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 | Y A A() (sage.groups.affine_gps.group_element.AffineGroupElement method) abelian_alexander_matrix() (sage.groups.finitely_presented.FinitelyPresentedGroup method) abelian_invariants() (sage.groups.finitely_presented.FinitelyPresentedGroup method) (sage.groups.free_group.FreeGroup_class method) AbelianGroup (class in sage.groups.group) AbelianGroup() (in module sage.groups.abelian_gps.abelian_group) AbelianGroup_class (class in sage.groups.abelian_gps.abelian_group) AbelianGroup_gap (class in sage.groups.abelian_gps.abelian_group_gap) AbelianGroup_subgroup (class in sage.groups.abelian_gps.abelian_group) AbelianGroupAutomorphism (class in sage.groups.abelian_gps.abelian_aut) AbelianGroupAutomorphismGroup (class in sage.groups.abelian_gps.abelian_aut) AbelianGroupAutomorphismGroup_gap (class in sage.groups.abelian_gps.abelian_aut) AbelianGroupAutomorphismGroup_subgroup (class in sage.groups.abelian_gps.abelian_aut) AbelianGroupElement (class in sage.groups.abelian_gps.abelian_group_element) AbelianGroupElement_gap (class in sage.groups.abelian_gps.abelian_group_gap) AbelianGroupElement_polycyclic (class in sage.groups.abelian_gps.abelian_group_gap) AbelianGroupElementBase (class in sage.groups.abelian_gps.element_base) AbelianGroupGap (class in sage.groups.abelian_gps.abelian_group_gap) AbelianGroupMap (class in sage.groups.abelian_gps.abelian_group_morphism) AbelianGroupMorphism (class in sage.groups.abelian_gps.abelian_group_morphism) AbelianGroupQuotient_gap (class in sage.groups.abelian_gps.abelian_group_gap) AbelianGroupSubgroup_gap (class in sage.groups.abelian_gps.abelian_group_gap) AbelianGroupWithValues() (in module sage.groups.abelian_gps.values) AbelianGroupWithValues_class (class in sage.groups.abelian_gps.values) AbelianGroupWithValuesElement (class in sage.groups.abelian_gps.values) AbelianGroupWithValuesEmbedding (class in sage.groups.abelian_gps.values) abelianization_map() (sage.groups.finitely_presented.FinitelyPresentedGroup method) abelianization_to_algebra() (sage.groups.finitely_presented.FinitelyPresentedGroup method) absolute_length() (sage.groups.perm_gps.permgroup_element.SymmetricGroupElement method) AbstractArgument (class in sage.groups.misc_gps.argument_groups) AbstractArgumentGroup (class in sage.groups.misc_gps.argument_groups) act_to_right() (sage.groups.group_semidirect_product.GroupSemidirectProduct method) action_on_root_indices() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup.Element method) adams_operation() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) AdditiveAbelianGroup() (in module sage.groups.additive_abelian.additive_abelian_group) AdditiveAbelianGroup_class (class in sage.groups.additive_abelian.additive_abelian_group) AdditiveAbelianGroup_fixed_gens (class in sage.groups.additive_abelian.additive_abelian_group) AdditiveAbelianGroupElement (class in sage.groups.additive_abelian.additive_abelian_group) AdditiveAbelianGroupWrapper (class in sage.groups.additive_abelian.additive_abelian_wrapper) AdditiveAbelianGroupWrapperElement (class in sage.groups.additive_abelian.additive_abelian_wrapper) adjoint() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) AffineGroup (class in sage.groups.affine_gps.affine_group) AffineGroupElement (class in sage.groups.affine_gps.group_element) alexander_matrix() (sage.groups.finitely_presented.FinitelyPresentedGroup method) alexander_polynomial() (sage.groups.braid.Braid method) algebra() (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) algebra_generators() (sage.groups.raag.CohomologyRAAG method) AlgebraicGroup (class in sage.groups.group) all_labeled_graphs() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) all_subgroups() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) AlternatingGroup (class in sage.groups.perm_gps.permgroup_named) AlternatingPresentation() (in module sage.groups.finitely_presented_named) ambient() (sage.groups.kernel_subgroup.KernelSubgroup method) (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.matrix_gps.matrix_group.MatrixGroup_base method) ambient_group() (sage.groups.abelian_gps.abelian_group.AbelianGroup_subgroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_subgroup method) an_element() (sage.groups.artin.ArtinGroup method) (sage.groups.braid.BraidGroup_class method) (sage.groups.conjugacy_classes.ConjugacyClass method) (sage.groups.group_exp.GroupExp_Class method) annular_khovanov_complex() (sage.groups.braid.Braid method) annular_khovanov_homology() (sage.groups.braid.Braid method) are_conjugate() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) ArgumentByElement (class in sage.groups.misc_gps.argument_groups) ArgumentByElementGroup (class in sage.groups.misc_gps.argument_groups) ArgumentGroup (in module sage.groups.misc_gps.argument_groups) ArgumentGroupFactory (class in sage.groups.misc_gps.argument_groups) ArtinGroup (class in sage.groups.artin) ArtinGroupElement (class in sage.groups.artin) as_AbelianGroup() (sage.groups.perm_gps.permgroup_named.CyclicPermutationGroup method) as_classical_group() (sage.groups.cubic_braid.CubicBraidGroup method) as_finitely_presented_group() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) as_matrix_group() (sage.groups.cubic_braid.CubicBraidGroup method) (sage.groups.matrix_gps.matrix_group.MatrixGroup_base method) as_permutation() (sage.groups.abelian_gps.abelian_group_element.AbelianGroupElement method) as_permutation_group() (sage.groups.artin.ArtinGroup method) (sage.groups.braid.BraidGroup_class method) (sage.groups.cubic_braid.CubicBraidGroup method) (sage.groups.finitely_presented.FinitelyPresentedGroup method) (sage.groups.matrix_gps.finitely_generated_gap.FinitelyGeneratedMatrixGroup_gap method) as_reflection_group() (sage.groups.cubic_braid.CubicBraidGroup method) AssionGroupS() (in module sage.groups.cubic_braid) AssionGroupU() (in module sage.groups.cubic_braid) AssionS (sage.groups.cubic_braid.CubicBraidGroup.type attribute) AssionU (sage.groups.cubic_braid.CubicBraidGroup.type attribute) aut() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) automorphism_group() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) (sage.groups.perm_gps.partn_ref.refinement_matrices.MatrixStruct method) B b() (sage.groups.affine_gps.group_element.AffineGroupElement method) B() (sage.groups.perm_gps.cubegroup.CubeGroup method) base() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) base_ring() (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) (sage.groups.perm_gps.permgroup_named.PermutationGroup_plg method) (sage.groups.perm_gps.permgroup_named.SuzukiGroup method) (sage.groups.semimonomial_transformations.semimonomial_transformation_group.SemimonomialTransformationGroup method) basis_from_generators() (in module sage.groups.additive_abelian.additive_abelian_wrapper) bilinear_form() (sage.groups.cactus_group.CactusGroup method) (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) BinaryDihedralGroup (class in sage.groups.matrix_gps.binary_dihedral) BinaryDihedralPresentation() (in module sage.groups.finitely_presented_named) blocks_all() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) Braid (class in sage.groups.braid) braid() (sage.groups.cubic_braid.CubicBraidElement method) braid_group() (sage.groups.cubic_braid.CubicBraidGroup method) BraidGroup() (in module sage.groups.braid) BraidGroup_class (class in sage.groups.braid) bsgs() (in module sage.groups.generic) burau_matrix() (sage.groups.artin.ArtinGroupElement method) (sage.groups.braid.Braid method) (sage.groups.cubic_braid.CubicBraidElement method) C CactusGroup (class in sage.groups.cactus_group) CactusGroup.Element (class in sage.groups.cactus_group) CactusPresentation() (in module sage.groups.finitely_presented_named) canonical_matrix() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup.Element method) canonical_relabeling() (sage.groups.perm_gps.partn_ref.refinement_matrices.MatrixStruct method) canonical_representation() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) cardinality() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.affine_gps.affine_group.AffineGroup method) (sage.groups.artin.ArtinGroup method) (sage.groups.braid.BraidGroup_class method) (sage.groups.conjugacy_classes.ConjugacyClassGAP method) (sage.groups.cubic_braid.CubicBraidGroup