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Asymptotic Expansions
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B
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C
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D
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E
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F
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G
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H
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I
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L
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M
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N
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O
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P
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Q
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R
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S
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T
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U
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V
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W
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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
base (sage.rings.asymptotic.growth_group.ExponentialGrowthElement attribute)
(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)
C
can_absorb() (in module sage.rings.asymptotic.term_monoid)
(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)
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 attribute)
(sage.rings.asymptotic.term_monoid.GenericTermMonoid attribute)
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)
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
default_locals() (sage.rings.asymptotic.misc.Locals method)
default_prec (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing attribute)
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 attribute)
(sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominatorSum attribute)
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.ExactTermMonoid attribute)
(sage.rings.asymptotic.term_monoid.GenericTermMonoid attribute)
(sage.rings.asymptotic.term_monoid.OTermMonoid attribute)
(sage.rings.asymptotic.term_monoid.TermWithCoefficientMonoid attribute)
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 attribute)
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)
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 attribute)
(sage.rings.asymptotic.term_monoid.GenericTermMonoid attribute)
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)
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 attribute)
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
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.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 attribute)
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 attribute)
(sage.rings.asymptotic.term_monoid.GenericTermMonoid attribute)
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
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