Index

_

__call__() (sage.structure.parent.Parent method) __contains__() (sage.structure.parent.Parent method) __mul__() (sage.structure.parent.Parent method) _an_element_() (sage.structure.parent.Parent method) _ascii_art_() (sage.structure.sage_object.SageObject method) _cache_key() (sage.structure.sage_object.SageObject method) _cartesian_product_of_elements() (sage.sets.cartesian_product.CartesianProduct method) _cmp_() (sage.structure.element.Element method)

_coerce_map_from_() (sage.structure.parent.Parent method) _convert_map_from_() (sage.structure.parent.Parent method) _get_action_() (sage.structure.parent.Parent method) _init_category_() (sage.structure.parent.Parent method) _populate_coercion_lists_() (sage.structure.parent.Parent method) _repr_option() (sage.structure.parent.Parent method) _richcmp_() (sage.structure.element.Element method)

A

A (class in sage.structure.misc) (class in sage.structure.test_factory) abelian_iterator() (in module sage.structure.gens_py) abs() (sage.structure.element.RingElement method) AbstractFamily (class in sage.sets.family) add1_immutable() (in module sage.structure.list_clone_timings) add1_internal() (in module sage.structure.list_clone_timings) add1_mutable() (in module sage.structure.list_clone_timings) add1_with() (in module sage.structure.list_clone_timings)

additive_order() (sage.structure.element.ModuleElement method) (sage.structure.element.RingElement method) AdditiveGroupElement (class in sage.structure.element) AlgebraElement (class in sage.structure.element) an_element() (sage.sets.cartesian_product.CartesianProduct method) (sage.sets.disjoint_union_enumerated_sets.DisjointUnionEnumeratedSets method) (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) (sage.sets.finite_set_maps.FiniteSetEndoMaps_N method) (sage.sets.finite_set_maps.FiniteSetMaps_MN method) (sage.sets.non_negative_integers.NonNegativeIntegers method) (sage.sets.positive_integers.PositiveIntegers method) (sage.sets.real_set.RealSet method) (sage.sets.set.Set_object method) (sage.structure.parent.Parent method) append() (sage.structure.element_wrapper.ElementWrapperTester method) (sage.structure.list_clone.ClonableList method) (sage.structure.sequence.Sequence_generic method) are_pairwise_disjoint() (sage.sets.real_set.RealSet static method) AttributeErrorMessage (class in sage.structure.misc)

B

bad_parent_warnings (sage.structure.debug_options.DebugOptions_class attribute) base() (sage.structure.category_object.CategoryObject method) base_change() (sage.structure.factorization.Factorization method) base_extend() (sage.structure.element.Element method) (sage.structure.formal_sum.FormalSums method) (sage.structure.parent_base.ParentWithBase method)

base_ring() (sage.structure.category_object.CategoryObject method) (sage.structure.element.Element method) bin_op() (in module sage.structure.element) (sage.structure.element.CoercionModel method) bla() (sage.structure.dynamic_class.TestClass method) breadth_first_search_iterator() (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_generic method) (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_graded method) (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_symmetric method)

C

CachedRepresentation (class in sage.structure.unique_representation) canonical_coercion() (in module sage.structure.element) (sage.structure.element.CoercionModel method) cardinality() (sage.sets.disjoint_set.DisjointSet_class method) (sage.sets.disjoint_union_enumerated_sets.DisjointUnionEnumeratedSets method) (sage.sets.family.EnumeratedFamily method) (sage.sets.family.FiniteFamily method) (sage.sets.family.LazyFamily method) (sage.sets.family.TrivialFamily method) (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) (sage.sets.finite_set_maps.FiniteSetMaps method) (sage.sets.integer_range.IntegerRangeFinite method) (sage.sets.real_set.RealSet method) (sage.sets.set.Set_object method) (sage.sets.set.Set_object_enumerated method) (sage.sets.set.Set_object_union method) (sage.structure.parent.Set_PythonType_class method) cartesian_factors() (sage.sets.cartesian_product.CartesianProduct method) cartesian_projection() (sage.sets.cartesian_product.CartesianProduct method) (sage.sets.cartesian_product.CartesianProduct.Element method) CartesianProduct (class in sage.sets.cartesian_product) CartesianProduct.Element (class in sage.sets.cartesian_product) categories() (sage.structure.category_object.CategoryObject method) category() (sage.structure.category_object.CategoryObject method) (sage.structure.element.Element method) (sage.structure.generators.Generators method) (sage.structure.parent.Parent method) (sage.structure.sage_object.SageObject method) CategoryObject (class in sage.structure.category_object) check() (sage.sets.finite_set_map_cy.FiniteSetMap_MN method) (sage.structure.list_clone.ClonableArray method) (sage.structure.list_clone.ClonableIntArray method) (sage.structure.list_clone_demo.IncreasingArray method) (sage.structure.list_clone_demo.IncreasingIntArray method) (sage.structure.list_clone_demo.IncreasingList method) (sage.structure.list_clone_demo.SortedList method) (sage.structure.list_clone_timings.IncreasingArraysPy.Element method) check_default_category() (in module sage.structure.category_object) clear_cache() (sage.sets.set_from_iterator.EnumeratedSetFromIterator method) ClonableArray (class in sage.structure.list_clone) ClonableElement (class in sage.structure.list_clone) ClonableIntArray (class in sage.structure.list_clone) ClonableList (class in sage.structure.list_clone) clone() (sage.structure.list_clone.ClonableElement method) closed() (sage.sets.real_set.RealSet static method) closed_open() (sage.sets.real_set.RealSet static method) closure() (sage.sets.real_set.InternalRealInterval method) cls (sage.structure.misc.AttributeErrorMessage attribute) codomain() (sage.sets.finite_set_map_cy.FiniteSetMap_MN method) (sage.sets.finite_set_maps.FiniteSetMaps_MN method) (sage.sets.finite_set_maps.FiniteSetMaps_Set method) coerce() (sage.structure.parent.Parent method) coerce_binop (in module sage.structure.element)

