Asymptotic Expansions#
The Asymptotic Ring#
The asymptotic ring, as well as its main documentation is contained in the module
Asymptotic Expansion Generators#
Some common asymptotic expansions can be generated in
Supplements#
Behind the scenes of working with asymptotic expressions a couple of additional classes and tools turn up. For instance the growth of each summand is managed in growth groups, see below.
Growth Groups#
The growth of a summand of an asymptotic expression is managed in
Term Monoids#
A summand of an asymptotic expression is basically a term out of the following monoid:
Miscellaneous#
Various useful functions and tools are collected in
Asymptotic Expansions — Table of Contents#
- Asymptotic Ring
- (Informal) Definition
- Introductory Examples
- More Examples
- Selected Technical Details
- Various
- Classes and Methods
AsymptoticExpansionB()O()compare_with_values()error_part()exact_part()exp()factorial()has_same_summands()invert()is_exact()is_little_o_of_one()limit()log()map_coefficients()monomial_coefficient()plot_comparison()pow()rpow()show()sqrt()subs()summandssymbolic_expression()truncate()variable_names()
AsymptoticRingAsymptoticRingFunctorNoConvergenceError
- Common Asymptotic Expansions
- (Asymptotic) Growth Groups
- Description of Growth Groups
- Creating a Growth Group
- Classes and Methods
AbstractGrowthGroupFunctorDecreasingGrowthElementErrorExponentialGrowthElementExponentialGrowthGroupExponentialGrowthGroupFunctorExponentialNonGrowthElementExponentialNonGrowthGroupExponentialNonGrowthGroupFunctorGenericGrowthElementGenericGrowthGroupGenericNonGrowthElementGenericNonGrowthGroupGrowthGroupGrowthGroupFactorGrowthGroupFactoryMonomialGrowthElementMonomialGrowthGroupMonomialGrowthGroupFunctorMonomialNonGrowthElementMonomialNonGrowthGroupMonomialNonGrowthGroupFunctorPartialConversionElementPartialConversionValueErrorVariable
- Cartesian Products of Growth Groups
- (Asymptotic) Term Monoids
- Asymptotic Expansions — Miscellaneous
- Functions, Classes and Methods
LocalsNotImplementedBZeroNotImplementedOZeroWithLocalsbidirectional_merge_overlapping()bidirectional_merge_sorted()combine_exceptions()log_string()parent_to_repr_short()repr_op()repr_short_to_parent()split_str_by_op()strip_symbolic()substitute_raise_exception()transform_category()
- Asymptotics of Multivariate Generating Series
- Introductory Examples
- Various
- Classes and Methods
FractionWithFactoredDenominatoralgebraic_dependence_certificate()algebraic_dependence_decomposition()asymptotic_decomposition()asymptotics()asymptotics_multiple()asymptotics_smooth()cohomology_decomposition()critical_cone()denominator()denominator_factored()denominator_ringdimension()grads()is_convenient_multiple_point()leinartas_decomposition()log_grads()maclaurin_coefficients()nullstellensatz_certificate()nullstellensatz_decomposition()numerator()numerator_ringquotient()relative_error()singular_ideal()smooth_critical_ideal()univariate_decomposition()
FractionWithFactoredDenominatorRingFractionWithFactoredDenominatorSumcoerce_point()diff_all()diff_op()diff_op_simple()diff_prod()diff_seq()direction()permutation_sign()subs_all()