sage-acsv: a SageMath package for Analytic Combinatorics in Several Variables¶

This package provides tools for the study of the asymptotic behavior of the sequence of coefficients of rational generating functions in several variables along a given direction.

The public interface of our toolbox is provided by the following functions and classes:

diagonal_asymptotics_combinatorial() – the central function of the package,
get_expansion_terms() – helper function for extracting the terms in the output expansion with more structure,
contributing_points_combinatorial() – computes all contributing points of a combinatorial multivariate rational function,
minimal_critical_points_combinatorial() – computes all non-zero minimal critical points of a combinatorial multivariate rational function,
critical_points() – compute all critical points of a combinatorial multivariate rational function,
ACSVSettings – a class for managing several package-global settings (like the default output format for diagonal_asymptotics_combinatorial(), or the backend used for Gröbner basis computations).

Quickstart¶

The easiest way to install the latest released version of the package is via PyPI simply by running

sage -pip install sage-acsv

or, alternatively, executing a cell containing

%pip install sage-acsv

in a SageMath Jupyter notebook.

The package can be run in an interactive environment in the browser using Binder. The asymptotics module includes a collection of examples illustrating how this package is used to extract coefficient asymptotics from multivariate rational combinatorial generating functions.

An article serving as an introduction to version 0.1.0 of the package and its internals can be found at [SageACSV23].

Reference Manual¶

All public-facing functions and classes in our package are documented in our reference manual.

Bibliography¶

[SageACSV23]

Benjamin Hackl, Andrew Luo, Stephen Melczer, Jesse Selover, and Elaine Wong, Rigorous Analytic Combinatorics in Several Variables in SageMath, Sém. Lothar. Combin., vol. 89B, no. 90, pp. 1–12, 2023; arXiv:2303.09603 [math.CO].