coerce_cmp() (in module sage.structure.element) coerce_embedding() (sage.structure.parent.Parent method) coerce_map_from() (sage.structure.parent.Parent method) coerce_map_from_c() (sage.structure.parent_old.Parent method) coerce_map_from_impl() (sage.structure.parent_old.Parent method) coercion_traceback() (in module sage.structure.element) CoercionException CoercionModel (class in sage.structure.element) CommutativeAlgebra (class in sage.structure.element) CommutativeAlgebraElement (class in sage.structure.element) CommutativeRingElement (class in sage.structure.element) complement() (sage.sets.real_set.RealSet method) construction() (sage.structure.parent.Parent method) contains() (sage.sets.real_set.InternalRealInterval method) (sage.sets.real_set.RealSet method) convert_map_from() (sage.structure.parent.Parent method) convex_hull() (sage.sets.real_set.InternalRealInterval method) count() (sage.structure.generators.Generators method) (sage.structure.generators.Generators_finite method) (sage.structure.generators.Generators_lazy_all method) (sage.structure.generators.Generators_naturals method) (sage.structure.generators.Generators_none method) (sage.structure.list_clone.ClonableArray method) create_key() (sage.structure.factory.UniqueFactory method) (sage.structure.test_factory.UniqueFactoryTester method) create_key_and_extra_args() (sage.structure.factory.UniqueFactory method) create_object() (sage.structure.factory.UniqueFactory method) (sage.structure.test_factory.UniqueFactoryTester method) cy_add1_immutable() (in module sage.structure.list_clone_timings_cy) cy_add1_internal() (in module sage.structure.list_clone_timings_cy) cy_add1_mutable() (in module sage.structure.list_clone_timings_cy) cy_add1_with() (in module sage.structure.list_clone_timings_cy)

D

db() (sage.structure.sage_object.SageObject method) DebugOptions_class (class in sage.structure.debug_options) Decorator (class in sage.sets.set_from_iterator) DedekindDomainElement (class in sage.structure.element) default_prec() (sage.structure.nonexact.Nonexact method) default_value() (sage.structure.global_options.GlobalOptions method) degree() (sage.structure.element.EuclideanDomainElement method) depth_first_search_iterator() (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_generic method) difference() (sage.sets.real_set.RealSet method) (sage.sets.set.Set_object method) (sage.sets.set.Set_object_enumerated method) dir_with_other_class() (in module sage.structure.misc) DisjointSet() (in module sage.sets.disjoint_set) DisjointSet_class (class in sage.sets.disjoint_set) DisjointSet_of_hashables (class in sage.sets.disjoint_set) DisjointSet_of_integers (class in sage.sets.disjoint_set)

