Résolution réelle des systèmes polynomiaux en dimension positive

2000-2025 Publications

• 2025
  • J. Elliott, M. Giesbrecht, E. Gillot, M. Safey El Din, E. Schost : “Refined bit complexity for the computation of at least onepoint per connected component of a smooth completeintersection real algebraic set”, (2025)
  • S. Naldi, M. Safey El Din, A. Taylor, W. Wang : “Solving generic parametric linear matrix inequalities”, ISSAC '25: International Symposium on Symbolic and Algebraic Computation, Guanajuato, Mexico (2025)
  • Ch. Eder, R. Mohr, M. Safey El Din : “Gröbner Bases for Polynomial Ideals and Applications”, chapter in The Computer Algebra System OSCAR: Algorithms and Examples, vol. 32, Algorithms and Computation in Mathematics, pp. 271-295, (Springer Nature Switzerland), (ISBN: 978-3-031-62127-7) (2025)
  • M. Safey El Din, G. Scholten, E. Trélat : “Probabilistic algorithm for computing all local minimizers of Morse functions on a compact domain”, (2025)
• 2024
  • S. Gopalakrishnan, V. Neiger, M. Safey El Din : “Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations”, Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation, ISSAC '24, Raleigh, NC, United States, pp. 400–409, (ACM), (ISBN: 9798400706967) (2024)
  • L. Gaillard, M. Safey El Din : “Solving parameter-dependent semi-algebraic systems”, Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation, ISSAC '24, Raleigh, NC, United States, pp. 447-456, (ACM), (ISBN: 9798400706967) (2024)
  • A. Colotti, J. García Fontán, A. Goldsztejn, S. Briot, F. Chaumette, O. Kermorgant, M. Safey El Din : “Determination of All Stable and Unstable Equilibria for Image-Point-Based Visual Servoing”, IEEE Transactions on Robotics, vol. 40, pp. 3406-3424, (IEEE) (2024)
  • R. Prébet, M. Safey El Din, E. Schost : “Computing roadmaps in unbounded smooth real algebraic sets II: algorithm and complexity”, (2024)
  • R. Prébet, M. Safey El Din, E. Schost : “Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results”, Journal of Symbolic Computation, vol. 120, pp. 102234, (Elsevier) (2024)
  • A. Ferguson, G. Ottaviani, M. Safey El Din, E. Turatti : “On the degree of varieties of sum of squares”, Journal of Pure and Applied Algebra, (Elsevier) (2024)
• 2023
  • Ch. Eder, P. Lairez, R. Mohr, M. Safey El Din : “A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System”, Journal of Symbolic Computation, vol. 119, pp. 1-21, (Elsevier) (2023)
  • A. Yabo, M. Safey El Din, J.‑B. Caillau, J.‑L. Gouzé : “Stability analysis of a bacterial growth model through computer algebra”, MathematicS In Action, vol. 12 (1), pp. 175-189, (Société de Mathématiques Appliquées et Industrielles (SMAI)) (2023)
  • J. Berthomieu, Ch. Eder, M. Safey El Din : “New efficient algorithms for computing Gröbner bases of saturation ideals (F4SAT) and colon ideals (Sparse-FGLM-colon)”, (2023)
  • A. Bostan, H. Notarantonio, M. Safey El Din : “Fast Algorithms for Discrete Differential Equations”, ISSAC 2023 - 48^th International Symposium on Symbolic and Algebraic Computation, Tromso, Norvège, Norway (2023)
  • S. Gopalakrishnan, V. Neiger, M. Safey El Din : “Refined F5 Algorithms for Ideals of Minors of Square Matrices”, ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, Tromsø, Norway (2023)
  • J.‑Ch. Faugère, G. Labahn, M. Safey El Din, E. Schost, Th. Vu : “Computing critical points for invariant algebraic systems”, Journal of Symbolic Computation, vol. 116, pp. 365-399, (Elsevier) (2023)
  • D. Henrion, S. Naldi, M. Safey El Din : “Algebraic certificates for the truncated moment problem”, (2023)
  • Ch. Eder, P. Lairez, R. Mohr, M. Safey El Din : “A Direttissimo Algorithm for Equidimensional Decomposition”, ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, Tromsø, Norway (2023)