method) (sage.groups.finitely_presented.FinitelyPresentedGroup method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.matrix_gps.binary_dihedral.BinaryDihedralGroup method) (sage.groups.matrix_gps.heisenberg.HeisenbergGroup method) (sage.groups.matrix_gps.linear.LinearMatrixGroup_generic method) (sage.groups.pari_group.PariGroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.PrimitiveGroupsOfDegree method) (sage.groups.perm_gps.permgroup_named.TransitiveGroupsOfDegree method) cartan_type() (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) center() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.matrix_gps.heisenberg.HeisenbergGroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) central_character() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) centralizer() (sage.groups.braid.Braid method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) centralizing_element() (sage.groups.cubic_braid.CubicBraidGroup method) character() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) character_table() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) characteristic_varieties() (sage.groups.finitely_presented.FinitelyPresentedGroup method) chart_exp1() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) chart_exp2() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) class_function() (sage.groups.libgap_mixin.GroupMixinLibGAP method) ClassFunction() (in module sage.groups.class_function) ClassFunction_gap (class in sage.groups.class_function) ClassFunction_libgap (class in sage.groups.class_function) classical_invariant_form() (sage.groups.cubic_braid.CubicBraidGroup method) coarsest_equitable_refinement() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) codegrees() (sage.groups.cubic_braid.CubicBraidGroup method) (sage.groups.perm_gps.permgroup_named.ComplexReflectionGroup method) cohomology() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.raag.RightAngledArtinGroup method) cohomology_part() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) CohomologyRAAG (class in sage.groups.raag) CohomologyRAAG.Element (class in sage.groups.raag) color_of_square() (in module sage.groups.perm_gps.cubegroup) colored_jones_polynomial() (sage.groups.braid.Braid method) commutator() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) ComplexReflectionGroup (class in sage.groups.perm_gps.permgroup_named) components_in_closure() (sage.groups.braid.Braid method) composition_series() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) conjugacy_class() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) conjugacy_class_iterator() (in module sage.groups.perm_gps.symgp_conjugacy_class) conjugacy_classes() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) conjugacy_classes_iterator() (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) conjugacy_classes_representatives() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) conjugacy_classes_subgroups() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) ConjugacyClass (class in sage.groups.conjugacy_classes) ConjugacyClassGAP (class in sage.groups.conjugacy_classes) conjugate() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) conjugating_braid() (sage.groups.braid.Braid method) conjugation() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) construction() (sage.groups.group_semidirect_product.GroupSemidirectProduct method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) cosets() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) cover() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupQuotient_gap method) cover_and_relations_from_invariants() (in module sage.groups.additive_abelian.additive_abelian_group) covering_matrix_ring() (sage.groups.abelian_gps.abelian_aut.AbelianGroupAutomorphismGroup_gap method) Coxeter (sage.groups.cubic_braid.CubicBraidGroup.type attribute) coxeter_group() (sage.groups.artin.ArtinGroup method) coxeter_group_element() (sage.groups.artin.ArtinGroupElement method) coxeter_matrix() (sage.groups.artin.ArtinGroup method) (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) coxeter_type() (sage.groups.artin.ArtinGroup method) CoxeterMatrixGroup (class in sage.groups.matrix_gps.coxeter_group) CoxeterMatrixGroup.Element (class in sage.groups.matrix_gps.coxeter_group) create_key_and_extra_args() (sage.groups.misc_gps.argument_groups.ArgumentGroupFactory method) create_object() (sage.groups.misc_gps.argument_groups.ArgumentGroupFactory method) create_poly() (in module sage.groups.perm_gps.cubegroup) CubeGroup (class in sage.groups.perm_gps.cubegroup) cubic_braid_subgroup() (sage.groups.cubic_braid.CubicBraidGroup method) CubicBraidElement (class in sage.groups.cubic_braid) CubicBraidGroup (class in sage.groups.cubic_braid) CubicBraidGroup.type (class in sage.groups.cubic_braid) cubie() (sage.groups.perm_gps.cubegroup.RubiksCube method) cubie_centers() (in module sage.groups.perm_gps.cubegroup) cubie_colors() (in module sage.groups.perm_gps.cubegroup) cubie_faces() (in module sage.groups.perm_gps.cubegroup) cycle_string() (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) cycle_tuples() (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) cycle_type() (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) cycles() (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) cyclic_slidings() (sage.groups.braid.Braid method) CyclicPermutationGroup (class in sage.groups.perm_gps.permgroup_named) CyclicPresentation() (in module sage.groups.finitely_presented_named) D D() (sage.groups.perm_gps.cubegroup.CubeGroup method) decompose() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) default_representative() (in module sage.groups.perm_gps.symgp_conjugacy_class) defining_morphism() (sage.groups.kernel_subgroup.KernelSubgroup method) deformed_burau_matrix() (sage.groups.braid.Braid method) degree() (sage.groups.affine_gps.affine_group.AffineGroup method) (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) (sage.groups.matrix_gps.matrix_group.MatrixGroup_generic method) (sage.groups.pari_group.PariGroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.TransitiveGroup method) (sage.groups.semimonomial_transformations.semimonomial_transformation_group.SemimonomialTransformationGroup method) degree_on_basis() (sage.groups.raag.CohomologyRAAG method) degrees() (sage.groups.cubic_braid.CubicBraidGroup method) (sage.groups.perm_gps.permgroup_named.ComplexReflectionGroup method) delta() (sage.groups.artin.FiniteTypeArtinGroup method) derived_series() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) descents() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup.Element method) determinant_character() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) dict() (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) DiCyclicGroup (class in sage.groups.perm_gps.permgroup_named) DiCyclicPresentation() (in module sage.groups.finitely_presented_named) DihedralGroup (class in sage.groups.perm_gps.permgroup_named) DihedralPresentation() (in module sage.groups.finitely_presented_named) dimension_of_TL_space() (sage.groups.braid.BraidGroup_class method) direct_product() (sage.groups.finitely_presented.FinitelyPresentedGroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) direct_product_permgroups() (in module sage.groups.perm_gps.permgroup) discrete_exp() (sage.groups.additive_abelian.additive_abelian_wrapper.AdditiveAbelianGroupWrapper method) discrete_log() (in module sage.groups.generic) (sage.groups.additive_abelian.additive_abelian_wrapper.AdditiveAbelianGroupWrapper method) discrete_log_generic() (in module sage.groups.generic) discrete_log_lambda() (in module sage.groups.generic) discrete_log_rho() (in module sage.groups.generic) disjoint_direct_product_decomposition() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) display() (sage.groups.perm_gps.partn_ref.refinement_matrices.MatrixStruct method) display2d() (sage.groups.perm_gps.cubegroup.CubeGroup method) domain() (sage.groups.abelian_gps.abelian_aut.AbelianGroupAutomorphismGroup_gap method) (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) dual_group() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) DualAbelianGroup_class (class in sage.groups.abelian_gps.dual_abelian_group) DualAbelianGroupElement (class in sage.groups.abelian_gps.dual_abelian_group_element) E Element (sage.groups.abelian_gps.abelian_aut.AbelianGroupAutomorphismGroup