Index A | B | C | D | E | F | G | H | I | K | L | M | N | O | P | Q | R | S | T | U | V | Z A absolute_base() (sage.rings.ring_extension.RingExtension_generic method) absolute_degree() (sage.rings.ring_extension.RingExtension_generic method) absolute_norm() (sage.rings.ideal.Ideal_generic method) additive_order() (sage.rings.ring_extension_element.RingExtensionElement method) Algebra (class in sage.rings.ring) algebraic_closure() (sage.rings.ring.Field method) AlgebraicField (class in sage.rings.abc) AlgebraicField_common (class in sage.rings.abc) AlgebraicRealField (class in sage.rings.abc) ambient() (sage.rings.quotient_ring.QuotientRing_nc method) an_embedding() (sage.rings.ring.Field method) AnInfinity (class in sage.rings.infinity) apply_morphism() (sage.rings.ideal.Ideal_generic method) associated_primes() (sage.rings.ideal.Ideal_generic method) B backend() (sage.rings.ring_extension.RingExtension_generic method) (sage.rings.ring_extension_element.RingExtensionElement method) base() (sage.rings.ring_extension.RingExtension_generic method) base_extend() (sage.rings.ring.Ring method) base_map() (sage.rings.morphism.RingHomomorphism_im_gens method) (sage.rings.ring_extension_morphism.RingExtensionHomomorphism method) base_ring() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.ideal.Ideal_generic method) bases() (sage.rings.ring_extension.RingExtension_generic method) basis() (sage.rings.derivation.RingDerivationModule method) basis_over() (sage.rings.ring_extension.RingExtensionWithBasis method) C CallableSymbolicExpressionRing (class in sage.rings.abc) category() (sage.rings.ideal.Ideal_generic method) (sage.rings.ring.Ring method) characteristic() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.localization.Localization method) (sage.rings.quotient_ring.QuotientRing_nc method) (sage.rings.ring_extension.RingExtension_generic method) charpoly() (sage.rings.ring_extension_element.RingExtensionWithBasisElement method) class_number() (sage.rings.fraction_field.FractionField_1poly_field method) codomain() (sage.rings.derivation.RingDerivation method) (sage.rings.derivation.RingDerivationModule method) common_base() (in module sage.rings.ring_extension) CommutativeAlgebra (class in sage.rings.ring) CommutativeRing (class in sage.rings.ring) ComplexBallField (class in sage.rings.abc) ComplexDoubleField (class in sage.rings.abc) ComplexField (class in sage.rings.abc) ComplexIntervalField (class in sage.rings.abc) construction() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.quotient_ring.QuotientRing_nc method) (sage.rings.ring_extension.RingExtension_generic method) cover() (sage.rings.quotient_ring.QuotientRing_nc method) cover_ring() (sage.rings.quotient_ring.QuotientRing_nc method) create_key_and_extra_args() (sage.rings.ring_extension.RingExtensionFactory method) create_object() (sage.rings.ring_extension.RingExtensionFactory method) Cyclic() (in module sage.rings.ideal) D DedekindDomain (class in sage.rings.ring) defining_ideal() (sage.rings.quotient_ring.QuotientRing_nc method) defining_morphism() (sage.rings.derivation.RingDerivationModule method) (sage.rings.ring_extension.RingExtension_generic method) degree() (sage.rings.ring_extension.RingExtension_generic method) degree_over() (sage.rings.ring_extension.RingExtension_generic method) denominator() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.localization.LocalizationElement method) (sage.rings.ring_extension_element.RingExtensionFractionFieldElement method) divides() (sage.rings.ideal.Ideal_principal method) domain() (sage.rings.derivation.RingDerivation method) (sage.rings.derivation.RingDerivationModule method) dual_basis() (sage.rings.derivation.RingDerivationModule method) E Element (sage.rings.homset.RingHomset_generic