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.

翻译：我们介绍了Matlab工具箱MacaulayLab，该工具箱实现了求解多元多项式系统和矩形多参数特征值问题的数值线性代数算法。其结构与功能是多年研究与算法开发的成果。我们展示了该软件的工作方式，并将其性能与PNLA、PHCpack及MultiParEig等其他软件包进行了比较。MacaulayLab的核心特性包括：通过统一方法解决两类关键问题、独立于所选多项式基与单项式序、以及能够处理无穷远处正维解集。该工具箱（含未来更新版本）及大量测试问题集均可免费在线获取。