attribute) (sage.groups.abelian_gps.abelian_aut.AbelianGroupAutomorphismGroup_gap attribute) (sage.groups.abelian_gps.abelian_aut.AbelianGroupAutomorphismGroup_subgroup attribute) (sage.groups.abelian_gps.abelian_group.AbelianGroup_class attribute) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap attribute) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class attribute) (sage.groups.abelian_gps.values.AbelianGroupWithValues_class attribute) (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_class attribute) (sage.groups.additive_abelian.additive_abelian_wrapper.AdditiveAbelianGroupWrapper attribute) (sage.groups.affine_gps.affine_group.AffineGroup attribute) (sage.groups.artin.ArtinGroup attribute) (sage.groups.artin.FiniteTypeArtinGroup attribute) (sage.groups.braid.BraidGroup_class attribute) (sage.groups.cubic_braid.CubicBraidGroup attribute) (sage.groups.finitely_presented.FinitelyPresentedGroup attribute) (sage.groups.free_group.FreeGroup_class attribute) (sage.groups.group_exp.GroupExp_Class attribute) (sage.groups.group_semidirect_product.GroupSemidirectProduct attribute) (sage.groups.libgap_group.GroupLibGAP attribute) (sage.groups.libgap_morphism.GroupHomset_libgap attribute) (sage.groups.matrix_gps.matrix_group.MatrixGroup_generic attribute) (sage.groups.matrix_gps.matrix_group_gap.MatrixGroup_gap attribute) (sage.groups.misc_gps.argument_groups.AbstractArgumentGroup attribute) (sage.groups.misc_gps.argument_groups.ArgumentByElementGroup attribute) (sage.groups.misc_gps.argument_groups.RootsOfUnityGroup attribute) (sage.groups.misc_gps.argument_groups.SignGroup attribute) (sage.groups.misc_gps.argument_groups.UnitCircleGroup attribute) (sage.groups.misc_gps.imaginary_groups.ImaginaryGroup attribute) (sage.groups.perm_gps.permgroup.PermutationGroup_generic attribute) (sage.groups.perm_gps.permgroup_named.SymmetricGroup attribute) (sage.groups.semimonomial_transformations.semimonomial_transformation_group.SemimonomialTransformationGroup attribute) element() (sage.groups.additive_abelian.additive_abelian_wrapper.AdditiveAbelianGroupWrapperElement method) elementary_divisors() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) ElementLibGAP (class in sage.groups.libgap_wrapper) epimorphisms() (sage.groups.braid.BraidGroup_class method) (sage.groups.finitely_presented.FinitelyPresentedGroup method) eps() (sage.groups.braid.RightQuantumWord method) equals() (sage.groups.abelian_gps.abelian_group.AbelianGroup_subgroup method) EuclideanGroup (class in sage.groups.affine_gps.euclidean_group) exp() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) exponent (sage.groups.misc_gps.argument_groups.UnitCirclePoint property) exponent() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_class method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) exponent_denominator() (sage.groups.misc_gps.argument_groups.RootOfUnity method) exponent_numerator() (sage.groups.misc_gps.argument_groups.RootOfUnity method) exponent_sum() (sage.groups.artin.ArtinGroupElement method) exponents() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupElement_gap method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupElement_polycyclic method) (sage.groups.abelian_gps.element_base.AbelianGroupElementBase method) exterior_power() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) F F() (sage.groups.perm_gps.cubegroup.CubeGroup method) faces() (sage.groups.perm_gps.cubegroup.CubeGroup method) facets() (sage.groups.perm_gps.cubegroup.CubeGroup method) (sage.groups.perm_gps.cubegroup.RubiksCube method) field_of_definition() (sage.groups.perm_gps.permgroup_named.PermutationGroup_pug method) finite_field_sqrt() (in module sage.groups.matrix_gps.unitary) FiniteGroup (class in sage.groups.group) finitely_presented_group() (sage.groups.finitely_presented.RewritingSystem method) FinitelyGeneratedAbelianPresentation() (in module sage.groups.finitely_presented_named) FinitelyGeneratedHeisenbergPresentation() (in module sage.groups.finitely_presented_named) FinitelyGeneratedMatrixGroup_gap (class in sage.groups.matrix_gps.finitely_generated_gap) FinitelyGeneratedMatrixGroup_generic (class in sage.groups.matrix_gps.finitely_generated) FinitelyPresentedGroup (class in sage.groups.finitely_presented) FinitelyPresentedGroupElement (class in sage.groups.finitely_presented) FiniteTypeArtinGroup (class in sage.groups.artin) FiniteTypeArtinGroupElement (class in sage.groups.artin) first_descent() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup.Element method) fitting_subgroup() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) fixed_points() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) fox_derivative() (sage.groups.free_group.FreeGroupElement method) frattini_subgroup() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) free_group() (sage.groups.finitely_presented.FinitelyPresentedGroup method) (sage.groups.finitely_presented.RewritingSystem method) FreeGroup() (in module sage.groups.free_group) FreeGroup_class (class in sage.groups.free_group) FreeGroupElement (class in sage.groups.free_group) from_gap_list() (in module sage.groups.perm_gps.permgroup) from_generators() (sage.groups.additive_abelian.additive_abelian_wrapper.AdditiveAbelianGroupWrapper static method) fundamental_weight() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) fundamental_weights() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) G gap() (sage.groups.class_function.ClassFunction_libgap method) (sage.groups.finitely_presented.RewritingSystem method) (sage.groups.libgap_morphism.GroupMorphism_libgap method) (sage.groups.libgap_wrapper.ElementLibGAP method) (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) gap_small_group() (sage.groups.perm_gps.permgroup_named.SmallPermutationGroup method) gcd() (sage.groups.braid.Braid method) gen() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group.AbelianGroup_subgroup method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) (sage.groups.abelian_gps.values.AbelianGroupWithValues_class method) (sage.groups.cactus_group.CactusGroup method) (sage.groups.cactus_group.PureCactusGroup method) (sage.groups.indexed_free_group.IndexedFreeAbelianGroup method) (sage.groups.indexed_free_group.IndexedFreeGroup method) (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.matrix_gps.finitely_generated.FinitelyGeneratedMatrixGroup_generic method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.raag.CohomologyRAAG method) (sage.groups.raag.RightAngledArtinGroup method) gen_names() (sage.groups.perm_gps.cubegroup.CubeGroup method) GeneralDihedralGroup (class in sage.groups.perm_gps.permgroup_named) generate_dense_graphs_edge_addition() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) generate_dense_graphs_vert_addition() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) generator_orders() (sage.groups.additive_abelian.additive_abelian_wrapper.AdditiveAbelianGroupWrapper method) generators() (sage.groups.libgap_wrapper.ParentLibGAP method) gens() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group.AbelianGroup_subgroup method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_fixed_gens method) (sage.groups.cactus_group.CactusGroup method) (sage.groups.cactus_group.PureCactusGroup method) (sage.groups.indexed_free_group.IndexedGroup method) (sage.groups.kernel_subgroup.KernelSubgroup method) (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) (sage.groups.matrix_gps.finitely_generated.FinitelyGeneratedMatrixGroup_generic method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.raag.CohomologyRAAG method) (sage.groups.raag.RightAngledArtinGroup method) (sage.groups.semimonomial_transformations.semimonomial_transformation_group.SemimonomialTransformationGroup method) gens_orders() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) gens_small() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) gens_values() (sage.groups.abelian_gps.values.AbelianGroupWithValues_class method) geometric_representation_generators() (sage.groups.cactus_group.CactusGroup method) get_autom() (sage.groups.semimonomial_transformations.semimonomial_transformation.SemimonomialTransformation method) get_orbits() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) get_perm() (sage.groups.semimonomial_transformations.semimonomial_transformation.SemimonomialTransformation