Laboratoire d'informatique de l'École polytechnique

Talk by Mohab Safey El Din: « msolve: a library for solving multivariate polynomial systems »

Speaker: Mohab Safey El Din (Sorbonne Université)
Location: Room Grace Hopper
Date: Tue, 7 Dec 2021, 11:00-12:00

Abstract: In this talk, we present a new open source library, developed with J. Berthomieu (Sorbonne Univ.) and C. Eder (TU Kaiserslautern) named msolve, for solving multivariate polynomial systems through computer algebra methods. Its core algorithmic framework relies on Gröbner bases and linear algebra based algorithms. This includes J.-C. Faugère’s F4 algorithm, recent variants of the FGLM change of ordering and real root isolation.This talk will cover a short presentation of the current functionalities provided by msolve, followed by an overview of the implemented algorithms which will motivate the design choices underlying the library. We will also compare the practical performances of msolve with leading computer algebra systems such as Magma, Maple, Singular, showing that msolve can tackle systems which were out of reach by the computer algebra software state-of-the-art. If time permits, we will report on new algorithmic developments for ideal theoretic operations (joint work with J. Berthomieu and C. Eder) and change of orderings algorithms (joint work with J. Berthomieu and V. Neiger).

Further details can be found on the webpage of the seminar: http://www.lix.polytechnique.fr/max/max-web/max/max-seminar.en.html