msolve: A Library for Solving Polynomial Systems
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We present a new open source C library dedicated to solving multivariate polynomial systems of dimension zero through computer algebra methods. The core algorithmic framework of 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 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 with leading computer algebra systems such as Magma, Maple, Singular on a wide range of systems with finitely many complex solutions, showing that can tackle systems which were out of reach by the computer algebra software state-of-the-art.
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