Mohab Safey El Din

Associate professor
Mohab.Safey[at]lip6.fr
Universite Pierre et Marie Curie (Paris 6)
INRIA Paris-Rocquencourt Research Center
Joint INRIA/UPMC/LIP6 Project-Team PolSys
Laboratoire d'Informatique de Paris 6

Research: Computer Algebra, Polynomial System Solving, Computational Real Algebraic Geometry

Projects:

ANR/NSFC international project EXACTA (Coordinator of the french part)
ECCA Project at LIAMA (joint-coordination with L. Zhi)
ANR Project GeoLMI (local coordinator, national coordination: D. Henrion)
ANR Project HPAC (participant, national coordination: J.G. Dumas)
Associate Team QOLAPS with NCSU and ARIC (coordinator)

Software: RAGLib Maple package dedicated to real solutions of polynomial systems

Students: Pierre-Jean Spaenlehauer (jointly supervised with Jean-Charles Faugère), Aurélien Greuet (jointly supervised with Vincent Cossart)

Publications:

Grobner bases and critical points: the unmixed case, J.-C. Faugère, M. Safey El Din, P.-J. Spaenlehauer
ISSAC 2012 Proceedings, to appear.
Preliminary version [pdf]

Variant Quantifier Elimination, H. Hong, M. Safey El Din
Journal of Symbolic Computation, to appear.
Preliminary version [pdf]

Global optimization of polynomials restricted to a smooth variety using sums of squares, A. Greuet, F. Guo, M. Safey El Din, L. Zhi
Journal of Symbolic Computation, 47(5):503-518, 2012.
Preliminary version [pdf]

Deciding reachability of the infimum of a multivariate polynomial, A. Greuet, M. Safey El Din
ISSAC 2011 Proceedings, San Jose, 2011.
Preliminary version [pdf]

Grobner bases of bihomogeneous ideals generated by polynomials of bidegree (1,1): algorithms and complexity, J.-C. Faugère, M. Safey El Din, P.-J. Spaenlehauer
Journal of Symbolic Computation, 46(4):406--437, 2011.
Preliminary version [pdf]

A baby steps/giant steps probabilistic algorithm for computing roadmaps in smooth bounded real hypersurfaces, M. Safey El Din, E. Schost
Discrete and Computational Geometry, 45(1):181--220, 2011.
Preliminary version [pdf]

Polynomial System Solver over the Reals: Algorithms, Complexity, Implementations and Applications, M. Safey El Din,
Habilitation Thesis, Univ. Pierre and Marie Curie (Paris 06), 2010.

Computing rational points in convex semi-algebraic sets and sums of squares decompositions, M. Safey El Din, L. Zhi
SIAM Journal on Optimization, 20(6):2876-2889, 2010.
Preliminary version [pdf]

Global Optimization of Polynomials Using Generalized Critical Values and Sums of Squares, F. Guo, M. Safey El Din, L. Zhi
ISSAC 2010 Proceedings, Munich, 2010.
Preliminary version [pdf]

Computing Loci of Rank Defects of Linear Matrices using Grobner Bases and Applications to Cryptology, J.C. Faugere, M. Safey El Din, P.J. Spaenlehauer
ISSAC 2010 Proceedings, Munich, 2010.
Preliminary version [pdf]

On the geometry of polar varieties, B. Bank, M. Giusti, J. Heintz, M. Safey El Din, E. Schost
Applicable Algebra in Engineering, Communication and Computing, 21(1): 33-83, 2010.
Preliminary version [pdf].

The Voronoi diagram of three lines H. Everett, D. Lazard, S. Lazard, M. Safey El Din,
Discrete and Computational Geometry, 42(1):94-130, 2009.
Preliminary version [pdf]

Variant real quantifier elimination: algorithm and application, H. Hong, M. Safey El Din,
ISSAC 2009 Proceedings, J. May (eds), South-Korea (Seoul), 2009.
Preliminary version [pdf]

De l'algèbre linéaire à la résolution des systèmes polynomiaux, J.C. Faugère, M. Safey El Din,
Chapitre de livre paru dans un ouvrage collectif sur les mathématiques appliquées, Pearson Editions, 2009

Computing the global optimum of a multivariate polynomial over the reals, M. Safey El Din,
ISSAC 2008 Proceedings, D. Jeffrey (eds), Austria (Hagenberg), 2008.
Preliminary version [pdf]

Classification of the Perspective-Three-Point problem, Discriminant variety and Real solving polynomial systems of inequalities J.-C. Faugere, G. Moroz, F. Rouillier, M. Safey El Din,
ISSAC 2008 Proceedings, D. Jeffrey (eds), Austria (Hagenberg), 2008.
Preliminary version [pdf]