DisjointUnionEnumeratedSets (class in sage.sets.disjoint_union_enumerated_sets) dispatch() (sage.structure.global_options.GlobalOptions method) divides() (sage.structure.element.CommutativeRingElement method) (sage.structure.element.FieldElement method) domain() (sage.sets.finite_set_map_cy.FiniteSetMap_MN method) (sage.sets.finite_set_maps.FiniteSetMaps_MN method) (sage.sets.finite_set_maps.FiniteSetMaps_Set method) DummyExampleForPicklingTest (class in sage.sets.set_from_iterator) DummyParent (class in sage.structure.element_wrapper) dump() (sage.structure.sage_object.SageObject method) dumps() (in module sage.structure.sage_object) (sage.structure.sage_object.SageObject method) dynamic_class() (in module sage.structure.dynamic_class) dynamic_class_internal() (in module sage.structure.dynamic_class) DynamicClasscallMetaclass (class in sage.structure.dynamic_class) DynamicInheritComparisonClasscallMetaclass (class in sage.structure.dynamic_class) DynamicInheritComparisonMetaclass (class in sage.structure.dynamic_class) DynamicMetaclass (class in sage.structure.dynamic_class)

E

Element (class in sage.structure.element) (sage.sets.finite_set_maps.FiniteSetEndoMaps_N attribute) (sage.sets.finite_set_maps.FiniteSetEndoMaps_Set attribute) (sage.sets.finite_set_maps.FiniteSetMaps_MN attribute) (sage.sets.finite_set_maps.FiniteSetMaps_Set attribute) (sage.sets.non_negative_integers.NonNegativeIntegers attribute) (sage.sets.totally_ordered_finite_set.TotallyOrderedFiniteSet attribute) (sage.structure.formal_sum.FormalSums attribute) (sage.structure.list_clone_demo.IncreasingArrays attribute) (sage.structure.list_clone_demo.IncreasingIntArrays attribute) (sage.structure.list_clone_demo.IncreasingLists attribute) (sage.structure.list_clone_demo.SortedLists attribute) Element() (sage.sets.disjoint_union_enumerated_sets.DisjointUnionEnumeratedSets method) element_class (sage.sets.integer_range.IntegerRange attribute) (sage.sets.real_set.InternalRealInterval attribute) element_class() (sage.structure.parent.Parent method) element_to_root_dict() (sage.sets.disjoint_set.DisjointSet_of_hashables method) (sage.sets.disjoint_set.DisjointSet_of_integers method) elements_of_depth_iterator() (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_generic method) ElementWithCachedMethod (class in sage.structure.element) ElementWrapper (class in sage.structure.element_wrapper) ElementWrapperTester (class in sage.structure.element_wrapper)

EltPair (class in sage.structure.parent) EnumeratedFamily (class in sage.sets.family) EnumeratedSetFromIterator (class in sage.sets.set_from_iterator) EnumeratedSetFromIterator_function_decorator (class in sage.sets.set_from_iterator) EnumeratedSetFromIterator_method_caller (class in sage.sets.set_from_iterator) EnumeratedSetFromIterator_method_decorator (class in sage.sets.set_from_iterator) EuclideanDomainElement (class in sage.structure.element) expand() (sage.structure.factorization.Factorization method) extend() (sage.structure.list_clone.ClonableList method) (sage.structure.sequence.Sequence_generic method)

F

f() (sage.sets.set_from_iterator.DummyExampleForPicklingTest method) Factorization (class in sage.structure.factorization) Family() (in module sage.sets.family) fibers() (in module sage.sets.finite_set_map_cy) (sage.sets.finite_set_map_cy.FiniteSetMap_MN method) fibers_args() (in module sage.sets.finite_set_map_cy) FieldElement (class in sage.structure.element) find() (sage.sets.disjoint_set.DisjointSet_of_hashables method) (sage.sets.disjoint_set.DisjointSet_of_integers method) FiniteEnumeratedSet (class in sage.sets.finite_enumerated_set) FiniteFamily (class in sage.sets.family) FiniteFamilyWithHiddenKeys (class in sage.sets.family) FiniteSetEndoMap_N (class in sage.sets.finite_set_map_cy) FiniteSetEndoMap_Set (class in sage.sets.finite_set_map_cy) FiniteSetEndoMaps_N (class in sage.sets.finite_set_maps) FiniteSetEndoMaps_Set (class in sage.sets.finite_set_maps)

FiniteSetMap_MN (class in sage.sets.finite_set_map_cy) FiniteSetMap_Set (class in sage.sets.finite_set_map_cy) FiniteSetMap_Set_from_dict() (in module sage.sets.finite_set_map_cy) FiniteSetMap_Set_from_list() (in module sage.sets.finite_set_map_cy) FiniteSetMaps (class in sage.sets.finite_set_maps) FiniteSetMaps_MN (class in sage.sets.finite_set_maps) FiniteSetMaps_Set (class in sage.sets.finite_set_maps) first() (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) (sage.sets.primes.Primes method) FormalSum (class in sage.structure.formal_sum) FormalSums (class in sage.structure.formal_sum) from_dict() (sage.sets.finite_set_map_cy.FiniteSetMap_Set class method) (sage.sets.finite_set_maps.FiniteSetMaps_Set method) from_integer (sage.sets.non_negative_integers.NonNegativeIntegers attribute) from_list() (sage.sets.finite_set_map_cy.FiniteSetMap_Set class method) frozenset() (sage.sets.set.Set_object_enumerated method)

