftZeroSemigroup method) then() (sage.categories.map.FormalCompositeMap method) to_graded_conversion() (sage.categories.filtered_algebras_with_basis.FilteredAlgebrasWithBasis.ParentMethods method) (sage.categories.filtered_modules_with_basis.FilteredModulesWithBasis.ParentMethods method) to_highest_weight() (sage.categories.crystals.Crystals.ElementMethods method) to_lowest_weight() (sage.categories.crystals.Crystals.ElementMethods method) to_matrix() (sage.categories.finite_complex_reflection_groups.FiniteComplexReflectionGroups.ElementMethods method) 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