Index A | B | C | D | E | F | G | H | I | L | M | N | O | P | Q | R | S | T | U | V | W | Z A absorb() (sage.rings.asymptotic.term_monoid.GenericTerm method) absorption() (in module sage.rings.asymptotic.term_monoid) AbstractGrowthGroupFunctor (class in sage.rings.asymptotic.growth_group) AdditiveMagmas (sage.rings.asymptotic.growth_group.GenericGrowthGroup attribute) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup attribute) algebraic_dependence_certificate() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) algebraic_dependence_decomposition() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) asymptotic_decomposition() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) asymptotic_expansions (in module sage.rings.asymptotic.asymptotic_expansion_generators) AsymptoticExpansion (class in sage.rings.asymptotic.asymptotic_ring) AsymptoticExpansionGenerators (class in sage.rings.asymptotic.asymptotic_expansion_generators) AsymptoticRing (class in sage.rings.asymptotic.asymptotic_ring) AsymptoticRingFunctor (class in sage.rings.asymptotic.asymptotic_ring) asymptotics() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) asymptotics_multiple() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) asymptotics_smooth() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) B B() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing static method) base (sage.rings.asymptotic.growth_group.ExponentialGrowthElement property) (sage.rings.asymptotic.growth_group.GrowthGroupFactor attribute) base_ring() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominatorRing method) bidirectional_merge_overlapping() (in module sage.rings.asymptotic.misc) bidirectional_merge_sorted() (in module sage.rings.asymptotic.misc) Binomial_kn_over_n() (sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators static method) BTerm (class in sage.rings.asymptotic.term_monoid) BTermMonoid (class in sage.rings.asymptotic.term_monoid) C can_absorb() (in module sage.rings.asymptotic.term_monoid) (sage.rings.asymptotic.term_monoid.BTerm method) (sage.rings.asymptotic.term_monoid.ExactTerm method) (sage.rings.asymptotic.term_monoid.GenericTerm method) (sage.rings.asymptotic.term_monoid.OTerm method) cartesian_injection() (sage.rings.asymptotic.growth_group_cartesian.GenericProduct method) CartesianProduct (sage.rings.asymptotic.growth_group.GenericGrowthGroup attribute) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct attribute) (sage.rings.asymptotic.growth_group_cartesian.MultivariateProduct attribute) (sage.rings.asymptotic.growth_group_cartesian.UnivariateProduct attribute) CartesianProductFactory (class in sage.rings.asymptotic.growth_group_cartesian) change_parameter() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) (sage.rings.asymptotic.term_monoid.GenericTermMonoid method) cls (sage.rings.asymptotic.growth_group.GrowthGroupFactor attribute) coefficient_ring (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing property) (sage.rings.asymptotic.term_monoid.GenericTermMonoid property) coefficients_of_generating_function() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) coerce_point() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) cohomology_decomposition() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) combine_exceptions() (in module sage.rings.asymptotic.misc) compare_with_values() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) construction() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup method) (sage.rings.asymptotic.growth_group.ExponentialNonGrowthGroup method) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup method) (sage.rings.asymptotic.growth_group.MonomialNonGrowthGroup method) (sage.rings.asymptotic.term_monoid.BTerm method) (sage.rings.asymptotic.term_monoid.GenericTerm method) (sage.rings.asymptotic.term_monoid.TermWithCoefficient method) create_key_and_extra_args() (sage.rings.asymptotic.growth_group.GrowthGroupFactory method) (sage.rings.asymptotic.growth_group_cartesian.CartesianProductFactory method) (sage.rings.asymptotic.term_monoid.TermMonoidFactory method) create_object() (sage.rings.asymptotic.growth_group.GrowthGroupFactory method) (sage.rings.asymptotic.growth_group_cartesian.CartesianProductFactory method) (sage.rings.asymptotic.term_monoid.TermMonoidFactory method) create_summand() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) critical_cone() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) D DecreasingGrowthElementError default_locals() (sage.rings.asymptotic.misc.Locals method) default_prec (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing property) DefaultTermMonoidFactory (in module sage.rings.asymptotic.term_monoid) denominator() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) denominator_factored() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) denominator_ring (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator property) (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominatorSum property) diff_all() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) diff_op() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) diff_op_simple() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) diff_prod() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) diff_seq() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) dimension() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) direction() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) DivisionRings (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup attribute) E Element (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing attribute) (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominatorRing attribute) (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup attribute) (sage.rings.asymptotic.growth_group.ExponentialNonGrowthGroup attribute) (sage.rings.asymptotic.growth_group.GenericGrowthGroup attribute) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup attribute) (sage.rings.asymptotic.growth_group.MonomialNonGrowthGroup attribute) (sage.rings.asymptotic.term_monoid.BTermMonoid attribute) (sage.rings.asymptotic.term_monoid.ExactTermMonoid attribute) (sage.rings.asymptotic.term_monoid.GenericTermMonoid attribute) (sage.rings.asymptotic.term_monoid.OTermMonoid attribute) (sage.rings.asymptotic.term_monoid.TermWithCoefficientMonoid attribute) error_part() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) exact_part() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) ExactTerm (class in sage.rings.asymptotic.term_monoid) ExactTermMonoid (class in sage.rings.asymptotic.term_monoid) exp() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct.Element method) exponent (sage.rings.asymptotic.growth_group.MonomialGrowthElement property) ExponentialGrowthElement (class in sage.rings.asymptotic.growth_group) ExponentialGrowthGroup (class in sage.rings.asymptotic.growth_group) ExponentialGrowthGroupFunctor (class in sage.rings.asymptotic.growth_group) ExponentialNonGrowthElement (class in sage.rings.asymptotic.growth_group) ExponentialNonGrowthGroup (class in sage.rings.asymptotic.growth_group) ExponentialNonGrowthGroupFunctor (class in sage.rings.asymptotic.growth_group) extend_by_non_growth_group (sage.rings.asymptotic.growth_group.GrowthGroupFactor attribute) extended_by_non_growth_group() (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) extract_variable_names() (sage.rings.asymptotic.growth_group.Variable static method) F factorial() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) factors() (sage.rings.asymptotic.growth_group.GenericGrowthElement method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct.Element method) factory() (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup class method) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup class method) FractionWithFactoredDenominator (class in sage.rings.asymptotic.asymptotics_multivariate_generating_functions) FractionWithFactoredDenominatorRing (class in sage.rings.asymptotic.asymptotics_multivariate_generating_functions) FractionWithFactoredDenominatorSum (class in sage.rings.asymptotic.asymptotics_multivariate_generating_functions) from_construction() (sage.rings.asymptotic.term_monoid.GenericTermMonoid method) G gen() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) GenericGrowthElement (class in sage.rings.asymptotic.growth_group) GenericGrowthGroup (class in sage.rings.asymptotic.growth_group) GenericNonGrowthElement (class in sage.rings.asymptotic.growth_group) GenericNonGrowthGroup (class in sage.rings.asymptotic.growth_group) GenericProduct (class in sage.rings.asymptotic.growth_group_cartesian) GenericProduct.Element (class in sage.rings.asymptotic.growth_group_cartesian) GenericTerm (class in sage.rings.asymptotic.term_monoid) GenericTermMonoid (class in sage.rings.asymptotic.term_monoid) gens() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup method) (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) gens_logarithmic() (sage.rings.asymptotic.growth_group.MonomialGrowthGroup method) gens_monomial() (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct method) grads() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) Groups (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup attribute) growth_group (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing property) (sage.rings.asymptotic.term_monoid.GenericTermMonoid property) GrowthGroup (in module sage.rings.asymptotic.growth_group) GrowthGroupFactor (class in sage.rings.asymptotic.growth_group) GrowthGroupFactory (class in sage.rings.asymptotic.growth_group) H HarmonicNumber() (sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators static method) has_same_summands() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) I ImplicitExpansion() (sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators static method) ImplicitExpansionPeriodicPart() (sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators static method) InverseFunctionAnalysis() (sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators static method) invert() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) is_compatible() (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) (sage.rings.asymptotic.growth_group.PartialConversionElement method) is_constant() (sage.rings.asymptotic.term_monoid.ExactTerm method) (sage.rings.asymptotic.term_monoid.GenericTerm method) is_convenient_multiple_point() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) is_exact() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) (sage.rings.asymptotic.term_monoid.ExactTerm method) (sage.rings.asymptotic.term_monoid.GenericTerm method) is_little_o_of_one() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) (sage.rings.asymptotic.term_monoid.ExactTerm method) (sage.rings.asymptotic.term_monoid.GenericTerm method) (sage.rings.asymptotic.term_monoid.OTerm method) is_lt_one() (sage.rings.asymptotic.growth_group.GenericGrowthElement method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct.Element method) is_monomial() (sage.rings.asymptotic.growth_group.Variable method) L le() (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) (sage.rings.asymptotic.term_monoid.GenericTermMonoid method) leinartas_decomposition() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) limit() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) Locals (class in sage.rings.asymptotic.misc) locals() (sage.rings.asymptotic.misc.WithLocals method) log() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) (sage.rings.asymptotic.growth_group.GenericGrowthElement method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct.Element method) log_factor() (sage.rings.asymptotic.growth_group.GenericGrowthElement method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct.Element method) log_grads() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) log_Stirling() (sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators static method) log_string() (in module sage.rings.asymptotic.misc) log_term() (sage.rings.asymptotic.term_monoid.ExactTerm method) (sage.rings.asymptotic.term_monoid.GenericTerm method) (sage.rings.asymptotic.term_monoid.OTerm method) M maclaurin_coefficients() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) Magmas (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup attribute) (sage.rings.asymptotic.growth_group.GenericGrowthGroup attribute) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup attribute) map_coefficients() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) merge() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRingFunctor method) (sage.rings.asymptotic.growth_group.AbstractGrowthGroupFunctor method) module sage.rings.asymptotic.asymptotic_expansion_generators sage.rings.asymptotic.asymptotic_ring sage.rings.asymptotic.asymptotics_multivariate_generating_functions sage.rings.asymptotic.growth_group