G

gcd() (sage.structure.factorization.Factorization method) gen() (sage.structure.parent_gens.ParentWithGens method) generator_orders() (sage.structure.parent_gens.ParentWithAdditiveAbelianGens method) (sage.structure.parent_gens.ParentWithMultiplicativeAbelianGens method) Generators (class in sage.structure.generators) Generators_finite (class in sage.structure.generators) Generators_lazy_all (class in sage.structure.generators) Generators_list (class in sage.structure.generators) Generators_naturals (class in sage.structure.generators) Generators_none (class in sage.structure.generators) generic_factory_reduce() (in module sage.structure.factory) generic_factory_unpickle() (in module sage.structure.factory) generic_power() (in module sage.structure.element) GenIter (class in sage.structure.generators) gens() (sage.structure.parent_gens.ParentWithGens method) gens_dict() (sage.structure.category_object.CategoryObject method) gens_dict_recursive() (sage.structure.category_object.CategoryObject method)

get_action() (sage.structure.parent.Parent method) get_action_c() (sage.structure.parent_old.Parent method) get_action_impl() (sage.structure.parent_old.Parent method) get_coercion_model() (in module sage.structure.element) get_flag() (in module sage.structure.proof.proof) get_from_index() (sage.structure.generators.Generators method) (sage.structure.generators.Generators_lazy_all method) (sage.structure.generators.Generators_list method) (sage.structure.generators.Generators_none method) get_interval() (sage.sets.real_set.RealSet method) get_object() (sage.structure.factory.UniqueFactory method) get_version() (sage.structure.factory.UniqueFactory method) getattr_from_other_class() (in module sage.structure.misc) getimage() (sage.sets.finite_set_map_cy.FiniteSetMap_MN method) (sage.sets.finite_set_map_cy.FiniteSetMap_Set method) GlobalOptions (class in sage.structure.global_options) graded_component() (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_generic method) graded_component_iterator() (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_generic method) (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_graded method) (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_symmetric method) guess_category() (in module sage.structure.category_object)

H

has_base() (sage.structure.category_object.CategoryObject method) has_coerce_map_from() (sage.structure.parent.Parent method) has_coerce_map_from_c() (sage.structure.parent_old.Parent method) has_coerce_map_from_impl() (sage.structure.parent_old.Parent method) has_key() (sage.sets.family.FiniteFamily method) have_same_parent() (in module sage.structure.element)

hidden_keys() (sage.sets.family.AbstractFamily method) (sage.sets.family.FiniteFamilyWithHiddenKeys method) Hom() (sage.structure.category_object.CategoryObject method) hom() (sage.structure.parent.Parent method) Hom() (sage.structure.parent.Parent method) hom() (sage.structure.parent_gens.ParentWithGens method)

I

image_set() (sage.sets.finite_set_map_cy.FiniteSetMap_MN method) (sage.sets.finite_set_map_cy.FiniteSetMap_Set method) IncreasingArray (class in sage.structure.list_clone_demo) IncreasingArrays (class in sage.structure.list_clone_demo) IncreasingArraysPy (class in sage.structure.list_clone_timings) IncreasingArraysPy.Element (class in sage.structure.list_clone_timings) IncreasingIntArray (class in sage.structure.list_clone_demo) IncreasingIntArrays (class in sage.structure.list_clone_demo) IncreasingList (class in sage.structure.list_clone_demo) IncreasingLists (class in sage.structure.list_clone_demo) index() (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) (sage.structure.list_clone.ClonableArray method) (sage.structure.list_clone.ClonableIntArray method) index_set() (sage.structure.generators.Generators method) (sage.structure.generators.Generators_none method) IndexedGenerators (class in sage.structure.indexed_generators) indices() (sage.structure.indexed_generators.IndexedGenerators method) inf() (sage.sets.real_set.RealSet method) InfinityElement (class in sage.structure.element) inject_variables() (sage.structure.category_object.CategoryObject method) injvar() (sage.structure.category_object.CategoryObject method) insert() (sage.structure.list_clone.ClonableList method) (sage.structure.sequence.Sequence_generic method) IntegerFactorization (class in sage.structure.factorization_integer) IntegerRange (class in sage.sets.integer_range) IntegerRangeEmpty (class in sage.sets.integer_range) IntegerRangeFinite (class in sage.sets.integer_range) IntegerRangeFromMiddle (class in sage.sets.integer_range) IntegerRangeInfinite (class in sage.sets.integer_range) IntegralDomainElement (class in sage.structure.element) interior() (sage.sets.real_set.InternalRealInterval method) InternalRealInterval (class in sage.sets.real_set) intersection() (sage.sets.real_set.InternalRealInterval method) (sage.sets.real_set.RealSet method) (sage.sets.set.Set_object method) (sage.sets.set.Set_object_enumerated method) inverse_family() (sage.sets.family.AbstractFamily method) inverse_mod() (sage.structure.element.CommutativeRingElement method) is_AdditiveGroupElement() (in module sage.structure.element) is_AlgebraElement() (in module sage.structure.element) is_atomic_repr() (sage.structure.parent.Parent method) is_coercion_cached() (sage.structure.parent.Parent method) is_commutative() (sage.structure.factorization.Factorization method) is_CommutativeAlgebraElement() (in module sage.structure.element) is_CommutativeRingElement() (in module sage.structure.element) is_connected() (sage.sets.real_set.InternalRealInterval method) is_conversion_cached() (sage.structure.parent.Parent method) is_DedekindDomainElement() (in module sage.structure.element)