method) get_v() (sage.groups.semimonomial_transformations.semimonomial_transformation.SemimonomialTransformation method) get_v_inverse() (sage.groups.semimonomial_transformations.semimonomial_transformation.SemimonomialTransformation method) GL() (in module sage.groups.matrix_gps.linear) GO() (in module sage.groups.matrix_gps.orthogonal) graph() (sage.groups.raag.RightAngledArtinGroup method) GraphStruct (class in sage.groups.perm_gps.partn_ref.refinement_graphs) Group (class in sage.groups.group) group() (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) group_generators() (sage.groups.cactus_group.CactusGroup method) (sage.groups.group_exp.GroupExp_Class method) (sage.groups.group_semidirect_product.GroupSemidirectProduct method) (sage.groups.indexed_free_group.IndexedGroup method) group_id() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) group_primitive_id() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.PrimitiveGroup method) GroupActionOnQuotientModule (class in sage.groups.matrix_gps.isometries) GroupActionOnSubmodule (class in sage.groups.matrix_gps.isometries) GroupExp (class in sage.groups.group_exp) GroupExp_Class (class in sage.groups.group_exp) GroupExpElement (class in sage.groups.group_exp) GroupHomset_libgap (class in sage.groups.libgap_morphism) GroupLibGAP (class in sage.groups.libgap_group) GroupMixinLibGAP (class in sage.groups.libgap_mixin) GroupMorphism_libgap (class in sage.groups.libgap_morphism) GroupMorphismWithGensImages (class in sage.groups.finitely_presented) GroupOfIsometries (class in sage.groups.matrix_gps.isometries) GroupSemidirectProduct (class in sage.groups.group_semidirect_product) GroupSemidirectProductElement (class in sage.groups.group_semidirect_product) GU() (in module sage.groups.matrix_gps.unitary) H hap_decorator() (in module sage.groups.perm_gps.permgroup) has_descent() (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) has_left_descent() (sage.groups.perm_gps.permgroup_element.SymmetricGroupElement method) has_order() (in module sage.groups.generic) has_regular_subgroup() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) has_right_descent() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup.Element method) HeisenbergGroup (class in sage.groups.matrix_gps.heisenberg) holomorph() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) homology() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) homology_part() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) I id() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) identity() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_fixed_gens method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) imag() (sage.groups.misc_gps.imaginary_groups.ImaginaryElement method) image() (sage.groups.abelian_gps.abelian_group_morphism.AbelianGroupMorphism method) (sage.groups.libgap_morphism.GroupMorphism_libgap method) (sage.groups.perm_gps.permgroup_morphism.PermutationGroupMorphism method) ImaginaryElement (class in sage.groups.misc_gps.imaginary_groups) ImaginaryGroup (class in sage.groups.misc_gps.imaginary_groups) index2singmaster() (in module sage.groups.perm_gps.cubegroup) index_set() (sage.groups.artin.ArtinGroup method) (sage.groups.cubic_braid.CubicBraidGroup method) (sage.groups.perm_gps.permgroup_named.ComplexReflectionGroup method) (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) IndexedFreeAbelianGroup (class in sage.groups.indexed_free_group) IndexedFreeAbelianGroup.Element (class in sage.groups.indexed_free_group) IndexedFreeGroup (class in sage.groups.indexed_free_group) IndexedFreeGroup.Element (class in sage.groups.indexed_free_group) IndexedGroup (class in sage.groups.indexed_free_group) induct() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) intersection() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) inv_list() (in module sage.groups.perm_gps.cubegroup) invariant_bilinear_form() (sage.groups.matrix_gps.isometries.GroupOfIsometries method) (sage.groups.matrix_gps.orthogonal.OrthogonalMatrixGroup_generic method) (sage.groups.matrix_gps.orthogonal_gap.OrthogonalMatrixGroup_gap method) invariant_form() (sage.groups.matrix_gps.orthogonal.OrthogonalMatrixGroup_generic method) (sage.groups.matrix_gps.orthogonal_gap.OrthogonalMatrixGroup_gap method) (sage.groups.matrix_gps.symplectic.SymplecticMatrixGroup_generic method) (sage.groups.matrix_gps.symplectic_gap.SymplecticMatrixGroup_gap method) (sage.groups.matrix_gps.unitary.UnitaryMatrixGroup_generic method) (sage.groups.matrix_gps.unitary_gap.UnitaryMatrixGroup_gap method) invariant_generators() (sage.groups.matrix_gps.finitely_generated_gap.FinitelyGeneratedMatrixGroup_gap method) invariant_quadratic_form() (sage.groups.matrix_gps.orthogonal.OrthogonalMatrixGroup_generic method) (sage.groups.matrix_gps.orthogonal_gap.OrthogonalMatrixGroup_gap method) invariants() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) invariants_of_degree() (sage.groups.matrix_gps.finitely_generated_gap.FinitelyGeneratedMatrixGroup_gap method) inverse() (sage.groups.libgap_wrapper.ElementLibGAP method) (sage.groups.matrix_gps.group_element.MatrixGroupElement_generic method) (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) invert_v() (sage.groups.semimonomial_transformations.semimonomial_transformation.SemimonomialTransformation method) irreducible_characters() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) irreducible_constituents() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) is_abelian() (sage.groups.group.AbelianGroup method) (sage.groups.group.Group method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.CyclicPermutationGroup method) (sage.groups.perm_gps.permgroup_named.DiCyclicGroup method) is_AbelianGroup() (in module sage.groups.abelian_gps.abelian_group) is_AbelianGroupElement() (in module sage.groups.abelian_gps.abelian_group_element) is_AbelianGroupMorphism() (in module sage.groups.abelian_gps.abelian_group_morphism) is_commutative() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) (sage.groups.group.Group method) (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.CyclicPermutationGroup method) (sage.groups.perm_gps.permgroup_named.DiCyclicGroup method) is_confluent() (sage.groups.finitely_presented.RewritingSystem method) is_conjugate() (sage.groups.libgap_wrapper.ElementLibGAP method) is_conjugated() (sage.groups.braid.Braid method) is_cyclic() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_class method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_DualAbelianGroup() (in module sage.groups.abelian_gps.dual_abelian_group) is_DualAbelianGroupElement() (in module sage.groups.abelian_gps.dual_abelian_group_element) is_elementary_abelian() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_finite() (sage.groups.cubic_braid.CubicBraidGroup method) (sage.groups.group.FiniteGroup method) (sage.groups.group.Group method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) is_FreeGroup() (in module sage.groups.free_group) is_Group() (in module sage.groups.group) is_irreducible() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) is_isomorphic() (in module sage.groups.perm_gps.partn_ref.refinement_lists) (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.partn_ref.refinement_matrices.MatrixStruct method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_MatrixGroup() (in module sage.groups.matrix_gps.matrix_group) is_MatrixGroupElement() (in module sage.groups.matrix_gps.group_element) is_minus_one() (sage.groups.misc_gps.argument_groups.Sign method) (sage.groups.misc_gps.argument_groups.UnitCirclePoint method) is_monomial() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_multiplicative() (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_class method) (sage.groups.group.Group method) is_nilpotent() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_normal() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup.PermutationGroup_subgroup method) is_one() (sage.groups.libgap_wrapper.ElementLibGAP method) (sage.groups.matrix_gps.group_element.MatrixGroupElement_generic method) (sage.groups.misc_gps.argument_groups.Sign method) (sage.groups.misc_gps.argument_groups.UnitCirclePoint method) is_p_group() (sage.groups.libgap_mixin.GroupMixinLibGAP method) is_perfect() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_periodic() (sage.groups.braid.Braid method) is_PermutationGroupElement() (in module