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- Mohab Safey El Din, Éric Schost
- ISSAC
- 2003

Let f<inf>1</inf>, ldots, f<inf>s</inf> be polynomials in <b>Q</b>[X<inf>1</inf>, ..., X<inf>n</inf>] that generate a radical ideal and let V be their complex zero-set. Suppose that V is smooth and… (More)

- Fabrice Rouillier, Marie-Françoise Roy, Mohab Safey El Din
- J. Complexity
- 2000

Deciding efficiently the emptiness of a real algebraic set defined by a single equation is a fundamental problem of computational real algebraic geometry. We propose an algorithm for this test. We… (More)

- Philippe Aubry, Fabrice Rouillier, Mohab Safey El Din
- J. Symb. Comput.
- 2002

Finding one point on each semi-algebraically connected component of a real algebraic variety, or at least deciding if such a variety is empty or not, is a fundamental problem of computational real… (More)

- Jean-Charles Faugère, Mohab Safey El Din, Pierre-Jean Spaenlehauer
- J. Symb. Comput.
- 2011

Solving multihomogeneous systems, as a wide range of structured algebraic systems occurring frequently in practical problems, is of first importance. Experimentally, solving these systems with… (More)

- Hazel Everett, Sylvain Lazard, Daniel Lazard, Mohab Safey El Din
- Symposium on Computational Geometry
- 2007

We give a complete description of the Voronoi diagram of three lines in R3. In particular, we show that the topology of the Voronoi diagram is invariant for three lines in general position, that is,… (More)

- Mohab Safey El Din
- Mathematics in Computer Science
- 2007

Let f be a polynomial in \({\mathbb{Q}}[X_1, \ldots , X_n]\) of degree D. We focus on testing the emptiness and computing at least one point in each connected component of the semi-algebraic set… (More)

- Mohab Safey El Din, Éric Schost
- Discrete & Computational Geometry
- 2004

Abstract
Computing at least one point in each connected component of a real
algebraic set is a basic subroutine to decide emptiness of
semi-algebraic sets, which is a fundamental algorithmic… (More)

- Aurélien Greuet, Mohab Safey El Din
- SIAM Journal on Optimization
- 2013

Let $f, f_1, \ldots, f_\nV$ be polynomials with rational coefficients in the indeterminates $\bfX=X_1, \ldots, X_n$ of maximum degree $D$ and $V$ be the set of common complex solutions of… (More)

- Mohab Safey El Din
- ISSAC
- 2008

Let f be a polynomial in Q[X<sub>1</sub>, ..., X<sub>n</sub>] of degree D. We provide an efficient algorithm in practice to compute the global supremum sup<sub>x∈ R<sup>n</sup></sub> f(x) of f (or… (More)

Let f be a polynomial in Q[X1, . . . , Xn] of degree D and, for t ∈ Q, let Ht ⊂ C n be the hypersurface defined by f − t = 0. The main result of this paper is an algorithm computing at least one… (More)