General Rings, Ideals, and Morphisms# Base Classes for Rings, Algebras and Fields# Rings Algebra CommutativeAlgebra CommutativeRing DedekindDomain EuclideanDomain Field IntegralDomain NoetherianRing PrincipalIdealDomain Ring is_Ring() Ideals# Ideals of commutative rings Cyclic() FieldIdeal() Ideal() Ideal_fractional Ideal_generic Ideal_pid Ideal_principal Katsura() is_Ideal() Monoid of ideals in a commutative ring IdealMonoid() IdealMonoid_c Ideals of non-commutative rings IdealMonoid_nc Ideal_nc Ring Morphisms# Homomorphisms of rings FrobeniusEndomorphism_generic RingHomomorphism RingHomomorphism_coercion RingHomomorphism_cover RingHomomorphism_from_base RingHomomorphism_from_fraction_field RingHomomorphism_from_quotient RingHomomorphism_im_gens RingMap RingMap_lift is_RingHomomorphism() Space of homomorphisms between two rings RingHomset() RingHomset_generic RingHomset_quo_ring is_RingHomset() Quotient Rings# Quotient Rings QuotientRing() QuotientRingIdeal_generic QuotientRingIdeal_principal QuotientRing_generic QuotientRing_nc is_QuotientRing() Quotient Ring Elements QuotientRingElement Fraction Fields# Fraction Field of Integral Domains FractionField() FractionFieldEmbedding FractionFieldEmbeddingSection FractionField_1poly_field FractionField_generic is_FractionField() Fraction Field Elements FractionFieldElement FractionFieldElement_1poly_field is_FractionFieldElement() make_element() make_element_old() Localization# Localization Localization LocalizationElement normalize_extra_units() Ring Extensions# Extension of rings RingExtensionFactory RingExtensionFractionField RingExtensionWithBasis RingExtensionWithGen RingExtension_generic common_base() generators() tower_bases() variable_names() Elements lying in extension of rings RingExtensionElement RingExtensionFractionFieldElement RingExtensionWithBasisElement Morphisms between extension of rings MapFreeModuleToRelativeRing MapRelativeRingToFreeModule RingExtensionBackendIsomorphism RingExtensionBackendReverseIsomorphism RingExtensionHomomorphism Utilities# Big O for various types (power series, p-adics, etc.) O() Signed and Unsigned Infinities AnInfinity FiniteNumber InfinityRing InfinityRing_class LessThanInfinity MinusInfinity PlusInfinity SignError UnsignedInfinity UnsignedInfinityRing UnsignedInfinityRing_class is_Infinite() test_comparison() test_signed_infinity() Support Python’s numbers abstract base class register_sage_classes() Derivation# Derivations RingDerivation RingDerivationModule RingDerivationWithTwist_generic RingDerivationWithoutTwist RingDerivationWithoutTwist_fraction_field RingDerivationWithoutTwist_function RingDerivationWithoutTwist_quotient RingDerivationWithoutTwist_wrapper RingDerivationWithoutTwist_zero Indices and Tables# Index Module Index Search Page