sage.groups.perm_gps.permgroup_element) is_PermutationGroupMorphism() (in module sage.groups.perm_gps.permgroup_morphism) is_pgroup() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_polycyclic() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_primitive() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_pseudoanosov() (sage.groups.braid.Braid method) is_rational() (sage.groups.conjugacy_classes.ConjugacyClass method) is_real() (sage.groups.conjugacy_classes.ConjugacyClass method) is_reducible() (sage.groups.braid.Braid method) is_regular() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_semi_regular() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_simple() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_solvable() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_subgroup() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_subgroup_of() (sage.groups.abelian_gps.abelian_aut.AbelianGroupAutomorphismGroup_gap method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) is_supersolvable() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_transitive() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) is_trivial() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) (sage.groups.abelian_gps.element_base.AbelianGroupElementBase method) (sage.groups.group.Group method) (sage.groups.matrix_gps.matrix_group.MatrixGroup_generic method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) isomorphic() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) isomorphism_to() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) isomorphism_type_info_simple_group() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) iteration() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) J JankoGroup (class in sage.groups.perm_gps.permgroup_named) jones_polynomial() (sage.groups.braid.Braid method) K kernel() (sage.groups.abelian_gps.abelian_group_morphism.AbelianGroupMorphism method) (sage.groups.libgap_morphism.GroupMorphism_libgap method) (sage.groups.perm_gps.permgroup_morphism.PermutationGroupMorphism method) KernelSubgroup (class in sage.groups.kernel_subgroup) KernelSubgroup.Element (class in sage.groups.kernel_subgroup) KleinFourGroup (class in sage.groups.perm_gps.permgroup_named) KleinFourPresentation() (in module sage.groups.finitely_presented_named) L L() (sage.groups.perm_gps.cubegroup.CubeGroup method) label() (sage.groups.pari_group.PariGroup method) largest_moved_point() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) lcm() (sage.groups.braid.Braid method) left_invariant_extension() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) left_invariant_frame() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) left_normal_form() (sage.groups.artin.FiniteTypeArtinGroupElement method) (sage.groups.braid.Braid method) left_translation() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) legal() (sage.groups.perm_gps.cubegroup.CubeGroup method) length() (sage.groups.indexed_free_group.IndexedFreeGroup.Element method) lie_algebra() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) lift() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupQuotient_gap method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupSubgroup_gap method) (sage.groups.kernel_subgroup.KernelSubgroup method) (sage.groups.libgap_morphism.GroupMorphism_libgap method) linear() (sage.groups.affine_gps.affine_group.AffineGroup method) linear_relation() (in module sage.groups.generic) linear_space() (sage.groups.affine_gps.affine_group.AffineGroup method) LinearMatrixGroup_gap (class in sage.groups.matrix_gps.linear_gap) LinearMatrixGroup_generic (class in sage.groups.matrix_gps.linear) links_gould_matrix() (sage.groups.braid.Braid method) links_gould_polynomial() (sage.groups.braid.Braid method) list() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) (sage.groups.abelian_gps.element_base.AbelianGroupElementBase method) (sage.groups.affine_gps.group_element.AffineGroupElement method) (sage.groups.conjugacy_classes.ConjugacyClass method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.matrix_gps.group_element.MatrixGroupElement_generic method) (sage.groups.matrix_gps.group_element_gap.MatrixGroupElement_gap method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) livf() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) LKB_matrix() (sage.groups.braid.Braid method) load_hap() (in module sage.groups.perm_gps.permgroup) log() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) lower_central_series() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) M major_index() (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) make_confluent() (sage.groups.finitely_presented.RewritingSystem method) make_permgroup_element() (in module sage.groups.perm_gps.permgroup_element) make_permgroup_element_v2() (in module sage.groups.perm_gps.permgroup_element) mapping_class_action() (sage.groups.braid.BraidGroup_class method) MappingClassGroupAction (class in sage.groups.braid) markov_trace() (sage.groups.braid.Braid method) MathieuGroup (class in sage.groups.perm_gps.permgroup_named) matrix() (sage.groups.abelian_gps.abelian_aut.AbelianGroupAutomorphism method) (sage.groups.affine_gps.group_element.AffineGroupElement method) (sage.groups.matrix_gps.group_element.MatrixGroupElement_generic method) (sage.groups.matrix_gps.group_element_gap.MatrixGroupElement_gap method) (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) matrix_degree() (sage.groups.perm_gps.permgroup_named.PermutationGroup_plg method) matrix_space() (sage.groups.affine_gps.affine_group.AffineGroup method) (sage.groups.matrix_gps.matrix_group.MatrixGroup_generic method) MatrixGroup() (in module sage.groups.matrix_gps.finitely_generated) MatrixGroup_base (class in sage.groups.matrix_gps.matrix_group) MatrixGroup_gap (class in sage.groups.matrix_gps.matrix_group_gap) MatrixGroup_generic (class in sage.groups.matrix_gps.matrix_group) MatrixGroupElement_gap (class in sage.groups.matrix_gps.group_element_gap) MatrixGroupElement_generic (class in sage.groups.matrix_gps.group_element) MatrixStruct (class in sage.groups.perm_gps.partn_ref.refinement_matrices) maximal_normal_subgroups() (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) merge_points() (in module sage.groups.generic) minimal_generating_set() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) minimal_normal_subgroups() (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) mirror_image() (sage.groups.braid.Braid method) mirror_involution() (sage.groups.braid.BraidGroup_class method) module sage.groups.abelian_gps.abelian_aut sage.groups.abelian_gps.abelian_group sage.groups.abelian_gps.abelian_group_element sage.groups.abelian_gps.abelian_group_gap sage.groups.abelian_gps.abelian_group_morphism sage.groups.abelian_gps.dual_abelian_group sage.groups.abelian_gps.dual_abelian_group_element sage.groups.abelian_gps.element_base sage.groups.abelian_gps.values sage.groups.additive_abelian.additive_abelian_group sage.groups.additive_abelian.additive_abelian_wrapper sage.groups.affine_gps.affine_group sage.groups.affine_gps.euclidean_group sage.groups.affine_gps.group_element sage.groups.artin sage.groups.braid sage.groups.cactus_group sage.groups.class_function sage.groups.conjugacy_classes sage.groups.cubic_braid sage.groups.finitely_presented sage.groups.finitely_presented_named sage.groups.free_group sage.groups.generic sage.groups.group sage.groups.group_exp sage.groups.group_semidirect_product sage.groups.groups_catalog sage.groups.indexed_free_group sage.groups.kernel_subgroup sage.groups.libgap_group sage.groups.libgap_mixin sage.groups.libgap_morphism sage.groups.libgap_wrapper sage.groups.lie_gps.nilpotent_lie_group sage.groups.matrix_gps.binary_dihedral sage.groups.matrix_gps.catalog sage.groups.matrix_gps.coxeter_group sage.groups.matrix_gps.finitely_generated sage.groups.matrix_gps.finitely_generated_gap sage.groups.matrix_gps.group_element sage.groups.matrix_gps.group_element_gap sage.groups.matrix_gps.heisenberg sage.groups.matrix_gps.isometries sage.groups.matrix_gps.linear sage.groups.matrix_gps.linear_gap sage.groups.matrix_gps.matrix_group sage.groups.matrix_gps.matrix_group_gap sage.groups.matrix_gps.named_group sage.groups.matrix_gps.named_group_gap sage.groups.matrix_gps.orthogonal sage.groups.matrix_gps.orthogonal_gap sage.groups.matrix_gps.symplectic