48 citations · 51 across the 12 of their papers we have counts for
14 papers
Computing points in connected components defined by a real inequation: algorithms, complexity and implementations, Part I
Jérémy Berthomieu, Edern Gillot, Mohab Safey El Din
We consider the problem of computing sample points in each connected component of a semi-algebraic set defined by the non-vanishing or the positivity of an n-variate polynomial of…
Multiword matrix multiplication over large finite fields in floating-point arithmetic
Jérémy Berthomieu, Stef Graillat, Dimitri Lesnoff +1
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…
Computing submatrices of the Hermite normal form of a structured polynomial matrix
Jérémy Berthomieu, Vincent Neiger, Hugo Passe
Following several decades of successive algorithmic improvements, works from the 2010s have showed how to compute the Hermite normal form (HNF) of a univariate polynomial matrix wi…
Extracting Linear Relations from Gröbner Bases for Formal Verification of And-Inverter Graphs
Daniela Kaufmann, Jérémy Berthomieu
Formal verification techniques based on computer algebra have proven highly effective for circuit verification. The circuit, given as an and-inverter graph, is encoded as a set of…
Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting
Jérémy Berthomieu, Rafael Mohr
We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifti…
Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems
Alin Bostan, Jérémy Berthomieu, Andrew Ferguson +1
We consider ideals involving the maximal minors of a polynomial matrix. For example, those arising in the computation of the critical values of a polynomial restricted to a variety…