We present a new open source C library msolve dedicated to solving multivariate
polynomial systems of dimension zero through computer algebra methods. The core …

Solving zero-dimensional polynomial systems using Gröbner bases is usually done by, first,
computing a Gröbner basis for the degree reverse lexicographic order, and next computing …

Many new ciphers target a concise algebraic description for efficient evaluation in a proof
system or a multi-party computation. This new target for optimization introduces algebraic …

This paper is concerned with linear algebra based methods for solving exactly polynomial
systems through so-called Gr\" obner bases, which allow one to compute modulo the …

The bottleneck of the SPARSE-FGLM algorithm for Gröbner bases change of order is an
iterative matrix-tall and skinny matrix product over a finite prime field. Our contribution is …

In this contribution, we consider a zero-dimensional polynomial system in $ n $ variables
defined over a field $\mathbb {K} $. In the context of computing a Rational Univariate …

This habilitation thesis deals with polynomial system solving through Gröbner bases
computations. It focuses on the link between multivariate polynomials and linear recurrence …

This article is concerned with the efficient computation of modular matrix multiplication C=
AB mod p, a key kernel in computer algebra. We focus on floating-point arithmetic, which …

Multivariate polynomial systems arising in numerous applications have special structures. In
particular, determinantal structures and invariant systems appear in a wide range of …