attribute) (sage.rings.homset.RingHomset_quo_ring attribute) (sage.rings.ideal_monoid.IdealMonoid_c attribute) (sage.rings.localization.Localization attribute) (sage.rings.quotient_ring.QuotientRing_nc attribute) (sage.rings.ring_extension.RingExtension_generic attribute) (sage.rings.ring_extension.RingExtensionFractionField attribute) (sage.rings.ring_extension.RingExtensionWithBasis attribute) embedded_primes() (sage.rings.ideal.Ideal_generic method) epsilon() (sage.rings.ring.Ring method) extend_to_fraction_field() (sage.rings.derivation.RingDerivationWithoutTwist method) (sage.rings.derivation.RingDerivationWithTwist_generic method) extension() (sage.rings.ring.CommutativeRing method) F factor() (sage.rings.localization.LocalizationElement method) Field (class in sage.rings.ring) FieldIdeal() (in module sage.rings.ideal) FiniteNumber (class in sage.rings.infinity) fraction_field() (sage.rings.infinity.InfinityRing_class method) (sage.rings.localization.Localization method) (sage.rings.ring.CommutativeRing method) (sage.rings.ring.Field method) (sage.rings.ring_extension.RingExtension_generic method) (sage.rings.ring_extension.RingExtensionWithBasis method) (sage.rings.ring_extension.RingExtensionWithGen method) FractionField() (in module sage.rings.fraction_field) FractionField_1poly_field (class in sage.rings.fraction_field) FractionField_generic (class in sage.rings.fraction_field) FractionFieldElement (class in sage.rings.fraction_field_element) FractionFieldElement_1poly_field (class in sage.rings.fraction_field_element) FractionFieldEmbedding (class in sage.rings.fraction_field) FractionFieldEmbeddingSection (class in sage.rings.fraction_field) free_module() (sage.rings.ring_extension.RingExtensionWithBasis method) free_resolution() (sage.rings.ideal.Ideal_generic method) FrobeniusEndomorphism_generic (class in sage.rings.morphism) from_base_ring() (sage.rings.ring_extension.RingExtension_generic method) function_field() (sage.rings.fraction_field.FractionField_1poly_field method) G gcd() (sage.rings.ideal.Ideal_pid method) gen() (sage.rings.derivation.RingDerivationModule method) (sage.rings.fraction_field.FractionField_generic method) (sage.rings.ideal.Ideal_generic method) (sage.rings.ideal.Ideal_principal method) (sage.rings.infinity.InfinityRing_class method) (sage.rings.infinity.UnsignedInfinityRing_class method) (sage.rings.localization.Localization method) (sage.rings.quotient_ring.QuotientRing_nc method) (sage.rings.ring_extension.RingExtension_generic method) generators() (in module sage.rings.ring_extension) gens() (sage.rings.derivation.RingDerivationModule method) (sage.rings.ideal.Ideal_generic method) (sage.rings.infinity.InfinityRing_class method) (sage.rings.infinity.UnsignedInfinityRing_class method) (sage.rings.localization.Localization method) (sage.rings.quotient_ring.QuotientRing_nc method) (sage.rings.ring_extension.RingExtension_generic method) (sage.rings.ring_extension.RingExtensionWithGen method) gens_reduced() (sage.rings.ideal.Ideal_generic method) graded_free_resolution() (sage.rings.ideal.Ideal_generic method) H has_coerce_map_from() (sage.rings.homset.RingHomset_generic method) hom() (sage.rings.ring_extension.RingExtension_generic method) I Ideal() (in module sage.rings.ideal) ideal() (sage.rings.quotient_ring.QuotientRing_nc method) Ideal_fractional (class in sage.rings.ideal) Ideal_generic (class in sage.rings.ideal) Ideal_nc (class in sage.rings.noncommutative_ideals) Ideal_pid (class in sage.rings.ideal) Ideal_principal (class in sage.rings.ideal) IdealMonoid() (in module sage.rings.ideal_monoid) IdealMonoid_c (class in sage.rings.ideal_monoid) IdealMonoid_nc (class in sage.rings.noncommutative_ideals) im_gens() (sage.rings.morphism.RingHomomorphism_im_gens