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msolve: A Library for Solving Polynomial Systems

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.
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Contributor : Jérémy Berthomieu <>
Submitted on : Tuesday, May 18, 2021 - 4:01:28 PM
Last modification on : Sunday, May 23, 2021 - 3:28:34 AM


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Jérémy Berthomieu, Christian Eder, Mohab Safey El Din. msolve: A Library for Solving Polynomial Systems. 2021 International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint Petersburg, Russia. ⟨10.1145/3452143.3465545⟩. ⟨hal-03191666v2⟩



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