sage.groups.matrix_gps.symplectic_gap sage.groups.matrix_gps.unitary sage.groups.matrix_gps.unitary_gap sage.groups.misc_gps.argument_groups sage.groups.misc_gps.imaginary_groups sage.groups.misc_gps.misc_groups sage.groups.pari_group sage.groups.perm_gps.constructor sage.groups.perm_gps.cubegroup sage.groups.perm_gps.partn_ref.canonical_augmentation sage.groups.perm_gps.partn_ref.data_structures sage.groups.perm_gps.partn_ref.refinement_graphs sage.groups.perm_gps.partn_ref.refinement_lists sage.groups.perm_gps.partn_ref.refinement_matrices sage.groups.perm_gps.permgroup sage.groups.perm_gps.permgroup_element sage.groups.perm_gps.permgroup_morphism sage.groups.perm_gps.permgroup_named sage.groups.perm_gps.permutation_groups_catalog sage.groups.perm_gps.symgp_conjugacy_class sage.groups.raag sage.groups.semimonomial_transformations.semimonomial_transformation sage.groups.semimonomial_transformations.semimonomial_transformation_group module_composition_factors() (sage.groups.matrix_gps.finitely_generated_gap.FinitelyGeneratedMatrixGroup_gap method) molien_series() (sage.groups.matrix_gps.finitely_generated_gap.FinitelyGeneratedMatrixGroup_gap method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) move() (sage.groups.perm_gps.cubegroup.CubeGroup method) (sage.groups.perm_gps.cubegroup.RubiksCube method) multiple() (in module sage.groups.generic) multiples (class in sage.groups.generic) multiplicative_order() (sage.groups.abelian_gps.element_base.AbelianGroupElementBase method) (sage.groups.libgap_wrapper.ElementLibGAP method) (sage.groups.matrix_gps.group_element_gap.MatrixGroupElement_gap method) (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) N n() (sage.groups.cactus_group.CactusGroup method) (sage.groups.cactus_group.PureCactusGroup method) NamedMatrixGroup_gap (class in sage.groups.matrix_gps.named_group_gap) NamedMatrixGroup_generic (class in sage.groups.matrix_gps.named_group) natural_homomorphism() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupQuotient_gap method) natural_map() (sage.groups.libgap_morphism.GroupHomset_libgap method) natural_representation() (sage.groups.matrix_gps.matrix_group.MatrixGroup_base method) next() (sage.groups.generic.multiples method) ngens() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.matrix_gps.finitely_generated.FinitelyGeneratedMatrixGroup_generic method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.raag.CohomologyRAAG method) (sage.groups.raag.RightAngledArtinGroup method) NilpotentLieGroup (class in sage.groups.lie_gps.nilpotent_lie_group) NilpotentLieGroup.Element (class in sage.groups.lie_gps.nilpotent_lie_group) non_fixed_points() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) norm() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) normal_subgroups() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) normalize_args_e() (in module sage.groups.matrix_gps.orthogonal) normalize_args_invariant_form() (in module sage.groups.matrix_gps.named_group) normalize_args_vectorspace() (in module sage.groups.matrix_gps.named_group) normalize_square_matrices() (in module sage.groups.matrix_gps.finitely_generated) normalizer() (sage.groups.libgap_wrapper.ElementLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) normalizes() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) nth_roots() (sage.groups.libgap_wrapper.ElementLibGAP method) number_of_subgroups() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) O one() (sage.groups.cactus_group.CactusGroup method) (sage.groups.group_exp.GroupExp_Class method) (sage.groups.group_semidirect_product.GroupSemidirectProduct method) (sage.groups.indexed_free_group.IndexedFreeAbelianGroup method) (sage.groups.indexed_free_group.IndexedFreeGroup method) (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.raag.RightAngledArtinGroup method) one_basis() (sage.groups.raag.CohomologyRAAG method) one_element() (sage.groups.raag.RightAngledArtinGroup method) OP_represent() (in module sage.groups.perm_gps.partn_ref.data_structures) opposite_semidirect_product() (sage.groups.group_semidirect_product.GroupSemidirectProduct method) orbit() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) orbit_partition() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) orbits() (sage.groups.perm_gps.permgroup.PermutationGroup_action method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) order() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupElement_gap method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) (sage.groups.abelian_gps.element_base.AbelianGroupElementBase method) (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_class method) (sage.groups.artin.ArtinGroup method) (sage.groups.braid.BraidGroup_class method) (sage.groups.cubic_braid.CubicBraidGroup method) (sage.groups.finitely_presented.FinitelyPresentedGroup method) (sage.groups.group.Group method) (sage.groups.indexed_free_group.IndexedGroup method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.libgap_wrapper.ElementLibGAP method) (sage.groups.matrix_gps.binary_dihedral.BinaryDihedralGroup method) (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) (sage.groups.matrix_gps.heisenberg.HeisenbergGroup method) (sage.groups.matrix_gps.linear.LinearMatrixGroup_generic method) (sage.groups.pari_group.PariGroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) (sage.groups.perm_gps.permgroup_named.SmallPermutationGroup method) (sage.groups.semimonomial_transformations.semimonomial_transformation_group.SemimonomialTransformationGroup method) order_from_bounds() (in module sage.groups.generic) order_from_multiple() (in module sage.groups.generic) OrthogonalMatrixGroup_gap (class in sage.groups.matrix_gps.orthogonal_gap) OrthogonalMatrixGroup_generic (class in sage.groups.matrix_gps.orthogonal) P ParentLibGAP (class in sage.groups.libgap_wrapper) PariGroup (class in sage.groups.pari_group) parse() (sage.groups.perm_gps.cubegroup.CubeGroup method) partition() (sage.groups.perm_gps.symgp_conjugacy_class.SymmetricGroupConjugacyClassMixin method) permutation() (sage.groups.braid.Braid method) permutation_group() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_fixed_gens method) (sage.groups.pari_group.PariGroup method) PermutationGroup() (in module sage.groups.perm_gps.permgroup) PermutationGroup_action (class in sage.groups.perm_gps.permgroup) PermutationGroup_generic (class in sage.groups.perm_gps.permgroup) PermutationGroup_plg (class in sage.groups.perm_gps.permgroup_named) PermutationGroup_pug (class in sage.groups.perm_gps.permgroup_named) PermutationGroup_subgroup (class in sage.groups.perm_gps.permgroup) PermutationGroup_symalt (class in sage.groups.perm_gps.permgroup_named) PermutationGroup_unique (class in sage.groups.perm_gps.permgroup_named) PermutationGroupElement (class in sage.groups.perm_gps.permgroup_element) PermutationGroupElement() (in module sage.groups.perm_gps.constructor) PermutationGroupMorphism (class in sage.groups.perm_gps.permgroup_morphism) PermutationGroupMorphism_from_gap (class in sage.groups.perm_gps.permgroup_morphism) PermutationGroupMorphism_id (class in sage.groups.perm_gps.permgroup_morphism) PermutationGroupMorphism_im_gens (class in sage.groups.perm_gps.permgroup_morphism) PermutationsConjugacyClass (class in sage.groups.perm_gps.symgp_conjugacy_class) PGL (class in sage.groups.perm_gps.permgroup_named) PGU (class in sage.groups.perm_gps.permgroup_named) plot() (sage.groups.braid.Braid method) (sage.groups.perm_gps.cubegroup.RubiksCube method) plot3d() (sage.groups.braid.Braid method) (sage.groups.perm_gps.cubegroup.RubiksCube method) plot3d_cube() (sage.groups.perm_gps.cubegroup.CubeGroup method) plot3d_cubie() (in module sage.groups.perm_gps.cubegroup) plot_cube() (sage.groups.perm_gps.cubegroup.CubeGroup method) poincare_series() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) polygon_plot3d() (in module sage.groups.perm_gps.cubegroup) positive_roots() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) preimage() (sage.groups.libgap_morphism.GroupMorphism_libgap method) presentation_two_generators() (sage.groups.braid.BraidGroup_class method) PrimitiveGroup (class in sage.groups.perm_gps.permgroup_named) PrimitiveGroups() (in module sage.groups.perm_gps.permgroup_named) PrimitiveGroupsAll (class in sage.groups.perm_gps.permgroup_named) PrimitiveGroupsOfDegree (class in