48 citations · 93 across the 21 of their papers we have counts for
25 papers
A complexity analysis of the F4 Gröbner basis algorithm with tracer data
Robin Kouba, Vincent Neiger, Mohab Safey El Din
We provide a new complexity bound for the computation of grevlex Gröbner bases in the generic zero-dimensional case, relying on Moreno-Socías' conjecture. We first formalize a prop…
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…
Faster change of order algorithm for Gröbner bases under shape and stability assumptions
Jérémy Berthomieu, Vincent Neiger, Mohab Safey El Din
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…
Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients
Victor Magron, Mohab Safey El Din, Trung-Hieu Vu
Assessing non-negativity of multivariate polynomials over the reals, through the computation of {\em certificates of non-negativity}, is a topical issue in polynomial optimization.…
Computing the dimension of real algebraic sets
Piere Lairez, Mohab Safey El Din
Let be the set of real common solutions to in and be the maximum total degree of the 's. We design an algorithm…
msolve: A Library for Solving Polynomial Systems
Jérémy Berthomieu, Christian Eder, Mohab Safey El Din
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…