5 Аспиранты (Научны(е)й руководител(и)ь / Со-руководитель)

• FERGUSON Andrew : Doctorant
• GARCIA FONTAN Jorge : Singularity and stability of sensor - based controller
• LE Huu Phuoc : Design and implementation of efficient algorithms in semi-algebraic geometry
• VU Thi Xuan : Faster algorithms for strutures polynomial systems and applications
• VU Trung Hieu : Certificats exacts de positivité pour l'optimisation polynomiale

2 Кандидаты наук 2012 - 2016

Публикации 1998-2020

• 2020
  • D. Henrion, S. Naldi, M. Safey El Din : “Real root finding for low rank linear matrices”, Applicable Algebra in Engineering, Communication and Computing, vol. 31, pp. 101-133 (2020)
• 2019
  • V. Magron, M. Safey El Din, M. Schweighofer : “Algorithms for Weighted Sums of Squares Decomposition of Non-negative Univariate Polynomials”, Journal of Symbolic Computation, vol. 93, pp. 200-220 (2019)
  • M. Safey El Din, Zh. Yang, L. Zhi : “Computing real radicals and S-radicals of polynomial systems”, Journal of Symbolic Computation, (Elsevier) (2019)
  • D. Henrion, S. Naldi, M. Safey El Din : “SPECTRA – a Maple library for solving linear matrix inequalities in exact arithmetic”, Optimization, Methods and Software, vol. 34 (1), pp. 62-78, (Taylor and Francis) (2019)
  • P. Lairez, M. Mezzarobba, M. Safey El Din : “Computing the volume of compact semi-algebraic sets”, ISSAC 2019 - International Symposium on Symbolic and Algebraic Computation, Beijing, China, (ACM) (2019)
• 2018
  • H. Fawzi, M. Safey El Din : “A lower bound on the positive semidefinite rank of convex bodies”, SIAM Journal on Applied Algebra and Geometry, vol. 2 (1), pp. 126-139, (SIAM) (2018)
  • M. Safey El Din, É. Schost : “Bit complexity for multi-homogeneous polynomial system solving Application to polynomial minimization”, Journal of Symbolic Computation, vol. 87, pp. 176-206, (Elsevier) (2018)
  • V. Magron, M. Safey El Din : “RealCertify: a Maple package for certifying non-negativity”, ACM Communications in Computer Algebra, vol. 52 (2), pp. 34-37, (Association for Computing Machinery (ACM)) (2018)
  • D. Henrion, S. Naldi, M. Safey El Din : “Exact algorithms for semidefinite programs with degenerate feasible set”, ISSAC 2018 - 43^rd International Symposium on Symbolic and Algebraic Computation, New York City, USA, pp. 17p. (2018)
  • V. Magron, M. Safey El Din : “On Exact Polya and Putinar’s Representations”, ISSAC '18 International Symposium on Symbolic and Algebraic Computation, New York, USA, pp. 279-286, (ACM) (2018)
  • M. Safey El Din, Zh. Yang, L. Zhi : “On the complexity of computing real radicals of polynomial systems”, ISSAC '18 - The 2018 ACM on International Symposium on Symbolic and Algebraic Computation, New-York, USA, pp. 351-358, (ACM) (2018)
  • C. Riener, M. Safey El Din : “Real root finding for equivariant semi-algebraic systems”, ISSAC 20018 - 43^rd International Symposium on Symbolic and Algebraic Computation, New-York, USA (2018)
  • V. Magron, M. Safey El Din : “On Exact Polya, Hilbert-Artin and Putinar’s Representations”, (2018)
  • Jonathan D. Hauenstein, M. Safey El Din, É. Schost, Th. Vu : “Solving determinantal systems using homotopy techniques”, (2018)
• 2017
  • M. Safey El Din, É. Schost : “A nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets”, Journal of the ACM (JACM), vol. 63 (6), pp. 48:1-48:37, (ACM) (2017)
  • B. Bonnard, O. Cots, J.‑Ch. Faugère, A. Jacquemard, J. Rouot, M. Safey El Din, Th. Verron : “Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to Magnetic Resonance Imaging”, (2017)
