{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/msolve-a-library-for-solving-polynomial","title":"msolve: A Library for Solving Polynomial Systems","arxiv_id":"2104.03572","date":"2021-04-08","proceeding":null,"authors":["Jérémy Berthomieu","Christian Eder","Mohab Safey El Din"],"abstract":"We present a new open source C library \\texttt{msolve} dedicated to solving multivariate polynomial systems of dimension zero through computer algebra methods. The core algorithmic framework of \\texttt{msolve} relies on Gr\\''obner bases and linear algebra based algorithms for polynomial system solving. It relies on Gr\\''obner basis computation w.r.t.\\ the degree reverse lexicographical order, Gr\\''obner conversion to a lexicographical Gr\\''obner basis and real solving of univariate polynomials. We explain in detail how these three main steps of the solving process are implemented, how we exploit \\texttt{AVX2} instruction processors and the more general implementation ideas we put into practice to better exploit the computational capabilities of this algorithmic framework. We compare the practical performances of \\texttt{msolve} with leading computer algebra systems such as \\textsc{Magma}, \\textsc{Maple}, \\textsc{Singular} on a wide range of systems with finitely many complex solutions, showing that \\texttt{msolve} can tackle systems which were out of reach by the computer algebra software state-of-the-art.","url_abs":"https://arxiv.org/abs/2104.03572v2","url_pdf":"https://arxiv.org/pdf/2104.03572v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"msolve-a-library-for-solving-polynomial","repo_url":"https://github.com/sumiya11/groebner.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2104.03572","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}