sage.groups.perm_gps.permgroup_named) product() (sage.groups.group_exp.GroupExp_Class method) (sage.groups.group_semidirect_product.GroupSemidirectProduct method) PS_represent() (in module sage.groups.perm_gps.partn_ref.data_structures) PSL (class in sage.groups.perm_gps.permgroup_named) PSp (class in sage.groups.perm_gps.permgroup_named) PSP (in module sage.groups.perm_gps.permgroup_named) PSU (class in sage.groups.perm_gps.permgroup_named) pure_conjugating_braid() (sage.groups.braid.Braid method) PureCactusGroup (class in sage.groups.cactus_group) pushforward() (sage.groups.libgap_morphism.GroupMorphism_libgap method) Q QuaternionGroup (class in sage.groups.perm_gps.permgroup_named) QuaternionMatrixGroupGF3() (in module sage.groups.matrix_gps.finitely_generated) QuaternionPresentation() (in module sage.groups.finitely_presented_named) quotient() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) (sage.groups.free_group.FreeGroup_class method) (sage.groups.group.Group method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) R R() (sage.groups.perm_gps.cubegroup.CubeGroup method) ramification_module_decomposition_hurwitz_curve() (sage.groups.perm_gps.permgroup_named.PSL method) ramification_module_decomposition_modular_curve() (sage.groups.perm_gps.permgroup_named.PSL method) random_element() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.dual_abelian_group.DualAbelianGroup_class method) (sage.groups.affine_gps.affine_group.AffineGroup method) (sage.groups.affine_gps.euclidean_group.EuclideanGroup method) (sage.groups.cactus_group.CactusGroup method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) random_tests() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) (in module sage.groups.perm_gps.partn_ref.refinement_matrices) rank() (sage.groups.free_group.FreeGroup_class method) (sage.groups.indexed_free_group.IndexedGroup method) real() (sage.groups.misc_gps.imaginary_groups.ImaginaryElement method) reduce() (sage.groups.finitely_presented.RewritingSystem method) reduced_word() (sage.groups.braid.RightQuantumWord method) reflection() (sage.groups.affine_gps.affine_group.AffineGroup method) (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) reflection_index_set() (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) reflections() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) relations() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupQuotient_gap method) (sage.groups.finitely_presented.FinitelyPresentedGroup method) repr2d() (sage.groups.perm_gps.cubegroup.CubeGroup method) representative() (sage.groups.conjugacy_classes.ConjugacyClass method) representative_action() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) restrict() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) retract() (sage.groups.abelian_gps.abelian_group_gap.AbelianGroupSubgroup_gap method) (sage.groups.kernel_subgroup.KernelSubgroup method) reverse() (sage.groups.braid.Braid method) rewriting_system() (sage.groups.finitely_presented.FinitelyPresentedGroup method) RewritingSystem (class in sage.groups.finitely_presented) reynolds_operator() (sage.groups.matrix_gps.finitely_generated_gap.FinitelyGeneratedMatrixGroup_gap method) right_angled_coxeter_group() (sage.groups.cactus_group.CactusGroup method) right_invariant_extension() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) right_invariant_frame() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) right_normal_form() (sage.groups.braid.Braid method) right_translation() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) RightAngledArtinGroup (class in sage.groups.raag) RightAngledArtinGroup.Element (class in sage.groups.raag) RightQuantumWord (class in sage.groups.braid) rigidity() (sage.groups.braid.Braid method) rivf() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) RootOfUnity (class in sage.groups.misc_gps.argument_groups) roots() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) RootsOfUnityGroup (class in sage.groups.misc_gps.argument_groups) rotation_list() (in module sage.groups.perm_gps.cubegroup) RubiksCube (class in sage.groups.perm_gps.cubegroup) rules() (sage.groups.finitely_presented.RewritingSystem method) run() (sage.groups.perm_gps.partn_ref.refinement_matrices.MatrixStruct method) S sage.groups.abelian_gps.abelian_aut module sage.groups.abelian_gps.abelian_group module sage.groups.abelian_gps.abelian_group_element module sage.groups.abelian_gps.abelian_group_gap module sage.groups.abelian_gps.abelian_group_morphism module sage.groups.abelian_gps.dual_abelian_group module sage.groups.abelian_gps.dual_abelian_group_element module sage.groups.abelian_gps.element_base module sage.groups.abelian_gps.values module sage.groups.additive_abelian.additive_abelian_group module sage.groups.additive_abelian.additive_abelian_wrapper module sage.groups.affine_gps.affine_group module sage.groups.affine_gps.euclidean_group module sage.groups.affine_gps.group_element module sage.groups.artin module sage.groups.braid module sage.groups.cactus_group module sage.groups.class_function module sage.groups.conjugacy_classes module sage.groups.cubic_braid module sage.groups.finitely_presented module sage.groups.finitely_presented_named module sage.groups.free_group module sage.groups.generic module sage.groups.group module sage.groups.group_exp module sage.groups.group_semidirect_product module sage.groups.groups_catalog module sage.groups.indexed_free_group module sage.groups.kernel_subgroup module sage.groups.libgap_group module sage.groups.libgap_mixin module sage.groups.libgap_morphism module sage.groups.libgap_wrapper module sage.groups.lie_gps.nilpotent_lie_group module sage.groups.matrix_gps.binary_dihedral module sage.groups.matrix_gps.catalog module sage.groups.matrix_gps.coxeter_group module sage.groups.matrix_gps.finitely_generated module sage.groups.matrix_gps.finitely_generated_gap module sage.groups.matrix_gps.group_element module sage.groups.matrix_gps.group_element_gap module sage.groups.matrix_gps.heisenberg module sage.groups.matrix_gps.isometries module sage.groups.matrix_gps.linear module sage.groups.matrix_gps.linear_gap module sage.groups.matrix_gps.matrix_group module sage.groups.matrix_gps.matrix_group_gap module sage.groups.matrix_gps.named_group module sage.groups.matrix_gps.named_group_gap module sage.groups.matrix_gps.orthogonal module sage.groups.matrix_gps.orthogonal_gap module sage.groups.matrix_gps.symplectic module sage.groups.matrix_gps.symplectic_gap module sage.groups.matrix_gps.unitary module sage.groups.matrix_gps.unitary_gap module sage.groups.misc_gps.argument_groups module sage.groups.misc_gps.imaginary_groups module sage.groups.misc_gps.misc_groups module sage.groups.pari_group module sage.groups.perm_gps.constructor module sage.groups.perm_gps.cubegroup module sage.groups.perm_gps.partn_ref.canonical_augmentation module sage.groups.perm_gps.partn_ref.data_structures module sage.groups.perm_gps.partn_ref.refinement_graphs module sage.groups.perm_gps.partn_ref.refinement_lists module sage.groups.perm_gps.partn_ref.refinement_matrices module sage.groups.perm_gps.permgroup module sage.groups.perm_gps.permgroup_element module sage.groups.perm_gps.permgroup_morphism module sage.groups.perm_gps.permgroup_named module sage.groups.perm_gps.permutation_groups_catalog module sage.groups.perm_gps.symgp_conjugacy_class module sage.groups.raag module sage.groups.semimonomial_transformations.semimonomial_transformation module sage.groups.semimonomial_transformations.semimonomial_transformation_group module SC_test_list_perms() (in module sage.groups.perm_gps.partn_ref.data_structures) scalar_product() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) scramble() (sage.groups.perm_gps.cubegroup.RubiksCube method) search_tree() (in module sage.groups.perm_gps.partn_ref.refinement_graphs) section() (sage.groups.libgap_morphism.GroupMorphism_libgap method) SemidihedralGroup (class in sage.groups.perm_gps.permgroup_named) semidirect_product() (sage.groups.finitely_presented.FinitelyPresentedGroup method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) SemimonomialActionMat (class in sage.groups.semimonomial_transformations.semimonomial_transformation_group) SemimonomialActionVec (class in sage.groups.semimonomial_transformations.semimonomial_transformation_group) SemimonomialTransformation (class in