• 2016
  • D. Henrion, S. Naldi, M. Safey El Din : “Exact algorithms for linear matrix inequalities”, SIAM Journal on Optimization, vol. 26 (4), pp. 2512-2539, (Society for Industrial and Applied Mathematics) (2016)
  • J.‑Ch. Faugère, M. Safey El Din, Th. Verron : “On the complexity of computing Gröbner bases for weighted homogeneous systems”, Journal of Symbolic Computation, vol. 76, pp. 107-141, (Elsevier) (2016)
  • D. Henrion, S. Naldi, M. Safey El Din : “Real root finding for determinants of linear matrices”, Journal of Symbolic Computation, vol. 74, pp. 205-238, (Elsevier) (2016)
  • M. Safey El Din, P.‑J. Spaenlehauer : “Critical Point Computations on Smooth Varieties: Degree and Complexity bounds”, International Symposium on Symbolic and Algebraic Computation (ISSAC), Waterloo, Canada, pp. 183-190, (ACM) (2016)
  • B. Bonnard, J.‑Ch. Faugère, A. Jacquemard, M. Safey El Din, Th. Verron : “Determinantal sets, singularities and application to optimal control in medical imagery”, International symposium on symbolic and algebraic computations, Waterloo, Canada, pp. 103-110, (ACM) (2016)
• 2015
  • F. Guo, M. Safey El Din, W. Chu, L. Zhi : “Optimizing a Parametric Linear Function over a Non-compact Real Algebraic Variety”, Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, Bath, United Kingdom, pp. 205-212, (ACM) (2015)
  • B. Bérard, S. Haddad, C. Picaronny, M. Safey El Din, M. Sassolas : “Polynomial Interrupt Timed Automata”, Proceedings of the 9^th Workshop on Reachability Problems (RP'15), vol. 9328, Lecture Notes in Computer Science, Warsaw, Poland, pp. 20-32, (Springer) (2015)
  • I. Bannwarth, M. Safey El Din : “Probabilistic Algorithm for Computing the Dimension of Real Algebraic Sets”, ISSAC'15 - 40^th International Symposium on Symbolic and Algebraic Computation, Bath, United Kingdom, pp. 37-44, (ACM) (2015)
  • D. Henrion, S. Naldi, M. Safey El Din : “Real root finding for rank defects in linear Hankel matrices”, International Symposium on Symbolic and Algebraic Computation (ISSAC), Bath, United Kingdom, pp. 221-228, (ACM) (2015)
  • M. Safey El Din : “Algorithmes efficaces en géométrie algébrique réelle”, chapter in Informatique Mathématique Une photographie en 2015, (CNRS Editions) (2015)
• 2014
  • S. Basu, M.‑F. Roy, M. Safey El Din, É. Schost : “A Baby Step--Giant Step Roadmap Algorithm for General Algebraic Sets”, Foundations of Computational Mathematics, vol. 14 (6), pp. 1117-1172, (Springer Verlag (Germany)) (2014)
  • B. Bank, M. Giusti, J. Heintz, M. Safey El Din : “Intrinsic complexity estimates in polynomial optimization”, Journal of Complexity, vol. 30 (4), pp. 430-443, (Elsevier) (2014)
  • A. Greuet, M. Safey El Din : “Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set”, SIAM Journal on Optimization, vol. 24 (3), pp. 1313-1343, (Society for Industrial and Applied Mathematics) (2014)
  • A. Bostan, Th. Combot, M. Safey El Din : “Computing necessary integrability conditions for planar parametrized homogeneous potentials”, ISSAC'14 - International Symposium on Symbolic and Algebraic Computation, Kobe, Japan, pp. 67-74, (ACM) (2014)
• 2013
  • J.‑Ch. Faugère, M. Safey El Din, P.‑J. Spaenlehauer : “On the Complexity of the Generalized MinRank Problem”, Journal of Symbolic Computation, vol. 55, pp. 30-58, (Elsevier), (ISBN: 0747-7171) (2013)
