Index A | C | D | E | F | G | I | L | M | N | P | R | S | T | U | V A augmentation() (sage.rings.valuation.inductive_valuation.NonFinalInductiveValuation method) augmentation_chain() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.InductiveValuation method) AugmentedValuation_base (class in sage.rings.valuation.augmented_valuation) AugmentedValuationFactory (class in sage.rings.valuation.augmented_valuation) C change_domain() (sage.rings.padics.padic_valuation.pAdicValuation_base method) (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.InfiniteInductiveValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) ClassicalFunctionFieldValuation_base (class in sage.rings.function_field.function_field_valuation) coefficients() (sage.rings.valuation.developing_valuation.DevelopingValuation method) create_key() (sage.rings.valuation.augmented_valuation.AugmentedValuationFactory method) (sage.rings.valuation.gauss_valuation.GaussValuationFactory method) (sage.rings.valuation.limit_valuation.LimitValuationFactory method) (sage.rings.valuation.scaled_valuation.ScaledValuationFactory method) (sage.rings.valuation.trivial_valuation.TrivialValuationFactory method) create_key_and_extra_args() (sage.rings.function_field.function_field_valuation.FunctionFieldValuationFactory method) (sage.rings.padics.padic_valuation.PadicValuationFactory method) create_key_and_extra_args_for_number_field() (sage.rings.padics.padic_valuation.PadicValuationFactory method) create_key_and_extra_args_for_number_field_from_ideal() (sage.rings.padics.padic_valuation.PadicValuationFactory method) create_key_and_extra_args_for_number_field_from_valuation() (sage.rings.padics.padic_valuation.PadicValuationFactory method) create_key_and_extra_args_from_place() (sage.rings.function_field.function_field_valuation.FunctionFieldValuationFactory method) create_key_and_extra_args_from_valuation() (sage.rings.function_field.function_field_valuation.FunctionFieldValuationFactory method) create_key_and_extra_args_from_valuation_on_isomorphic_field() (sage.rings.function_field.function_field_valuation.FunctionFieldValuationFactory method) create_key_for_integers() (sage.rings.padics.padic_valuation.PadicValuationFactory method) create_key_for_local_ring() (sage.rings.padics.padic_valuation.PadicValuationFactory method) create_object() (sage.rings.function_field.function_field_valuation.FunctionFieldValuationFactory method) (sage.rings.padics.padic_valuation.PadicValuationFactory method) (sage.rings.valuation.augmented_valuation.AugmentedValuationFactory method) (sage.rings.valuation.gauss_valuation.GaussValuationFactory method) (sage.rings.valuation.limit_valuation.LimitValuationFactory method) (sage.rings.valuation.scaled_valuation.ScaledValuationFactory method) (sage.rings.valuation.trivial_valuation.TrivialValuationFactory method) D denominator() (sage.rings.valuation.value_group.DiscreteValueGroup method) DevelopingValuation (class in sage.rings.valuation.developing_valuation) DiscreteFunctionFieldValuation_base (class in sage.rings.function_field.function_field_valuation) DiscretePseudoValuation (class in sage.rings.valuation.valuation) DiscretePseudoValuationSpace (class in sage.rings.valuation.valuation_space) DiscretePseudoValuationSpace.ElementMethods (class in sage.rings.valuation.valuation_space) DiscreteValuation (class in sage.rings.valuation.valuation) DiscreteValuationCodomain (class in sage.rings.valuation.value_group) DiscreteValueGroup (class in sage.rings.valuation.value_group) DiscreteValueSemigroup (class in sage.rings.valuation.value_group) E E() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.InductiveValuation method) effective_degree() (sage.rings.valuation.developing_valuation.DevelopingValuation method) element_with_valuation() (sage.rings.function_field.function_field_valuation.RationalFunctionFieldValuation_base method) (sage.rings.padics.padic_valuation.pAdicValuation_padic method) (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.InductiveValuation method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.mapped_valuation.MappedValuation_base method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) equivalence_decomposition() (sage.rings.valuation.inductive_valuation.NonFinalInductiveValuation method) equivalence_reciprocal() (sage.rings.valuation.inductive_valuation.InductiveValuation method) equivalence_unit() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.InductiveValuation method) extension() (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) extensions() (sage.rings.function_field.function_field_valuation.DiscreteFunctionFieldValuation_base method) (sage.rings.function_field.function_field_valuation.InducedRationalFunctionFieldValuation_base method) (sage.rings.padics.padic_valuation.pAdicFromLimitValuation method) (sage.rings.padics.padic_valuation.pAdicValuation_base method) (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.FiniteInductiveValuation