method) in_base() (sage.rings.ring_extension_element.RingExtensionElement method) InfinityRing_class (class in sage.rings.infinity) IntegerModRing (class in sage.rings.abc) IntegralDomain (class in sage.rings.ring) interpolation() (sage.rings.generic.ProductTree method) inverse() (sage.rings.morphism.RingHomomorphism method) (sage.rings.morphism.RingHomomorphism_from_base method) (sage.rings.morphism.RingHomomorphism_from_fraction_field method) inverse_image() (sage.rings.morphism.RingHomomorphism method) inverse_of_unit() (sage.rings.localization.LocalizationElement method) is_commutative() (sage.rings.infinity.InfinityRing_class method) (sage.rings.quotient_ring.QuotientRing_nc method) is_defined_over() (sage.rings.ring_extension.RingExtension_generic method) is_exact() (sage.rings.fraction_field.FractionField_generic method) is_field() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.localization.Localization method) (sage.rings.quotient_ring.QuotientRing_nc method) (sage.rings.ring.Field method) (sage.rings.ring.Ring method) (sage.rings.ring_extension.RingExtension_generic method) is_finite() (sage.rings.fraction_field.FractionField_generic method) is_finite_over() (sage.rings.ring_extension.RingExtension_generic method) is_FractionField() (in module sage.rings.fraction_field) is_FractionFieldElement() (in module sage.rings.fraction_field_element) is_free_over() (sage.rings.ring_extension.RingExtension_generic method) is_Ideal() (in module sage.rings.ideal) is_identity() (sage.rings.ring_extension_morphism.RingExtensionHomomorphism method) is_Infinite() (in module sage.rings.infinity) is_injective() (sage.rings.fraction_field.FractionFieldEmbedding method) (sage.rings.ring_extension_morphism.MapFreeModuleToRelativeRing method) (sage.rings.ring_extension_morphism.MapRelativeRingToFreeModule method) (sage.rings.ring_extension_morphism.RingExtensionHomomorphism method) is_integral() (sage.rings.fraction_field_element.FractionFieldElement_1poly_field method) is_integral_domain() (sage.rings.quotient_ring.QuotientRing_nc method) is_invertible() (sage.rings.morphism.RingHomomorphism method) is_maximal() (sage.rings.ideal.Ideal_generic method) (sage.rings.ideal.Ideal_pid method) is_nilpotent() (sage.rings.ring_extension_element.RingExtensionElement method) is_noetherian() (sage.rings.quotient_ring.QuotientRing_nc method) is_one() (sage.rings.fraction_field_element.FractionFieldElement method) is_primary() (sage.rings.ideal.Ideal_generic method) is_prime() (sage.rings.ideal.Ideal_generic method) (sage.rings.ideal.Ideal_pid method) (sage.rings.ring_extension_element.RingExtensionElement method) is_principal() (sage.rings.ideal.Ideal_generic method) (sage.rings.ideal.Ideal_principal method) is_QuotientRing() (in module sage.rings.quotient_ring) is_Ring() (in module sage.rings.ring) is_RingHomset() (in module sage.rings.homset) is_square() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.ring_extension_element.RingExtensionElement method) is_surjective() (sage.rings.fraction_field.FractionFieldEmbedding method) (sage.rings.morphism.RingHomomorphism method) (sage.rings.ring_extension_morphism.MapFreeModuleToRelativeRing method) (sage.rings.ring_extension_morphism.MapRelativeRingToFreeModule method) (sage.rings.ring_extension_morphism.RingExtensionHomomorphism method) is_trivial() (sage.rings.ideal.Ideal_generic method) is_unit() (sage.rings.localization.LocalizationElement method) (sage.rings.quotient_ring_element.QuotientRingElement method) (sage.rings.ring_extension_element.RingExtensionElement method) is_zero() (sage.rings.derivation.RingDerivationWithoutTwist method) (sage.rings.derivation.RingDerivationWithoutTwist_function method) (sage.rings.derivation.RingDerivationWithoutTwist_zero