  • Q. Guo, M. Safey El Din, L. Zhi : “Computing rational solutions of linear matrix inequalities”, ISSAC 2013 - International Symposium on Symbolic and Algebraic Computation, Boston, United States (2013)
  • M. Safey El Din : “Critical Point Methods and Effective Real Algebraic Geometry: New Results and Trends”, ISSAC 2013 - 38^th International Symposium on Symbolic and Algebraic Computation, M. Kauers (Ed.), Boston, United States, pp. 5-6, (ACM) (2013)
  • J.‑Ch. Faugère, M. Safey El Din, Th. Verron : “On the complexity of Computing Gröbner Bases for Quasi-homogeneous Systems”, Proceedings of the 38^th international symposium on symbolic and algebraic computation, Boston, Maine, USA, pp. 189-196, (ACM), (ISBN: 978-1-4503-2059-7) (2013)
  • M. Safey El Din, E. Tsigaridas : “A probabilistic algorithm to compute the real dimension of a semi-algebraic set”, (2013)
• 2012
  • A. Greuet, F. Guo, M. Safey El Din, L. Zhi : “Global optimization of polynomials restricted to a smooth variety using sums of squares”, Journal of Symbolic Computation, vol. 47 (5), Duluth, MN, USA, pp. 503-518, (Academic Press, Inc.) (2012)
  • H. Hong, M. Safey El Din : “Variant Quantifier Elimination”, Journal of Symbolic Computation, vol. 47 (7), pp. 883-901 (2012)
  • J.‑Ch. Faugère, M. Safey El Din, P.‑J. Spaenlehauer : “Critical Points and Gröbner Bases: the Unmixed Case”, ISSAC 2012 - International Symposium on Symbolic and Algebraic Computation - 2012, Grenoble, FranceNew York, NY, USA, pp. 162-169, (ACM), (ISBN: 978-1-4503-1269) (2012)
• 2011
  • M. Safey El Din, É. Schost : “A baby steps/giant steps Monte Carlo algorithm for computing roadmaps in smooth compact real hypersurfaces”, Discrete and Computational Geometry, vol. 45 (1), pp. 181-220, (ISBN: 0179-5376) (2011)
  • J.‑Ch. Faugère, M. Safey El Din, P.‑J. Spaenlehauer : “Gröbner Bases of Bihomogeneous Ideals Generated by Polynomials of Bidegree (1,1): Algorithms and Complexity”, Journal of Symbolic Computation, vol. 46 (4), Duluth, MN, USA, pp. 406-437, (Academic Press, Inc.), (ISBN: 0747-7171) (2011)
  • A. Greuet, M. Safey El Din : “Deciding reachability of the infimum of a multivariate polynomial”, ISSAC 2011 - 36^th International Symposium on Symbolic and Algebraic Computation, San Jose, USA, pp. 131-138, (ACM), (ISBN: 978-1-4503-0675-1) (2011)
• 2010
  • M. Safey El Din, L. Zhi : “Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions”, SIAM Journal on Optimization, vol. 20 (6), pp. 2876-2889, (SIAM) (2010)
  • B. Bank, M. Giusti, J. Heintz, M. Safey El Din, É. Schost : “On the geometry of polar varieties”, Applicable Algebra in Engineering, Communication and Computing, vol. 21 (1), pp. 33-83, (ISBN: 0938-1279) (2010)
  • J.‑Ch. Faugère, M. Safey El Din, P.‑J. Spaenlehauer : “Computing Loci of Rank Defects of Linear Matrices using Grobner Bases and Applications to Cryptology”, ISSAC 2010 - 35^th International Symposium on Symbolic and Algebraic Computation, Munich, Germany, pp. 257-264, (ACM), (ISBN: 978-1-4503-0150-3) (2010)
  • M. Safey El Din : “Fast Algorithms for Real Solving Polynomial Systems of Inequalities/inequations”, SIAM Conference on Parallel Processing and Scientific Computing -- High Performance Symbolic Computing, Seattle, USA, (SIAM) (2010)
  • F. Guo, M. Safey El Din, L. Zhi : “Global Optimization of Polynomials Using Generalized Critical Values and Sums of Squares”, ISSAC 2010 - 35^th International Symposium on Symbolic and Algebraic Computation, Munich, Germany, pp. 107-114, (ACM), (ISBN: 978-1-4503-0150-3) (2010)