method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.scaled_valuation.ScaledValuation_generic method) (sage.rings.valuation.trivial_valuation.TrivialDiscreteValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) F F() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.InductiveValuation method) FinalAugmentedValuation (class in sage.rings.valuation.augmented_valuation) FinalFiniteAugmentedValuation (class in sage.rings.valuation.augmented_valuation) FinalInductiveValuation (class in sage.rings.valuation.inductive_valuation) FiniteAugmentedValuation (class in sage.rings.valuation.augmented_valuation) FiniteExtensionFromInfiniteValuation (class in sage.rings.valuation.mapped_valuation) FiniteExtensionFromLimitValuation (class in sage.rings.valuation.mapped_valuation) FiniteInductiveValuation (class in sage.rings.valuation.inductive_valuation) FiniteRationalFunctionFieldValuation (class in sage.rings.function_field.function_field_valuation) FunctionFieldExtensionMappedValuation (class in sage.rings.function_field.function_field_valuation) FunctionFieldFromLimitValuation (class in sage.rings.function_field.function_field_valuation) FunctionFieldMappedValuation_base (class in sage.rings.function_field.function_field_valuation) FunctionFieldMappedValuationRelative_base (class in sage.rings.function_field.function_field_valuation) FunctionFieldValuation_base (class in sage.rings.function_field.function_field_valuation) FunctionFieldValuationFactory (class in sage.rings.function_field.function_field_valuation) G GaussValuation_generic (class in sage.rings.valuation.gauss_valuation) GaussValuationFactory (class in sage.rings.valuation.gauss_valuation) gen() (sage.rings.valuation.value_group.DiscreteValueGroup method) gens() (sage.rings.valuation.value_group.DiscreteValueSemigroup method) I index() (sage.rings.valuation.value_group.DiscreteValueGroup method) InducedRationalFunctionFieldValuation_base (class in sage.rings.function_field.function_field_valuation) InductiveValuation (class in sage.rings.valuation.inductive_valuation) InfiniteAugmentedValuation (class in sage.rings.valuation.augmented_valuation) InfiniteDiscretePseudoValuation (class in sage.rings.valuation.valuation) InfiniteInductiveValuation (class in sage.rings.valuation.inductive_valuation) InfiniteRationalFunctionFieldValuation (class in sage.rings.function_field.function_field_valuation) inverse() (sage.rings.padics.padic_valuation.pAdicValuation_int method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) is_discrete_pseudo_valuation() (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) is_discrete_valuation() (sage.rings.function_field.function_field_valuation.FunctionFieldMappedValuation_base method) (sage.rings.valuation.valuation.DiscreteValuation method) (sage.rings.valuation.valuation.InfiniteDiscretePseudoValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) is_equivalence_irreducible() (sage.rings.valuation.inductive_valuation.NonFinalInductiveValuation method) is_equivalence_unit() (sage.rings.valuation.inductive_valuation.InductiveValuation method) is_equivalent() (sage.rings.valuation.valuation.DiscretePseudoValuation method) is_gauss_valuation() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.InductiveValuation method) is_group() (sage.rings.valuation.value_group.DiscreteValueSemigroup method) is_key() (sage.rings.valuation.inductive_valuation.NonFinalInductiveValuation method) is_minimal() (sage.rings.valuation.inductive_valuation.NonFinalInductiveValuation method) is_negative_pseudo_valuation() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.trivial_valuation.TrivialDiscretePseudoValuation_base method) (sage.rings.valuation.valuation.NegativeInfiniteDiscretePseudoValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) is_totally_ramified() (sage.rings.padics.padic_valuation.pAdicValuation_base method) is_trivial() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.trivial_valuation.TrivialDiscretePseudoValuation_base method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) (sage.rings.valuation.value_group.DiscreteValueGroup method) (sage.rings.valuation.value_group.DiscreteValueSemigroup method) is_unramified() (sage.rings.padics.padic_valuation.pAdicValuation_base method) L lift() (sage.rings.function_field.function_field_valuation.InducedRationalFunctionFieldValuation_base method) (sage.rings.padics.padic_valuation.pAdicValuation_base method) (sage.rings.padics.padic_valuation.pAdicValuation_padic method) (sage.rings.valuation.augmented_valuation.FinalAugmentedValuation method) (sage.rings.valuation.augmented_valuation.NonFinalAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.mapped_valuation.MappedValuation_base method) (sage.rings.valuation.scaled_valuation.ScaledValuation_generic method) (sage.rings.valuation.trivial_valuation.TrivialDiscretePseudoValuation method) (sage.rings.valuation.trivial_valuation.TrivialDiscreteValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) lift_to_key() (sage.rings.valuation.augmented_valuation.NonFinalAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.NonFinalInductiveValuation