SageMath Asymptotic Ring

SageMath's Asymptotic Ring provides a framework for symbolic asymptotic expansions. It combines growth groups with coefficient rings and supports arithmetic with exact terms and asymptotic error terms in one or several variables.

The framework handles polynomial, logarithmic, and exponential growth and provides operations such as multiplication, powers, logarithms, and exponentials of expansions. The SageMath reference manual contains extensive worked examples and describes the available growth groups and term types.

This entry concerns the asymptotic-expansion component of SageMath, not the whole computer algebra system. It is distributed as part of SageMath and is distinct from the separate dependent_bterms extension for explicit error bounds with a dependent secondary variable.