  • M. Safey El Din : “Stability Analysis of Numerical Schemes with a Variant Quantifier Elimination Algorithm over the Reals”, Hybrid Methodologies for Symbolic-Numeric Computation, Berkeley, USA (2010)
  • M. Safey El Din : “Résolution de systèmes polynomiaux sur les réels : algorithmes, complexité, implantations et applications”, хабилитация, Защита диссертаций 10.12.2010 (2010)
• 2009
  • H. Everett, D. Lazard, S. Lazard, M. Safey El Din : “The Voronoi diagram of three lines”, Discrete and Computational Geometry, vol. 42 (1), pp. 94-130, (ISBN: 0179-5376) (2009)
  • H. Hong, M. Safey El Din : “Variant real quantifier elimination: algorithm and application”, ISSAC '09: the 2009 international symposium on Symbolic and algebraic computation, Seoul, South Korea, pp. 183-190, (ACM), (ISBN: 978-1-60558-609-0) (2009)
  • J.‑Ch. Faugère, M. Safey El Din : “De l’algèbre linéaire à la résolution des systèmes polynomiaux”, chapitre de Mathématiques Appliquées (L3), pp. 331-388, (Pearson), (ISBN: 978-2-7440-7352-6) (2009)
  • M. Safey El Din, L. Zhi : “Computing rational points in convex semi-algebraic sets and SOS decompositions”, n°RR-7045, INRIA (2009)
• 2008
  • J.‑Ch. Faugère, G. Moroz, F. Rouillier, M. Safey El Din : “Classification of the Perspective-Three-Point problem, discriminant variety and real solving polynomial systems of inequalities”, ISSAC 2008 - 21^st International Symposium on Symbolic and Algebraic Computation, D. Jeffrey (Ed.), Hagenberg, Austria, pp. 79-86, (ACM), (ISBN: 978-1-59593-904-3) (2008)
  • M. Safey El Din : “Practical and Theoretical Issues for the Computation of Generalized Critical Values of a Polynomial Mapping”, Computer Mathematics: 8^th Asian Symposium, ASCM 2007. Revised and Invited Papers, vol. 5081, Lecture Notes in Computer Science, Singapore, Singapore, pp. 42-56, (Springer-Verlag), (ISBN: 978-3-540-87826-1) (2008)
• 2007
  • M. Safey El Din : “Testing Sign Conditions on a Multivariate Polynomial and Applications”, Mathematics in Computer Science, vol. 1 (1), pp. 177-207, (ISBN: 1661-8270) (2007)
  • M. Safey El Din : “Algorithmes efficaces en géométrie algébrique réelle”, Journées Nationales de Calcul Formel, Marseille, France, pp. 1-126 (2007)
  • M. Safey El Din, Ph. Trébuchet : “POSIX threads polynomials(PTPol): a scalable implementation of univariate arithmetic operations”, PASCO 2007 - 2007 international workshop on Parallel symbolic computation, London, Ontario, Canada, pp. 104-106, (ACM), (ISBN: 978-1-59593-741-4) (2007)
  • M. Safey El Din : “Real solving polynomial systems of inequalities: the case of bounded sets of solutions”, Mathematical Aspects of Computer and Information Sciences 2007, Paris, France (2007)
  • H. Everett, D. Lazard, S. Lazard, M. Safey El Din : “The Voronoi diagram of three lines”, 23^rd Annual Symposium on Computational Geometry (SoCG'07), Gyeongju, South Korea, pp. 255-264 (2007)
• 2006
  • M. Mezzarobba, M. Safey El Din : “Computing roadmaps in smooth real algebraic sets”, Transgressive Computing 2006, J.-G. Dumas (Ed.), Granada, Spain, pp. 327-338 (2006)
  • M. Safey El Din : “Critical Point Method: theory and practice using Grobner Bases”, Special Semester on Groebner Bases, Linz, Austria (2006)
  • M. Safey El Din : “Generalized critical values and testing sign conditions on a polynomial”, Proceedings of International Conference on Mathematical Aspects of Computer and Information Sciences, D. Wang, Zh. Zheng (Eds.), Beijing, China, pp. 61-84 (2006)