is_disjoint_from() (sage.sets.real_set.RealSet method) is_Element() (in module sage.structure.element) is_empty() (sage.sets.real_set.InternalRealInterval method) (sage.sets.real_set.RealSet method) (sage.sets.set.Set_object method) is_EuclideanDomainElement() (in module sage.structure.element) is_exact() (sage.structure.parent.Parent method) is_extension_type() (in module sage.structure.misc) is_FieldElement() (in module sage.structure.element) is_finite() (sage.sets.set.Set_object method) (sage.sets.set.Set_object_difference method) (sage.sets.set.Set_object_enumerated method) (sage.sets.set.Set_object_intersection method) (sage.sets.set.Set_object_symmetric_difference method) (sage.sets.set.Set_object_union method) is_immutable() (sage.structure.list_clone.ClonableElement method) (sage.structure.mutability.Mutability method) (sage.structure.sequence.Sequence_generic method) is_included_in() (sage.sets.real_set.RealSet method) is_InfinityElement() (in module sage.structure.element) is_integral() (sage.structure.factorization.Factorization method) is_IntegralDomainElement() (in module sage.structure.element) is_Matrix() (in module sage.structure.element) is_ModuleElement() (in module sage.structure.element) is_MonoidElement() (in module sage.structure.element) is_MultiplicativeGroupElement() (in module sage.structure.element) is_mutable() (sage.structure.list_clone.ClonableElement method) (sage.structure.mutability.Mutability method) (sage.structure.sequence.Sequence_generic method) is_nilpotent() (sage.structure.element.IntegralDomainElement method) (sage.structure.element.RingElement method) is_one() (sage.structure.element.RingElement method) is_Parent() (in module sage.structure.parent) is_parent_of() (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) (sage.sets.set_from_iterator.EnumeratedSetFromIterator method) is_ParentWithAdditiveAbelianGens() (in module sage.structure.parent_gens) is_ParentWithBase() (in module sage.structure.parent_base) is_ParentWithGens() (in module sage.structure.parent_gens) is_ParentWithMultiplicativeAbelianGens() (in module sage.structure.parent_gens) is_point() (sage.sets.real_set.InternalRealInterval method) is_prime() (sage.structure.element.RingElement method) is_PrincipalIdealDomainElement() (in module sage.structure.element) is_RingElement() (in module sage.structure.element) is_Set() (in module sage.sets.set) is_square() (sage.structure.element.CommutativeRingElement method) is_unit() (sage.structure.element.FieldElement method) is_Vector() (in module sage.structure.element) is_zero() (sage.structure.element.Element method) issubset() (sage.sets.set.Set_object_enumerated method) issuperset() (sage.sets.set.Set_object_enumerated method) items() (sage.sets.finite_set_map_cy.FiniteSetMap_MN method) (sage.sets.finite_set_map_cy.FiniteSetMap_Set method) iteritems() (sage.structure.coerce_dict.MonoDict method) (sage.structure.coerce_dict.TripleDict method)

K

keys() (sage.sets.family.EnumeratedFamily method) (sage.sets.family.FiniteFamily method) (sage.sets.family.LazyFamily method) (sage.sets.family.TrivialFamily method)