method) (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.infinity.InfinityRing_class method) K Katsura() (in module sage.rings.ideal) kernel() (sage.rings.morphism.RingHomomorphism method) (sage.rings.morphism.RingHomomorphism_cover method) krull_dimension() (sage.rings.localization.Localization method) L lc() (sage.rings.quotient_ring_element.QuotientRingElement method) lcm() (sage.rings.infinity.AnInfinity method) leaves() (sage.rings.generic.ProductTree method) less_than_infinity() (sage.rings.infinity.UnsignedInfinityRing_class method) LessThanInfinity (class in sage.rings.infinity) lift() (sage.rings.morphism.RingHomomorphism method) (sage.rings.quotient_ring.QuotientRing_nc method) (sage.rings.quotient_ring_element.QuotientRingElement method) lifting_map() (sage.rings.quotient_ring.QuotientRing_nc method) list() (sage.rings.derivation.RingDerivationWithoutTwist method) (sage.rings.derivation.RingDerivationWithoutTwist_function method) (sage.rings.derivation.RingDerivationWithoutTwist_wrapper method) (sage.rings.derivation.RingDerivationWithoutTwist_zero method) (sage.rings.derivation.RingDerivationWithTwist_generic method) lm() (sage.rings.quotient_ring_element.QuotientRingElement method) Localization (class in sage.rings.localization) LocalizationElement (class in sage.rings.localization) lt() (sage.rings.quotient_ring_element.QuotientRingElement method) M make_element() (in module sage.rings.fraction_field_element) make_element_old() (in module sage.rings.fraction_field_element) MapFreeModuleToRelativeRing (class in sage.rings.ring_extension_morphism) MapRelativeRingToFreeModule (class in sage.rings.ring_extension_morphism) matrix() (sage.rings.ring_extension_element.RingExtensionWithBasisElement method) maximal_order() (sage.rings.fraction_field.FractionField_1poly_field method) minimal_associated_primes() (sage.rings.ideal.Ideal_generic method) minpoly() (sage.rings.ring_extension_element.RingExtensionWithBasisElement method) MinusInfinity (class in sage.rings.infinity) module sage.rings.abc sage.rings.big_oh sage.rings.derivation sage.rings.fraction_field sage.rings.fraction_field_element sage.rings.generic sage.rings.homset sage.rings.ideal sage.rings.ideal_monoid sage.rings.infinity sage.rings.localization sage.rings.morphism sage.rings.noncommutative_ideals sage.rings.numbers_abc sage.rings.quotient_ring sage.rings.quotient_ring_element sage.rings.ring sage.rings.ring_extension sage.rings.ring_extension_element sage.rings.ring_extension_morphism modulus() (sage.rings.ring_extension.RingExtensionWithGen method) monomial_coefficients() (sage.rings.derivation.RingDerivationWithoutTwist method) monomials() (sage.rings.quotient_ring_element.QuotientRingElement method) morphism_from_cover() (sage.rings.morphism.RingHomomorphism_from_quotient method) multiplicative_order() (sage.rings.ring_extension_element.RingExtensionElement method) N natural_map() (sage.rings.homset.RingHomset_generic method) ngens() (sage.rings.derivation.RingDerivationModule method) (sage.rings.fraction_field.FractionField_generic method) (sage.rings.ideal.Ideal_generic method) (sage.rings.infinity.InfinityRing_class method) (sage.rings.infinity.UnsignedInfinityRing_class method) (sage.rings.localization.Localization method) (sage.rings.quotient_ring.QuotientRing_nc method) (sage.rings.ring_extension.RingExtension_generic method) NoetherianRing (class in sage.rings.ring) norm() (sage.rings.ideal.Ideal_generic method) (sage.rings.ring_extension_element.RingExtensionWithBasisElement method) normalize_extra_units() (in module sage.rings.localization) nth_root() (sage.rings.fraction_field_element.FractionFieldElement method) NumberField_cyclotomic (class in sage.rings.abc) NumberField_quadratic (class in