sage.groups.semimonomial_transformations.semimonomial_transformation) SemimonomialTransformationGroup (class in sage.groups.semimonomial_transformations.semimonomial_transformation_group) set() (sage.groups.conjugacy_classes.ConjugacyClass method) (sage.groups.conjugacy_classes.ConjugacyClassGAP method) (sage.groups.perm_gps.symgp_conjugacy_class.PermutationsConjugacyClass method) (sage.groups.perm_gps.symgp_conjugacy_class.SymmetricGroupConjugacyClass method) short_name() (sage.groups.additive_abelian.additive_abelian_group.AdditiveAbelianGroup_class method) show() (sage.groups.perm_gps.cubegroup.RubiksCube method) show3d() (sage.groups.perm_gps.cubegroup.RubiksCube method) Sign (class in sage.groups.misc_gps.argument_groups) sign() (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) sign_representation() (sage.groups.matrix_gps.matrix_group.MatrixGroup_base method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) signature() (sage.groups.pari_group.PariGroup method) SignGroup (class in sage.groups.misc_gps.argument_groups) simple_reflection() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) (sage.groups.perm_gps.permgroup_named.ComplexReflectionGroup method) (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) simple_reflections() (sage.groups.cubic_braid.CubicBraidGroup method) simple_root_index() (sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup method) simplification_isomorphism() (sage.groups.finitely_presented.FinitelyPresentedGroup method) simplified() (sage.groups.finitely_presented.FinitelyPresentedGroup method) SL() (in module sage.groups.matrix_gps.linear) sliding_circuits() (sage.groups.braid.Braid method) sliding_circuits_element() (sage.groups.braid.Braid method) smallest_moved_point() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) SmallPermutationGroup (class in sage.groups.perm_gps.permgroup_named) SO() (in module sage.groups.matrix_gps.orthogonal) socle() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) solvable_radical() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) solve() (sage.groups.perm_gps.cubegroup.CubeGroup method) (sage.groups.perm_gps.cubegroup.RubiksCube method) some_elements() (sage.groups.affine_gps.affine_group.AffineGroup method) (sage.groups.artin.ArtinGroup method) (sage.groups.braid.BraidGroup_class method) sorted_presentation() (sage.groups.finitely_presented.FinitelyPresentedGroup method) Sp() (in module sage.groups.matrix_gps.symplectic) SplitMetacyclicGroup (class in sage.groups.perm_gps.permgroup_named) stabilizer() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) standardize_generator() (in module sage.groups.perm_gps.constructor) step() (sage.groups.lie_gps.nilpotent_lie_group.NilpotentLieGroup method) strands() (sage.groups.braid.Braid method) (sage.groups.braid.BraidGroup_class method) (sage.groups.cubic_braid.CubicBraidGroup method) string_to_tuples() (in module sage.groups.perm_gps.constructor) strong_generating_system() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) structure_description() (in module sage.groups.generic) (sage.groups.finitely_presented.FinitelyPresentedGroup method) (sage.groups.matrix_gps.matrix_group_gap.MatrixGroup_gap method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) SU() (in module sage.groups.matrix_gps.unitary) Subgroup (sage.groups.abelian_gps.abelian_group.AbelianGroup_class attribute) (sage.groups.perm_gps.permgroup.PermutationGroup_generic attribute) subgroup() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap method) (sage.groups.libgap_wrapper.ParentLibGAP method) (sage.groups.matrix_gps.matrix_group.MatrixGroup_base method) (sage.groups.matrix_gps.matrix_group_gap.MatrixGroup_gap method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) subgroup_reduced() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) subgroups() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) super_summit_set() (sage.groups.braid.Braid method) super_summit_set_element() (sage.groups.braid.Braid method) SuzukiGroup (class in sage.groups.perm_gps.permgroup_named) SuzukiSporadicGroup (class in sage.groups.perm_gps.permgroup_named) syllables() (sage.groups.free_group.FreeGroupElement method) sylow_subgroup() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) symmetric_power() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) SymmetricGroup (class in sage.groups.perm_gps.permgroup_named) SymmetricGroupConjugacyClass (class in sage.groups.perm_gps.symgp_conjugacy_class) SymmetricGroupConjugacyClassMixin (class in sage.groups.perm_gps.symgp_conjugacy_class) SymmetricGroupElement (class in sage.groups.perm_gps.permgroup_element) SymmetricPresentation() (in module sage.groups.finitely_presented_named) SymplecticMatrixGroup_gap (class in sage.groups.matrix_gps.symplectic_gap) SymplecticMatrixGroup_generic (class in sage.groups.matrix_gps.symplectic) T tensor_product() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) thurston_type() (sage.groups.braid.Braid method) Tietze() (sage.groups.finitely_presented.FinitelyPresentedGroupElement method) (sage.groups.free_group.FreeGroupElement method) TL_basis_with_drain() (sage.groups.braid.BraidGroup_class method) TL_matrix() (sage.groups.braid.Braid method) TL_representation() (sage.groups.braid.BraidGroup_class method) to_matrix() (sage.groups.cactus_group.CactusGroup.Element method) to_opposite() (sage.groups.group_semidirect_product.GroupSemidirectProductElement method) to_permutation() (sage.groups.cactus_group.CactusGroup.Element method) to_word_list() (sage.groups.indexed_free_group.IndexedFreeGroup.Element method) torsion_subgroup() (sage.groups.abelian_gps.abelian_group.AbelianGroup_class method) (sage.groups.additive_abelian.additive_abelian_wrapper.AdditiveAbelianGroupWrapper method) trajectory() (sage.groups.braid.Braid method) transitive_number() (sage.groups.pari_group.PariGroup method) (sage.groups.perm_gps.permgroup_named.TransitiveGroup method) TransitiveGroup (class in sage.groups.perm_gps.permgroup_named) TransitiveGroups() (in module sage.groups.perm_gps.permgroup_named) TransitiveGroupsAll (class in sage.groups.perm_gps.permgroup_named) TransitiveGroupsOfDegree (class in sage.groups.perm_gps.permgroup_named) translation() (sage.groups.affine_gps.affine_group.AffineGroup method) transversals() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) trivial_character() (sage.groups.libgap_mixin.GroupMixinLibGAP method) (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) tropical_coordinates() (sage.groups.braid.Braid method) tuple() (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) tuples() (sage.groups.braid.RightQuantumWord method) U U() (sage.groups.perm_gps.cubegroup.CubeGroup method) ultra_summit_set() (sage.groups.braid.Braid method) ultra_summit_set_element() (sage.groups.braid.Braid method) undo() (sage.groups.perm_gps.cubegroup.RubiksCube method) UnitaryMatrixGroup_gap (class in sage.groups.matrix_gps.unitary_gap) UnitaryMatrixGroup_generic (class in sage.groups.matrix_gps.unitary) UnitCircleGroup (class in sage.groups.misc_gps.argument_groups) UnitCirclePoint (class in sage.groups.misc_gps.argument_groups) universe() (sage.groups.additive_abelian.additive_abelian_wrapper.AdditiveAbelianGroupWrapper method) UnwrappingMorphism (class in sage.groups.additive_abelian.additive_abelian_wrapper) upper_central_series() (sage.groups.perm_gps.permgroup.PermutationGroup_generic method) V value() (sage.groups.abelian_gps.values.AbelianGroupWithValuesElement method) values() (sage.groups.class_function.ClassFunction_gap method) (sage.groups.class_function.ClassFunction_libgap method) values_embedding() (sage.groups.abelian_gps.values.AbelianGroupWithValues_class method) values_group() (sage.groups.abelian_gps.values.AbelianGroupWithValues_class method) vector_space() (sage.groups.affine_gps.affine_group.AffineGroup method) W word_problem() (in module sage.groups.abelian_gps.abelian_group) (sage.groups.abelian_gps.abelian_group_element.AbelianGroupElement method) (sage.groups.abelian_gps.dual_abelian_group_element.DualAbelianGroupElement method) (sage.groups.matrix_gps.group_element_gap.MatrixGroupElement_gap method) (sage.groups.perm_gps.permgroup_element.PermutationGroupElement method) X xproj() (in module sage.groups.perm_gps.cubegroup) Y young_subgroup() (sage.groups.perm_gps.permgroup_named.SymmetricGroup method) yproj() (in module sage.groups.perm_gps.cubegroup)