L

last() (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) latex_name() (sage.structure.category_object.CategoryObject method) latex_variable_names() (sage.structure.category_object.CategoryObject method) LazyFamily (class in sage.sets.family) lcm() (sage.structure.element.PrincipalIdealDomainElement method) (sage.structure.factorization.Factorization method) le() (sage.sets.totally_ordered_finite_set.TotallyOrderedFiniteSet method) leading_coefficient() (sage.structure.element.EuclideanDomainElement method) list() (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) (sage.sets.set.Set_object_enumerated method) (sage.structure.generators.Generators method) (sage.structure.generators.Generators_lazy_all method) (sage.structure.generators.Generators_list method) (sage.structure.generators.Generators_none method) (sage.structure.list_clone.ClonableIntArray method) (sage.structure.parent_old.Parent method)

load() (in module sage.structure.sage_object) loads() (in module sage.structure.sage_object) localvars (class in sage.structure.category_object) (class in sage.structure.parent_gens) lookup_global() (in module sage.structure.factory) lower() (sage.sets.real_set.InternalRealInterval method) lower_closed() (sage.sets.real_set.InternalRealInterval method) lower_open() (sage.sets.real_set.InternalRealInterval method)

M

M (in module sage.structure.dynamic_class) make_element() (in module sage.structure.element) make_finite_gens() (in module sage.structure.generators) make_list_gens() (in module sage.structure.generators) map() (sage.sets.family.AbstractFamily method) Matrix (class in sage.structure.element) MinusInfinityElement (class in sage.structure.element) mod() (sage.structure.element.CommutativeRingElement method)

ModuleElement (class in sage.structure.element) MonoDict (class in sage.structure.coerce_dict) MonoDictEraser (class in sage.structure.coerce_dict) MonoidElement (class in sage.structure.element) multiplicative_iterator() (in module sage.structure.gens_py) multiplicative_order() (sage.structure.element.MonoidElement method) (sage.structure.element.RingElement method) MultiplicativeGroupElement (class in sage.structure.element) Mutability (class in sage.structure.mutability)

N

N() (sage.structure.element.Element method) n() (sage.structure.element.Element method) n_components() (sage.sets.real_set.RealSet method) naive_search_iterator() (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_generic method) name (sage.structure.misc.AttributeErrorMessage attribute) NamedBinopMethod (class in sage.structure.element) next() (sage.sets.integer_range.IntegerRangeFromMiddle method) (sage.sets.non_negative_integers.NonNegativeIntegers method) (sage.sets.primes.Primes method) (sage.structure.generators.GenIter method) ngens() (sage.structure.parent_gens.ParentWithGens method)

Nonexact (class in sage.structure.nonexact) NonNegativeIntegers (class in sage.sets.non_negative_integers) normalize() (sage.sets.real_set.RealSet static method) (sage.structure.list_clone.NormalizedClonableList method) (sage.structure.list_clone_demo.SortedList method) normalize_names() (in module sage.structure.parent) (in module sage.structure.parent_gens) (sage.structure.category_object.CategoryObject method) NormalizedClonableList (class in sage.structure.list_clone) number_of_subsets() (sage.sets.disjoint_set.DisjointSet_class method) numerical_approx() (sage.structure.element.Element method)

O

obj() (sage.structure.generators.Generators method) object() (sage.sets.set.Set_object method) (sage.structure.parent.Set_PythonType_class method) (sage.structure.parent.Set_generic method) objgen() (sage.structure.category_object.CategoryObject method) objgens() (sage.structure.category_object.CategoryObject method) one() (sage.sets.finite_set_maps.FiniteSetEndoMaps_N method)

OP_represent() (in module sage.sets.disjoint_set) open() (sage.sets.real_set.RealSet static method) open_closed() (sage.sets.real_set.RealSet static method) order() (sage.structure.element.AdditiveGroupElement method) (sage.structure.element.ModuleElement method) (sage.structure.element.MonoidElement method) (sage.structure.element.MultiplicativeGroupElement method) other_keys() (sage.structure.factory.UniqueFactory method)

P

Parent (class in sage.structure.parent) (class in sage.structure.parent_old) parent() (in module sage.structure.element) (sage.structure.element.Element method) (sage.structure.sage_object.SageObject method) ParentWithAdditiveAbelianGens (class in sage.structure.parent_gens) ParentWithBase (class in sage.structure.parent_base) ParentWithGens (class in sage.structure.parent_gens) ParentWithMultiplicativeAbelianGens (class in sage.structure.parent_gens) picklejar() (in module sage.structure.sage_object) PlusInfinityElement (class in sage.structure.element) point() (sage.sets.real_set.RealSet static method)

pop() (sage.structure.list_clone.ClonableList method) (sage.structure.sequence.Sequence_generic method) PositiveIntegers (class in sage.sets.positive_integers) powers() (sage.structure.element.MonoidElement method) (sage.structure.element.RingElement method) prefix() (sage.structure.indexed_generators.IndexedGenerators method) Primes (class in sage.sets.primes) PrincipalIdealDomainElement (class in sage.structure.element) print_options() (sage.structure.indexed_generators.IndexedGenerators method) prod() (sage.structure.factorization.Factorization method) PS_represent() (in module sage.sets.disjoint_set)