sage.rings.abc) numerator() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.localization.LocalizationElement method) (sage.rings.ring_extension_element.RingExtensionFractionFieldElement method) O O() (in module sage.rings.big_oh) one() (sage.rings.ring.Ring method) Order (class in sage.rings.abc) order() (sage.rings.ring.Ring method) P pAdicField (class in sage.rings.abc) pAdicRing (class in sage.rings.abc) PlusInfinity (class in sage.rings.infinity) polynomial() (sage.rings.ring_extension_element.RingExtensionWithBasisElement method) postcompose() (sage.rings.derivation.RingDerivationWithoutTwist method) (sage.rings.derivation.RingDerivationWithTwist_generic method) power() (sage.rings.morphism.FrobeniusEndomorphism_generic method) precompose() (sage.rings.derivation.RingDerivationWithoutTwist method) (sage.rings.derivation.RingDerivationWithTwist_generic method) primary_decomposition() (sage.rings.ideal.Ideal_generic method) PrincipalIdealDomain (class in sage.rings.ring) print_options() (sage.rings.ring_extension.RingExtension_generic method) prod_with_derivative() (in module sage.rings.generic) ProductTree (class in sage.rings.generic) pth_power() (sage.rings.derivation.RingDerivationWithoutTwist method) pushforward() (sage.rings.morphism.RingHomomorphism method) Python Enhancement Proposals PEP 3141 Q QuotientRing() (in module sage.rings.quotient_ring) QuotientRing_generic (class in sage.rings.quotient_ring) QuotientRing_nc (class in sage.rings.quotient_ring) QuotientRingElement (class in sage.rings.quotient_ring_element) QuotientRingIdeal_generic (class in sage.rings.quotient_ring) QuotientRingIdeal_principal (class in sage.rings.quotient_ring) R radical() (sage.rings.ideal.Ideal_pid method) (sage.rings.quotient_ring.QuotientRingIdeal_generic method) random_element() (sage.rings.derivation.RingDerivationModule method) (sage.rings.fraction_field.FractionField_generic method) (sage.rings.ideal.Ideal_generic method) (sage.rings.quotient_ring.QuotientRing_nc method) (sage.rings.ring_extension.RingExtension_generic method) RealBallField (class in sage.rings.abc) RealDoubleField (class in sage.rings.abc) RealField (class in sage.rings.abc) RealIntervalField (class in sage.rings.abc) reduce() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.fraction_field_element.FractionFieldElement_1poly_field method) (sage.rings.ideal.Ideal_generic method) (sage.rings.ideal.Ideal_pid method) (sage.rings.quotient_ring_element.QuotientRingElement method) relative_degree() (sage.rings.ring_extension.RingExtension_generic method) remainders() (sage.rings.generic.ProductTree method) residue_field() (sage.rings.ideal.Ideal_pid method) retract() (sage.rings.quotient_ring.QuotientRing_nc method) Ring (class in sage.rings.ring) ring() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.ideal.Ideal_generic method) (sage.rings.ideal_monoid.IdealMonoid_c method) (sage.rings.ring_extension.RingExtensionFractionField method) ring_of_constants() (sage.rings.derivation.RingDerivationModule method) ring_of_integers() (sage.rings.fraction_field.FractionField_1poly_field method) RingDerivation (class in sage.rings.derivation) RingDerivationModule (class in sage.rings.derivation) RingDerivationWithoutTwist (class in sage.rings.derivation) RingDerivationWithoutTwist_fraction_field (class in sage.rings.derivation) RingDerivationWithoutTwist_function (class in sage.rings.derivation) RingDerivationWithoutTwist_quotient (class in sage.rings.derivation) RingDerivationWithoutTwist_wrapper (class in sage.rings.derivation) RingDerivationWithoutTwist_zero (class in sage.rings.derivation) RingDerivationWithTwist_generic (class in sage.rings.derivation) RingExtension_generic (class in sage.rings.ring_extension) RingExtensionBackendIsomorphism (class in