Multivariate Power Series in Maple

TL;DR

This paper introduces the MultivariatePowerSeries Maple library, enabling efficient manipulation and analysis of formal multivariate power series with user-friendly features and advanced mathematical methods.

Contribution

The paper presents a new Maple library that implements methods like Weierstrass Preparation and Hensel's lemma for multivariate power series, with performance comparisons.

Findings

Library provides easy-to-use interface for multivariate power series

Implementation uses lazy evaluation and object-oriented features

Experimental results show competitive performance

Abstract

We present MultivariatePowerSeries, a Maple library introduced in Maple 2021, providing a variety of methods to study formal multivariate power series and univariate polynomials over such series. This library offers a simple and easy-to-use user interface. Its implementation relies on lazy evaluation techniques and takes advantage of Maple's features for object-oriented programming. The exposed methods include Weierstrass Preparation Theorem and factorization via Hensel's lemma. The computational performance is demonstrated by means of an experimental comparison with software counterparts.