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- Mohab Safey El Din, Ã‰ric 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 andâ€¦ (More)

- Fabrice Rouillier, Marie-FranÃ§oise 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. Weâ€¦ (More)

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

- Mohab Safey El Din, Ã‰ric Schost
- Discrete & Computational Geometry
- 2004

Computing at least one point in each connected component of a real algebraic set is a basic subroutine to decide emptiness of semialgebraic sets, which is a fundamental algorithmic problem inâ€¦ (More)

Let f be a polynomial in Q[X1, . . . , Xn] of degree D and, for t âˆˆ Q, let Ht âŠ‚ C n be the hypersurface defined by f âˆ’ t = 0. The main result of this paper is an algorithm computing at least oneâ€¦ (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>xâˆˆ R<sup>n</sup></sub> f(x) of f (orâ€¦ (More)

- Bernd Bank, Marc Giusti, Joos Heintz, Mohab Safey El Din, Ã‰ric Schost
- Applicable Algebra in Engineering, Communicationâ€¦
- 2009

We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation ofâ€¦ (More)

- Jean-Charles FaugÃ¨re, 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 withâ€¦ (More)

- Hazel Everett, Daniel Lazard, Sylvain Lazard, Mohab Safey El Din
- Discrete & 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,â€¦ (More)

- Mohab Safey El Din, Ã‰ric Schost
- Discrete & Computational Geometry
- 2011

We consider the problem of constructing roadmaps of real algebraic sets. This problem was introduced by Canny to answer connectivity questions and solve motion planning problems. Given s polynomialâ€¦ (More)