  • V. Magron, M. Safey El Din, T.‑H. VU : “Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients”, SIAM Journal on Optimization, vol. 33 (1), (Society for Industrial and Applied Mathematics) (2023)
  • J. Capco, M. Safey El Din, J. Schicho : “Positive dimensional parametric polynomial systems, connectivity queries and applications in robotics”, Journal of Symbolic Computation, vol. 115, pp. 320-345, (Elsevier) (2023)
• 2022
  • J. Berthomieu, A. Bostan, A. Ferguson, M. Safey El Din : “Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems”, Journal of Algebra, vol. 602, pp. 154-180, (Elsevier) (2022)
  • D. Chablat, R. Prébet, M. Safey El Din, D. Salunkhe, Ph. Wenger : “Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry”, ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Lille, France (2022)
  • P. Trutman, M. Safey El Din, D. Henrion, T. Pajdla : “Globally Optimal Solution to Inverse Kinematics of 7DOF Serial Manipulator”, IEEE Robotics and Automation Letters, vol. 7 (3), pp. 6012-6019, (IEEE) (2022)
  • J. Berthomieu, M. Safey El Din : “Guessing Gröbner Bases of Structured Ideals of Relations of Sequences”, Journal of Symbolic Computation, vol. 111, pp. 1-26, (Elsevier) (2022)
  • V. Magron, M. Safey El Din, M. Schweighofer, T. Vu : “Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients”, International Symposium on Symbolic and Algebraic Computation (ISSAC), Lille, France (2022)
  • J. Berthomieu, A. Ferguson, M. Safey El Din : “Computing the set of asymptotic critical values of polynomial mappings from smooth algebraic sets”, (2022)
  • J. García Fontán, A. Nayak, S. Briot, M. Safey El Din : “Singularity Analysis for the Perspective-Four and Five-Line Problems”, International Journal of Computer Vision, vol. 130, pp. 909-932, (Springer Verlag) (2022)
  • H. Le, M. Safey El Din : “Solving parametric systems of polynomial equations over the reals through Hermite matrices”, Journal of Symbolic Computation, vol. 112, pp. 25-61, (Elsevier) (2022)
  • A. Bostan, F. Chyzak, H. Notarantonio, M. Safey El Din : “Algorithms for discrete differential equations of order 1”, ISSAC 2022 - 47^th International Symposium on Symbolic and Algebraic Computation, Lille, France, pp. 101–110 (2022)
  • J. Berthomieu, V. Neiger, M. Safey El Din : “Faster change of order algorithm for Gröbner bases under shape and stability assumptions”, 47^th International Symposium on Symbolic and Algebraic Computation, Lille, France (2022)
• 2021
  • V. Magron, M. Safey El Din : “On Exact Reznick, Hilbert-Artin and Putinar’s Representations”, Journal of Symbolic Computation, vol. 107, pp. 221-250, (Elsevier) (2021)
  • H. Le, M. Safey El Din : “Faster One Block Quantifier Elimination for Regular Polynomial Systems of Equations”, Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation (ISSAC '21), Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation, Saint Petersburg, Russian Federation, pp. 265–272 (2021)
  • J. Berthomieu, Ch. Eder, M. Safey El Din : “msolve: A Library for Solving Polynomial Systems”, ISSAC '21: Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation, Saint Petersburg, Russian Federation, pp. 51-58 (2021)
  • D. Henrion, S. Naldi, M. Safey El Din : “Exact algorithms for semidefinite programs with degenerate feasible set”, Journal of Symbolic Computation, vol. 104, pp. 942-959, (Elsevier) (2021)
  • Jonathan D. Hauenstein, M. Safey El Din, E. Schost, Th. Vu : “Solving determinantal systems using homotopy techniques”, Journal of Symbolic Computation, vol. 104, pp. 754-804, (Elsevier) (2021)
  • J. Berthomieu, A. Ferguson, M. Safey El Din : “On the computation of asymptotic critical values of polynomial maps and applications”, (2021)
  • B. Pascual‑Escudero, A. Nayak, S. Briot, O. Kermorgant, Ph. Martinet, M. Safey El Din, F. Chaumette : “Complete Singularity Analysis for the Perspective-Four-Point Problem”, International Journal of Computer Vision, vol. 129 (4), pp. 1217–1237, (Springer Verlag) (2021)
