Solving Multivariate Polynomial Systems and Rectangular Multiparameter Eigenvalue Problems with MacaulayLab
摘要
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result of several years of research and algorithmic development. We demonstrate how the software works and compare its performance with other software packages, such as PNLA, PHCpack, and MultiParEig. Some core features of MacaulayLab are the fact that it solves two key problems via one common approach, works independently of the chosen polynomial basis and monomial order, and is capable of dealing with positive-dimensional solution sets at infinity. The toolbox (including its future updates) and a large collection of test problems are freely available online.
关键词
引用
@article{arxiv.2605.20884,
title = {Solving Multivariate Polynomial Systems and Rectangular Multiparameter Eigenvalue Problems with MacaulayLab},
author = {Christof Vermeersch and Bart De Moor},
journal= {arXiv preprint arXiv:2605.20884},
year = {2026}
}
备注
Since the manuscript is currently undergoing review, we anticipate several improvements in the upcoming revision. In particular, the comparison with other software packages will be expanded significantly