Q

quo_rem() (sage.structure.element.EuclideanDomainElement method) (sage.structure.element.FieldElement method)

R

radical() (sage.structure.factorization.Factorization method) radical_value() (sage.structure.factorization.Factorization method) random_element() (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) rank() (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) (sage.sets.integer_range.IntegerRangeFinite method) (sage.sets.integer_range.IntegerRangeInfinite method) RealSet (class in sage.sets.real_set) RecursivelyEnumeratedSet() (in module sage.sets.recursively_enumerated_set) RecursivelyEnumeratedSet_generic (class in sage.sets.recursively_enumerated_set) RecursivelyEnumeratedSet_graded (class in sage.sets.recursively_enumerated_set) RecursivelyEnumeratedSet_symmetric (class in sage.sets.recursively_enumerated_set) reduce() (sage.structure.formal_sum.FormalSum method) reduce_data() (sage.structure.factory.UniqueFactory method) refine_category_hash_check (sage.structure.debug_options.DebugOptions_class attribute) register_action() (sage.structure.parent.Parent method) register_coercion() (sage.structure.parent.Parent method)

register_conversion() (sage.structure.parent.Parent method) register_embedding() (sage.structure.parent.Parent method) register_factory_unpickle() (in module sage.structure.factory) register_unpickle_override() (in module sage.structure.sage_object) remove() (sage.structure.list_clone.ClonableList method) (sage.structure.sequence.Sequence_generic method) rename() (sage.structure.sage_object.SageObject method) require_immutable() (in module sage.structure.mutability) require_mutable() (in module sage.structure.mutability) reset() (sage.structure.global_options.GlobalOptions method) reset_name() (sage.structure.sage_object.SageObject method) reverse() (sage.structure.sequence.Sequence_generic method) RingElement (class in sage.structure.element) root_to_elements_dict() (sage.sets.disjoint_set.DisjointSet_of_hashables method) (sage.sets.disjoint_set.DisjointSet_of_integers method)

S

sage.misc.proof (module) sage.sets.cartesian_product (module) sage.sets.disjoint_set (module) sage.sets.disjoint_union_enumerated_sets (module) sage.sets.family (module) sage.sets.finite_enumerated_set (module) sage.sets.finite_set_map_cy (module) sage.sets.finite_set_maps (module) sage.sets.integer_range (module) sage.sets.non_negative_integers (module) sage.sets.positive_integers (module) sage.sets.primes (module) sage.sets.real_set (module) sage.sets.recursively_enumerated_set (module) sage.sets.set (module) sage.sets.set_from_iterator (module) sage.sets.totally_ordered_finite_set (module) sage.structure.category_object (module) sage.structure.coerce_dict (module) sage.structure.coerce_exceptions (module) sage.structure.debug_options (module) sage.structure.dynamic_class (module) sage.structure.element (module) sage.structure.element_wrapper (module) sage.structure.factorization (module) sage.structure.factorization_integer (module) sage.structure.factory (module) sage.structure.formal_sum (module) sage.structure.generators (module) sage.structure.gens_py (module) sage.structure.global_options (module) sage.structure.indexed_generators (module) sage.structure.list_clone (module) sage.structure.list_clone_demo (module) sage.structure.list_clone_timings (module) sage.structure.list_clone_timings_cy (module) sage.structure.misc (module) sage.structure.mutability (module) sage.structure.nonexact (module) sage.structure.parent (module) sage.structure.parent_base (module) sage.structure.parent_gens (module) sage.structure.parent_old (module) sage.structure.proof.proof (module)