Practical and theoretical issues for the computation of generalized critical values of a polynomial mapping and its applications, M. Safey El Din
LNAI Proceedings of the Asian Symposium on Computer Mathematics (ASCM) 2007, Vol. 5081, Singapoure, 2008.
Preliminary version [pdf]

Testing Sign Conditions on a Multivariate Polynomial and Applications, M. Safey El Din,
Mathematics in Computer Science Journal, Special inaugural issue on algorithms and complexity, H. Hong and C. Yap (Guest editors), Birkhauser, 31 pages, 2007.
Preliminary version [ps], [pdf]

The Voronoi diagram of three lines in $R^3$, H. Everett, D. Lazard, S. Lazard, M. Safey El Din,
Symposium on Computational Geometry, 27 pages, 2007.
Preliminary version [ps][pdf]

Algorithmes efficaces en géométrie algébrique réelle, (Efficient algorithms in real algebraic geometry in french), M. Safey El Din,
Invited course at National Days of Computer Algebra,
notes du cours dispensé aux Journées Nationales du Calcul Formel 2007, 126 pages.
(version de janvier 2007) [pdf]

POSIX Threads Polynomials (PTPol): a scalable implementation of univariate arithmetic operations, M. Safey El Din, P. Trébuchet,
PASCO'2007 (Parrallel Symbolic Computation), 2007, 3 pages.
Preliminary version [pdf]

Generalized critical values and testing sign conditions on a polynomial, M. Safey El Din,
Proceedings of Mathematical Aspects of Computer and Information Science, 24 pages, Beijing, 2006.
Preliminary version [ps], [pdf]

Computing roadmaps in smooth real algebraic sets, M. Mezzarobba, M. Safey El Din,
Proceedings of Transgressive Computing 2006, J.-G. Dumas (Eds), pp.327-338, 2006.
Preliminary version [pdf]

Finding sampling points on real hypersurfaces is easier in singular situations, M. Safey El Din,
MEGA Conference, 6 pages, 2005.
MEGA 2005 [ps], [pdf]

Properness defects of projections and computation of one point in each connected component of a real algebraic set, M. Safey El Din, E. Schost,
Discrete and Computational Geometry, Vol.32 Number 3, pp. 417-430, Sept. 2004.
Preliminary version in gzipped format [ps]

Generalized critical values and solving polynomial inequalities, M. Safey El Din,
Extended abstract, Proc. International Conference on Polynomial System Solving (ICPSS), in honor of D. Lazard, Paris, 2004.
[ps] [pdf]

On the practical computation of one point in each connected component of a semi-algebraic set defined by a polynomial systems of equations and non-strict inequalities, C. Le Guernic, F. Rouillier, M. Safey El Din,
in Proceedings of EACA'04 conference, L.Gonzalez-Vega and T. Recio Eds, 2004.
Preliminary version in format [ps] [pdf]

Polar varieties and computation of one point in each connected component of a smooth real algebraic set, M. Safey El Din, E. Schost,
in Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, Philadelphia PA, 224-231, ACM Press, 2003.
Preliminary version in gzipped format [ps]

Real Solving for positive dimensional systems, P. Aubry, F. Rouillier, M. Safey El Din,
Journal of Symbolic Computation, Vol. 34 (6), 543-560, December 2002.
Preliminary version in gzipped format [ps]

Resolution reelle des systemes polynomiaux en dimension positive, M. Safey El Din,
PhD Thesis of Pierre et Marie Curie University, 2001.
[pdf]

Solving the Birkhoff Interpolation Problem via the Critical Point Method : an Expermiental Study, F. Rouillier, M. Safey El Din, E. Schost,
Lecture Notes in Computer Science, Automated deduction in geometry, ADG'2000, Zurich, Switzerland, September 25-27, revised papers, Editors: J. Richter-Gebert, D. Wang, Springer-Verlag, Heidelberg.
Preliminary version in gzipped format [ps]

Finding at least one point in each connected component of a real algebraic set defined by a single equation, F. Rouillier, M.-F. Roy, M. Safey El Din,
Journal of Complexity, vol. 16, 716-750, 2000.
Preliminary version in format [pdf]

New Structure Theorems for subresultants, H. Lombardi, M.-F. Roy, M. Safey El Din,
Journal of Symbolic Computation, Special Issue on Symbolic Computation in Algebra, Analysis and Geometry, Avril/Mai 2000.
Preliminary version in format [pdf]