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

base (sage.rings.asymptotic.growth_group.ExponentialGrowthElement attribute)
base_ring() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominatorRing method)
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)
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.MonomialGrowthGroup 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_prec (sage.rings.asymptotic.asymptotic_ring.AsymptoticRing attribute)
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.GenericGrowthGroup attribute)
(sage.rings.asymptotic.growth_group.MonomialGrowthGroup 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)
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)
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)
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)
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

invert() (sage.rings.asymptotic.asymptotic_ring.AsymptoticExpansion 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)
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)
merge_overlapping() (in module sage.rings.asymptotic.misc)
MonomialGrowthElement (class in sage.rings.asymptotic.growth_group)
MonomialGrowthGroup (class in sage.rings.asymptotic.growth_group)
MonomialGrowthGroupFunctor (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
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)
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)
rename_keyword (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominatorRing attribute)
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_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)
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

TermMonoid (in module sage.rings.asymptotic.term_monoid)
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

underlying_class() (in module sage.rings.asymptotic.misc)
univariate_decomposition() (sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator method)
UnivariateProduct (class in sage.rings.asymptotic.growth_group_cartesian)

V

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)

Z

ZeroCoefficientError