method) LimitValuation_generic (class in sage.rings.valuation.limit_valuation) LimitValuationFactory (class in sage.rings.valuation.limit_valuation) lower_bound() (sage.rings.valuation.augmented_valuation.FiniteAugmentedValuation method) (sage.rings.valuation.augmented_valuation.InfiniteAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.mapped_valuation.FiniteExtensionFromInfiniteValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) M mac_lane_approximant() (sage.rings.valuation.valuation.DiscreteValuation method) mac_lane_approximants() (sage.rings.valuation.valuation.DiscreteValuation method) mac_lane_step() (sage.rings.valuation.inductive_valuation.NonFinalInductiveValuation method) MacLaneApproximantNode (class in sage.rings.valuation.valuation) MacLaneLimitValuation (class in sage.rings.valuation.limit_valuation) MappedValuation_base (class in sage.rings.valuation.mapped_valuation) minimal_representative() (sage.rings.valuation.inductive_valuation.NonFinalInductiveValuation method) module sage.rings.function_field.function_field_valuation sage.rings.padics.padic_valuation sage.rings.valuation.augmented_valuation sage.rings.valuation.developing_valuation sage.rings.valuation.gauss_valuation sage.rings.valuation.inductive_valuation sage.rings.valuation.limit_valuation sage.rings.valuation.mapped_valuation sage.rings.valuation.scaled_valuation sage.rings.valuation.trivial_valuation sage.rings.valuation.valuation sage.rings.valuation.valuation_space sage.rings.valuation.value_group monic_integral_model() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.inductive_valuation.InductiveValuation method) montes_factorization() (sage.rings.valuation.valuation.DiscreteValuation method) mu() (sage.rings.valuation.inductive_valuation.InductiveValuation method) N NegativeInfiniteDiscretePseudoValuation (class in sage.rings.valuation.valuation) newton_polygon() (sage.rings.valuation.developing_valuation.DevelopingValuation method) NonClassicalRationalFunctionFieldValuation (class in sage.rings.function_field.function_field_valuation) NonFinalAugmentedValuation (class in sage.rings.valuation.augmented_valuation) NonFinalFiniteAugmentedValuation (class in sage.rings.valuation.augmented_valuation) NonFinalInductiveValuation (class in sage.rings.valuation.inductive_valuation) numerator() (sage.rings.valuation.value_group.DiscreteValueGroup method) P p() (sage.rings.padics.padic_valuation.pAdicValuation_base method) pAdicFromLimitValuation (class in sage.rings.padics.padic_valuation) pAdicValuation_base (class in sage.rings.padics.padic_valuation) pAdicValuation_int (class in sage.rings.padics.padic_valuation) pAdicValuation_padic (class in sage.rings.padics.padic_valuation) PadicValuationFactory (class in sage.rings.padics.padic_valuation) phi() (sage.rings.valuation.developing_valuation.DevelopingValuation method) psi() (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) R RationalFunctionFieldMappedValuation (class in sage.rings.function_field.function_field_valuation) RationalFunctionFieldValuation_base (class in sage.rings.function_field.function_field_valuation) reduce() (sage.rings.function_field.function_field_valuation.InducedRationalFunctionFieldValuation_base method) (sage.rings.padics.padic_valuation.pAdicValuation_base method) (sage.rings.padics.padic_valuation.pAdicValuation_padic method) (sage.rings.valuation.augmented_valuation.FinalAugmentedValuation method) (sage.rings.valuation.augmented_valuation.NonFinalAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.LimitValuation_generic method) (sage.rings.valuation.mapped_valuation.MappedValuation_base method) (sage.rings.valuation.scaled_valuation.ScaledValuation_generic method) (sage.rings.valuation.trivial_valuation.TrivialDiscretePseudoValuation method) (sage.rings.valuation.trivial_valuation.TrivialDiscreteValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) residue_field() (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) residue_ring() (sage.rings.function_field.function_field_valuation.InducedRationalFunctionFieldValuation_base method) (sage.rings.function_field.function_field_valuation.NonClassicalRationalFunctionFieldValuation method) (sage.rings.padics.padic_valuation.pAdicValuation_int method) (sage.rings.padics.padic_valuation.pAdicValuation_padic method) (sage.rings.valuation.augmented_valuation.FinalAugmentedValuation method) (sage.rings.valuation.augmented_valuation.NonFinalAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.mapped_valuation.MappedValuation_base method) (sage.rings.valuation.scaled_valuation.ScaledValuation_generic method) (sage.rings.valuation.trivial_valuation.TrivialDiscretePseudoValuation method) (sage.rings.valuation.trivial_valuation.TrivialDiscreteValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) restriction() (sage.rings.function_field.function_field_valuation.FunctionFieldExtensionMappedValuation