sage.structure.sage_object (module) sage.structure.sequence (module) sage.structure.test_factory (module) sage.structure.unique_representation (module) SageObject (class in sage.structure.sage_object) save() (in module sage.structure.sage_object) (sage.structure.sage_object.SageObject method) SC_test_list_perms() (in module sage.sets.disjoint_set) seeds() (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_generic method) seq() (in module sage.structure.sequence) Sequence() (in module sage.structure.sequence) Sequence_generic (class in sage.structure.sequence) Set() (in module sage.sets.set) set() (sage.sets.set.Set_object_enumerated method) set_coercion_model() (in module sage.structure.element) set_default_prec() (sage.structure.nonexact.Nonexact method) set_from_function (in module sage.sets.set_from_iterator) set_from_method (in module sage.sets.set_from_iterator) Set_generic (class in sage.structure.parent) set_immutable() (sage.structure.list_clone.ClonableElement method) (sage.structure.mutability.Mutability method) (sage.structure.sequence.Sequence_generic method) Set_object (class in sage.sets.set) Set_object_binary (class in sage.sets.set) Set_object_difference (class in sage.sets.set) Set_object_enumerated (class in sage.sets.set) Set_object_intersection (class in sage.sets.set) Set_object_symmetric_difference (class in sage.sets.set) Set_object_union (class in sage.sets.set) Set_PythonType() (in module sage.structure.parent) Set_PythonType_class (class in sage.structure.parent) setimage() (sage.sets.finite_set_map_cy.FiniteSetMap_MN method) (sage.sets.finite_set_map_cy.FiniteSetMap_Set method) short_repr() (sage.structure.parent.EltPair method) simplify() (sage.structure.factorization.Factorization method) some_elements() (sage.sets.non_negative_integers.NonNegativeIntegers method) sort() (sage.structure.factorization.Factorization method) (sage.structure.sequence.Sequence_generic method) SortedList (class in sage.structure.list_clone_demo) SortedLists (class in sage.structure.list_clone_demo) sqrt() (sage.structure.element.CommutativeRingElement method) subs() (sage.structure.element.Element method) subsets() (sage.sets.set.Set_object method) substitute() (sage.structure.element.Element method) successors (sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_generic attribute) summand_projection() (sage.sets.cartesian_product.CartesianProduct method) sup() (sage.sets.real_set.RealSet method) symmetric_difference() (sage.sets.set.Set_object method) (sage.sets.set.Set_object_enumerated method)

T

TestClass (class in sage.structure.dynamic_class) to_digraph() (sage.sets.disjoint_set.DisjointSet_of_hashables method) (sage.sets.disjoint_set.DisjointSet_of_integers method) TotallyOrderedFiniteSet (class in sage.sets.totally_ordered_finite_set) TotallyOrderedFiniteSetElement (class in sage.sets.totally_ordered_finite_set)

TripleDict (class in sage.structure.coerce_dict) TripleDictEraser (class in sage.structure.coerce_dict) TrivialFamily (class in sage.sets.family)

U

unbounded_above_closed() (sage.sets.real_set.RealSet static method) unbounded_above_open() (sage.sets.real_set.RealSet static method) unbounded_below_closed() (sage.sets.real_set.RealSet static method) unbounded_below_open() (sage.sets.real_set.RealSet static method) union() (sage.sets.disjoint_set.DisjointSet_of_hashables method) (sage.sets.disjoint_set.DisjointSet_of_integers method) (sage.sets.real_set.RealSet method) (sage.sets.set.Set_object method) (sage.sets.set.Set_object_enumerated method) unique_parent_warnings (sage.structure.debug_options.DebugOptions_class attribute) UniqueFactory (class in sage.structure.factory) UniqueFactoryTester (class in sage.structure.test_factory) UniqueRepresentation (class in sage.structure.unique_representation)

unit() (sage.structure.factorization.Factorization method) universe() (sage.structure.factorization.Factorization method) (sage.structure.sequence.Sequence_generic method) unpickle_all() (in module sage.structure.sage_object) unpickle_global() (in module sage.structure.sage_object) unrank() (sage.sets.finite_enumerated_set.FiniteEnumeratedSet method) (sage.sets.integer_range.IntegerRangeFinite method) (sage.sets.integer_range.IntegerRangeInfinite method) (sage.sets.non_negative_integers.NonNegativeIntegers method) (sage.sets.primes.Primes method) (sage.sets.set_from_iterator.EnumeratedSetFromIterator method) unreduce() (in module sage.structure.unique_representation) upper() (sage.sets.real_set.InternalRealInterval method) upper_closed() (sage.sets.real_set.InternalRealInterval method) upper_open() (sage.sets.real_set.InternalRealInterval method)

V

value (sage.structure.element_wrapper.ElementWrapper attribute) value() (sage.structure.factorization.Factorization method) values() (sage.sets.family.FiniteFamily method) variable_name() (sage.structure.category_object.CategoryObject method)

variable_names() (sage.structure.category_object.CategoryObject method) Vector (class in sage.structure.element) version() (sage.structure.sage_object.SageObject method)

W

WithProof (class in sage.structure.proof.proof)

Z

zip() (sage.sets.family.AbstractFamily method)