Solving Multivariate Polynomial Systems and Rectangular Multiparameter Eigenvalue Problems with MacaulayLab
For researchers in polynomial system solving and eigenvalue problems, MacaulayLab provides a unified, efficient, and freely available toolbox with unique capabilities, though it is an incremental contribution over existing software.
MacaulayLab is a Matlab toolbox that solves multivariate polynomial systems and rectangular multiparameter eigenvalue problems using numerical linear algebra algorithms. It outperforms PNLA, PHCpack, and MultiParEig on test problems and handles positive-dimensional solution sets at infinity.
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.