  • B. Bérard, S. Haddad, C. Picaronny, M. Safey El Din, M. Sassolas : “Polynomial interrupt timed automata: Verification and expressiveness”, Information and Computation, vol. 277, pp. 104580, (Elsevier) (2021)
  • J. Berthomieu, A. Ferguson, M. Safey El Din : “Towards fast one-block quantifier elimination through generalised critical values”, ACM Communications in Computer Algebra, vol. 54 (3), Kalamata, Greece, pp. 109-113, (Association for Computing Machinery (ACM)) (2021)
  • M. Safey El Din, Zh. Yang, L. Zhi : “Computing real radicals and S-radicals of polynomial systems”, Journal of Symbolic Computation, vol. 102, pp. 259-278, (Elsevier) (2021)
  • P. Lairez, M. Safey El Din : “Computing the dimension of real algebraic sets”, ISSAC 2021 - 46^th International Symposium on Symbolic and Algebraic Computation, Saint-Pétersbourg, Russian Federation, pp. 257-264 (2021)
  • G. Labahn, M. Safey El Din, E. Schost, Th. Vu : “Homotopy techniques for solving sparse column support determinantal polynomial systems”, Journal of Complexity, vol. 66, pp. 101557, (Elsevier) (2021)
• 2020
  • J. Capco, M. Safey El Din, J. Schicho : “Robots, computer algebra and eight connected components”, ISSAC '20: International Symposium on Symbolic and Algebraic Computation, ISSAC'20: Proceedings of the 45^th International Symposium on Symbolic and Algebraic Computation, Kalamata / Virtual, Greece, pp. 62-69, (ACM) (2020)
  • M. Safey El Din, Ch. Yap : “Special Issue on Symbolic and Algebraic Computation: ISSAC 2017”, Journal of Symbolic Computation, vol. 98, (Elsevier) (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, (Springer Verlag) (2020)
  • H. Le, M. Safey El Din, T. De Wolff : “Computing the real isolated points of an algebraic hypersurface”, ISSAC '20: International Symposium on Symbolic and Algebraic Computation, Proceedings of the 45^th International Symposium on Symbolic and Algebraic Computation, Kalamata / Virtual, Greece, pp. 297–304 (2020)
  • N. Kaihnsa, Y. Ren, M. Safey El Din, J. Martini : “Cooperativity, absolute interaction, and algebraic optimization”, Journal of Mathematical Biology, (Springer) (2020)
• 2019
  • P. Lairez, M. Mezzarobba, M. Safey El Din : “Computing the volume of compact semi-algebraic sets”, ISSAC'19, Beijing, China, (ACM) (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 & Francis) (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, (Elsevier) (2019)
• 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, United States, 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, United States (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, United States, pp. 17p. (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, (Society for Industrial and Applied Mathematics) (2018)
  • V. Magron, M. Safey El Din : “On Exact Polya and Putinar’s Representations”, Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, New-York, United States, pp. 279-286, (ACM) (2018)
  • M. Safey El Din, E. Schost : “Bit complexity for multi-homogeneous polynomial system solving Application to polynomial minimization”, Journal of Symbolic Computation, vol. 87, pp. 176-206, (Elsevier) (2018)
• 2017
  • M. Safey El Din, E. 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, (Association for Computing Machinery) (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)
  • 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)
  • 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)
  • 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)
  • M. Safey El Din, P.‑J. Spaenlehauer : “Critical Point Computations on Smooth Varieties: Degree and Complexity bounds”, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, Waterloo, Canada, pp. 183-190 (2016)
• 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)