method) (sage.rings.function_field.function_field_valuation.FunctionFieldMappedValuationRelative_base method) (sage.rings.function_field.function_field_valuation.InducedRationalFunctionFieldValuation_base method) (sage.rings.padics.padic_valuation.pAdicValuation_base method) (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.mapped_valuation.FiniteExtensionFromInfiniteValuation method) (sage.rings.valuation.scaled_valuation.ScaledValuation_generic method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) S sage.rings.function_field.function_field_valuation module sage.rings.padics.padic_valuation module sage.rings.valuation.augmented_valuation module sage.rings.valuation.developing_valuation module sage.rings.valuation.gauss_valuation module sage.rings.valuation.inductive_valuation module sage.rings.valuation.limit_valuation module sage.rings.valuation.mapped_valuation module sage.rings.valuation.scaled_valuation module sage.rings.valuation.trivial_valuation module sage.rings.valuation.valuation module sage.rings.valuation.valuation_space module sage.rings.valuation.value_group module scale() (sage.rings.function_field.function_field_valuation.FunctionFieldFromLimitValuation method) (sage.rings.function_field.function_field_valuation.FunctionFieldMappedValuation_base method) (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) ScaleAction (class in sage.rings.valuation.valuation_space) ScaledValuation_generic (class in sage.rings.valuation.scaled_valuation) ScaledValuationFactory (class in sage.rings.valuation.scaled_valuation) separating_element() (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) shift() (sage.rings.padics.padic_valuation.pAdicValuation_padic method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) simplify() (sage.rings.function_field.function_field_valuation.InducedRationalFunctionFieldValuation_base method) (sage.rings.padics.padic_valuation.pAdicValuation_int method) (sage.rings.padics.padic_valuation.pAdicValuation_padic method) (sage.rings.valuation.augmented_valuation.FiniteAugmentedValuation method) (sage.rings.valuation.augmented_valuation.InfiniteAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.mapped_valuation.FiniteExtensionFromInfiniteValuation method) (sage.rings.valuation.mapped_valuation.MappedValuation_base method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) some_elements() (sage.rings.valuation.value_group.DiscreteValueGroup method) (sage.rings.valuation.value_group.DiscreteValueSemigroup method) T TrivialDiscretePseudoValuation (class in sage.rings.valuation.trivial_valuation) TrivialDiscretePseudoValuation_base (class in sage.rings.valuation.trivial_valuation) TrivialDiscreteValuation (class in sage.rings.valuation.trivial_valuation) TrivialValuationFactory (class in sage.rings.valuation.trivial_valuation) U uniformizer() (sage.rings.function_field.function_field_valuation.InducedRationalFunctionFieldValuation_base method) (sage.rings.padics.padic_valuation.pAdicValuation_int method) (sage.rings.padics.padic_valuation.pAdicValuation_padic method) (sage.rings.valuation.augmented_valuation.AugmentedValuation_base method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.mapped_valuation.MappedValuation_base method) (sage.rings.valuation.scaled_valuation.ScaledValuation_generic method) (sage.rings.valuation.trivial_valuation.TrivialDiscretePseudoValuation_base method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) upper_bound() (sage.rings.valuation.augmented_valuation.FiniteAugmentedValuation method) (sage.rings.valuation.augmented_valuation.InfiniteAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.mapped_valuation.FiniteExtensionFromInfiniteValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) V valuations() (sage.rings.valuation.augmented_valuation.FiniteAugmentedValuation method) (sage.rings.valuation.augmented_valuation.InfiniteAugmentedValuation method) (sage.rings.valuation.developing_valuation.DevelopingValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) value_group() (sage.rings.function_field.function_field_valuation.InducedRationalFunctionFieldValuation_base method) (sage.rings.valuation.augmented_valuation.FiniteAugmentedValuation method) (sage.rings.valuation.augmented_valuation.InfiniteAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.trivial_valuation.TrivialDiscretePseudoValuation method) (sage.rings.valuation.trivial_valuation.TrivialDiscreteValuation method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method) value_semigroup() (sage.rings.padics.padic_valuation.pAdicValuation_base method) (sage.rings.valuation.augmented_valuation.FiniteAugmentedValuation method) (sage.rings.valuation.augmented_valuation.InfiniteAugmentedValuation method) (sage.rings.valuation.gauss_valuation.GaussValuation_generic method) (sage.rings.valuation.limit_valuation.MacLaneLimitValuation method) (sage.rings.valuation.scaled_valuation.ScaledValuation_generic method) (sage.rings.valuation.valuation_space.DiscretePseudoValuationSpace.ElementMethods method)