sage.rings.ring_extension_morphism) RingExtensionBackendReverseIsomorphism (class in sage.rings.ring_extension_morphism) RingExtensionElement (class in sage.rings.ring_extension_element) RingExtensionFactory (class in sage.rings.ring_extension) RingExtensionFractionField (class in sage.rings.ring_extension) RingExtensionFractionFieldElement (class in sage.rings.ring_extension_element) RingExtensionHomomorphism (class in sage.rings.ring_extension_morphism) RingExtensionWithBasis (class in sage.rings.ring_extension) RingExtensionWithBasisElement (class in sage.rings.ring_extension_element) RingExtensionWithGen (class in sage.rings.ring_extension) RingHomomorphism (class in sage.rings.morphism) RingHomomorphism_cover (class in sage.rings.morphism) RingHomomorphism_from_base (class in sage.rings.morphism) RingHomomorphism_from_fraction_field (class in sage.rings.morphism) RingHomomorphism_from_quotient (class in sage.rings.morphism) RingHomomorphism_im_gens (class in sage.rings.morphism) RingHomset() (in module sage.rings.homset) RingHomset_generic (class in sage.rings.homset) RingHomset_quo_ring (class in sage.rings.homset) RingMap (class in sage.rings.morphism) RingMap_lift (class in sage.rings.morphism) root() (sage.rings.generic.ProductTree method) S sage.rings.abc module sage.rings.big_oh module sage.rings.derivation module sage.rings.fraction_field module sage.rings.fraction_field_element module sage.rings.generic module sage.rings.homset module sage.rings.ideal module sage.rings.ideal_monoid module sage.rings.infinity module sage.rings.localization module sage.rings.morphism module sage.rings.noncommutative_ideals module sage.rings.numbers_abc module sage.rings.quotient_ring module sage.rings.quotient_ring_element module sage.rings.ring module sage.rings.ring_extension module sage.rings.ring_extension_element module sage.rings.ring_extension_morphism module section() (sage.rings.fraction_field.FractionFieldEmbedding method) side() (sage.rings.noncommutative_ideals.Ideal_nc method) sign() (sage.rings.infinity.FiniteNumber method) (sage.rings.infinity.LessThanInfinity method) SignError some_elements() (sage.rings.derivation.RingDerivationModule method) (sage.rings.fraction_field.FractionField_generic method) specialization() (sage.rings.fraction_field_element.FractionFieldElement method) sqrt() (sage.rings.infinity.FiniteNumber method) (sage.rings.infinity.MinusInfinity method) (sage.rings.infinity.PlusInfinity method) (sage.rings.ring_extension_element.RingExtensionElement method) subs() (sage.rings.fraction_field_element.FractionFieldElement method) support() (sage.rings.fraction_field_element.FractionFieldElement_1poly_field method) SymbolicRing (class in sage.rings.abc) T term_order() (sage.rings.quotient_ring.QuotientRing_nc method) test_comparison() (in module sage.rings.infinity) test_signed_infinity() (in module sage.rings.infinity) tower_bases() (in module sage.rings.ring_extension) trace() (sage.rings.ring_extension_element.RingExtensionWithBasisElement method) twisting_morphism() (sage.rings.derivation.RingDerivationModule method) U underlying_map() (sage.rings.morphism.RingHomomorphism_from_base method) UniversalCyclotomicField (class in sage.rings.abc) UnsignedInfinity (class in sage.rings.infinity) UnsignedInfinityRing_class (class in sage.rings.infinity) V valuation() (sage.rings.fraction_field_element.FractionFieldElement method) variable_names() (in module sage.rings.ring_extension) variables() (sage.rings.quotient_ring_element.QuotientRingElement method) vector() (sage.rings.ring_extension_element.RingExtensionWithBasisElement method) Z zero() (sage.rings.homset.RingHomset_generic method) (sage.rings.ring.Ring method) zeta() (sage.rings.ring.Ring method) zeta_order() (sage.rings.ring.Ring method)