48 citations · 93 across the 21 of their papers we have counts for
5 papers · 1 filter
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…
On the computation of asymptotic critical values of polynomial maps and applications
Jérémy Berthomieu, Andrew Ferguson, Mohab Safey El Din
Let be a polynomial tuple in and let . We consider the problem of comput…
Faster One Block Quantifier Elimination for Regular Polynomial Systems of Equations
Huu Phuoc Le, Mohab Safey El Din
Quantifier elimination over the reals is a central problem in computational real algebraic geometry, polynomial system solving and symbolic computation. Given a semi-algebraic form…