sage.rings.asymptotic.growth_group_cartesian sage.rings.asymptotic.misc sage.rings.asymptotic.term_monoid monomial_coefficient() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) MonomialGrowthElement (class in sage.rings.asymptotic.growth_group) MonomialGrowthGroup (class in sage.rings.asymptotic.growth_group) MonomialGrowthGroupFunctor (class in sage.rings.asymptotic.growth_group) MonomialNonGrowthElement (class in sage.rings.asymptotic.growth_group) MonomialNonGrowthGroup (class in sage.rings.asymptotic.growth_group) MonomialNonGrowthGroupFunctor (class in sage.rings.asymptotic.growth_group) MultivariateProduct (class in sage.rings.asymptotic.growth_group_cartesian) N ngens() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) NoConvergenceError non_growth_group() (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup method) (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup method) NotImplementedBZero NotImplementedOZero nullstellensatz_certificate() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) nullstellensatz_decomposition() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) numerator() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) numerator_ring (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator property) O O() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) OTerm (class in sage.rings.asymptotic.term_monoid) OTermMonoid (class in sage.rings.asymptotic.term_monoid) P parent_to_repr_short() (in module sage.rings.asymptotic.misc) PartialConversionElement (class in sage.rings.asymptotic.growth_group) PartialConversionValueError permutation_sign() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) plot_comparison() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) Posets (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup attribute) (sage.rings.asymptotic.growth_group.GenericGrowthGroup attribute) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup attribute) pow() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) Q quotient() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) R rank (sage.rings.asymptotic.asymptotic_ring.AsymptoticRingFunctor attribute) (sage.rings.asymptotic.growth_group.AbstractGrowthGroupFunctor attribute) relative_error() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) repr_op() (in module sage.rings.asymptotic.misc) repr_short_to_parent() (in module sage.rings.asymptotic.misc) rpow() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) (sage.rings.asymptotic.growth_group.GenericGrowthElement method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct.Element method) (sage.rings.asymptotic.term_monoid.ExactTerm method) (sage.rings.asymptotic.term_monoid.GenericTerm method) (sage.rings.asymptotic.term_monoid.OTerm method) S sage.rings.asymptotic.asymptotic_expansion_generators module sage.rings.asymptotic.asymptotic_ring module sage.rings.asymptotic.asymptotics_multivariate_generating_functions module sage.rings.asymptotic.growth_group module sage.rings.asymptotic.growth_group_cartesian module sage.rings.asymptotic.misc module sage.rings.asymptotic.term_monoid module Sets (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup attribute) (sage.rings.asymptotic.growth_group.GenericGrowthGroup attribute) (sage.rings.asymptotic.growth_group.MonomialGrowthGroup attribute) show() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) singular_ideal() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) SingularityAnalysis() (sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators static method) smooth_critical_ideal() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) some_elements() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) (sage.rings.asymptotic.growth_group.ExponentialGrowthGroup method) (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct method) (sage.rings.asymptotic.term_monoid.BTermMonoid method) (sage.rings.asymptotic.term_monoid.GenericTermMonoid method) (sage.rings.asymptotic.term_monoid.TermWithCoefficientMonoid method) split() (sage.rings.asymptotic.growth_group.PartialConversionElement method) split_str_by_op() (in module sage.rings.asymptotic.misc) sqrt() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) Stirling() (sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators static method) strip_symbolic() (in module sage.rings.asymptotic.misc) subs() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) subs_all() (in module sage.rings.asymptotic.asymptotics_multivariate_generating_functions) substitute() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) substitute_raise_exception() (in module sage.rings.asymptotic.misc) sum() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominatorSum method) summands (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion property) symbolic_expression() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) T term_monoid() (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) (sage.rings.asymptotic.term_monoid.GenericTermMonoid method) term_monoid_factory (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing property) (sage.rings.asymptotic.term_monoid.GenericTermMonoid property) TermMonoidFactory (class in sage.rings.asymptotic.term_monoid) TermWithCoefficient (class in sage.rings.asymptotic.term_monoid) TermWithCoefficientMonoid (class in sage.rings.asymptotic.term_monoid) transform_category() (in module sage.rings.asymptotic.misc) truncate() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) U univariate_decomposition() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method) UnivariateProduct (class in sage.rings.asymptotic.growth_group_cartesian) V var (sage.rings.asymptotic.growth_group.GrowthGroupFactor attribute) Variable (class in sage.rings.asymptotic.growth_group) variable_names() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion method) (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing method) (sage.rings.asymptotic.growth_group.GenericGrowthElement method) (sage.rings.asymptotic.growth_group.GenericGrowthGroup method) (sage.rings.asymptotic.growth_group.Variable method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct method) (sage.rings.asymptotic.growth_group_cartesian.GenericProduct.Element method) (sage.rings.asymptotic.term_monoid.GenericTerm method) W whole_and_parts() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominatorSum method) WithLocals (class in sage.rings.asymptotic.misc) Z ZeroCoefficientError