  • M. Safey El Din, Ph. Trébuchet : “Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry”, n°RR-6001, 46 pages, INRIA (2006)
• 2005
  • M. Safey El Din : “Finding Sampling Points on Real Hypersurfaces in Easier in Singular Situations”, MEGA 2005 - 8^th International Symposium on Effective Methods in Algebraic Geometry, Porto Conte, Alghero, Sardinia, Italy (2005)
  • M. Safey El Din : “Computing Sampling Points on a Singular Real Hypersurface using Lagrange’s System”, n°RR-5464, 19 pages, INRIA (2005)
• 2004
  • M. Safey El Din, É. Schost : “Properness Defects of Projections and Computation of at Least One Point in Each Connected Component of a Real Algebraic Set”, Discrete and computational geometry, vol. 32 (3), pp. 417-430 (2004)
  • C. Le Guernic, F. Rouillier, M. Safey El Din : “Computing sampling points in a semi-algebraic set defined by non-strict inequalities, Application to Pattern-Matching Problems”, EACA 2004 - Encuentro de Álgebra Computacional y Aplicaciones, Santander, Spain, (ACM Press) (2004)
  • M. Safey El Din : “Generalized Critical Values and Solving Polynomial Inequalities”, 1^st International Conference on Polynomial System Solving, Paris, France (2004)
  • C. Le Guernic, M. Safey El Din : “On the practical computation of one point in each connected component of a semi-algebraic set defined by a polynomial system of equations and non-strict inequalities”, n°RR-5079, INRIA (2004)
  • M. Safey El Din, Ph. Trébuchet : “Strong Bi-homogeneous Bézout’s Theorem and degree bounds for algebraic optimization”, n°RR-5071, INRIA (2004)
• 2003
  • M. Safey El Din, É. Schost : “Polar varieties and computation of one point in each connected component of a smooth real algebraic set”, International Symposium on Symbolic and Algebraic Computation 2003 - ISSAC'2003, Philadelphie, PA, USA, pp. 224-231, (ACM Press) (2003)
• 2002
  • Ph. Aubry, F. Rouillier, M. Safey El Din : “Real solving for positive dimensional systems”, Journal of Symbolic Computation, vol. 34 (6), pp. 543-560 (2002)
  • M. Safey El Din, É. Schost : “Properness defects of projections and computation of one point in each connected component of a real algebraic set”, n°RR-4598, INRIA (2002)
• 2001
  • M. Safey El Din : “Résolution réelle des systèmes polynomiaux en dimension positive”, диссертация, Защита диссертаций 05.01.2001, Научны(е)й руководител(и)ь Lazard, D. (2001)
• 2000
  • F. Rouillier, M.‑F. Roy, M. Safey El Din : “Finding at least one point in each connected component of a real algebraic set defined by a single equation”, Journal of complexity, vol. 16 (4), pp. 716-750, (ISBN: 0885-064X) (2000)
  • H. Lombardi, M.‑F. Roy, M. Safey El Din : “New structure theorems for subresultants”, Journal of symbolic computation, vol. 29 (4-5), pp. 663-690 (2000)
  • F. Rouillier, M. Safey El Din, É. Schost : “Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study”, Third International Workshop on Automated Deduction in Geometry - ADG'2000, vol. 2061, Lecture Notes in Computer Science, D. Wang, J. Richter-Gebert (Eds.), Zurich, Switzerland, pp. 26-40, (Springer) (2000)
  • Ph. Aubry, F. Rouillier, M. Safey El Din : “Real solving for positive dimensional systems”, LIP6, (Rapport de recherche) (2000)
• 1998
  • M.‑F. Roy, M. Safey El Din : “New subresultant algorithms”, LIP6, (Rapport de recherche) (1998)
  • F. Rouillier, M.‑F. Roy, M. Safey El Din : “Testing emptiness of real hypersurfaces, real algebraic sets, and real semi-algebraic sets”, LIP6, (Rapport de recherche) (1998)