  • B. Bérard, S. Haddad, C. Picaronny, M. Safey El Din, M. Sassolas : “Polynomial Interrupt Timed Automata”, The 9^th Workshop on Reachability Problems (RP'15), vol. 9328, Lecture Notes in Computer Science, Warsaw, Poland, pp. 20-32, (Springer) (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)
  • 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)
  • M. Safey El Din : “Algorithmes efficaces en géométrie algébrique réelle”, chapter in Informatique Mathématique Une photographie en 2015, (CNRS Editions), (ISBN: 978-2-271-08791-1) (2015)
• 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 Press) (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)
  • S. Basu, M.‑F. Roy, M. Safey El Din, E. Schost : “A Baby Step–Giant Step Roadmap Algorithm for General Algebraic Sets”, Foundations of Computational Mathematics, vol. 14 (6), pp. 1117-1172, (Springer Verlag) (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) (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, Boston, United States, pp. 5-6 (2013)
  • J.‑Ch. Faugère, M. Safey El Din, Th. Verron : “On the Complexity of Computing Gröbner Bases for Quasi-homogeneous Systems”, ISSAC '13 : Proceedings of the 38^th International Symposium on Symbolic and Algebraic Computation, Boston, Maine, United States, pp. 189-196, (ACM) (2013)
  • M. Safey El Din, E. Tsigaridas : “A probabilistic algorithm to compute the real dimension of a semi-algebraic set”, (2013)
• 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, France, pp. 162-169, (ACM) (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), pp. 503-518, (Elsevier) (2012)
  • H. Hong, M. Safey El Din : “Variant Quantifier Elimination”, Journal of Symbolic Computation, vol. 47 (7), International Symposium on Symbolic and Algebraic Computation (ISSAC 2009), pp. 883-901, (Elsevier) (2012)
• 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), pp. 406-437, (Elsevier) (2011)
  • M. Safey El Din, E. 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, (Springer Verlag) (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, United States, pp. 131-138, (ACM) (2011)
• 2010
  • M. Safey El Din : “Résolution de systèmes polynomiaux sur les réels : algorithmes, complexité, implantations et applications”, habilitation, phd defence 12/10/2010 (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, United States (2010)
  • F. Guo, M. Safey El Din, L. Zhi : “Global Optimization of Polynomials Using Generalized Critical Values and Sums of Squares”, ISSAC '10: Proceedings of the 2010 international symposium on Symbolic and algebraic computation, Munich, Germany, pp. 107-114, (ACM) (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, United States, (SIAM) (2010)
  • B. Bank, M. Giusti, J. Heintz, M. Safey El Din, E. Schost : “On the geometry of polar varieties”, Applicable Algebra in Engineering, Communication and Computing, vol. 21 (1), pp. 33-83, (Springer Verlag) (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, (Society for Industrial and Applied Mathematics) (2010)
  • J.‑Ch. Faugère, M. Safey El Din, P.‑J. Spaenlehauer : “Computing Loci of Rank Defects of Linear Matrices using Gröbner Bases and Applications to Cryptology”, ISSAC 2010 - 35^th International Symposium on Symbolic and Algebraic Computation, Munich, Germany, pp. 257-264, (ACM) (2010)
• 2009
  • H. Hong, M. Safey El Din : “Variant real quantifier elimination: algorithm and application”, ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation, Seoul, Korea, Republic of, pp. 183-190, (ACM) (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)
  • 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, (Springer Verlag) (2009)
• 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) (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, Hagenberg, Austria, pp. 79-86, (ACM) (2008)
• 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)
  • M. Safey El Din : “Testing Sign Conditions on a Multivariate Polynomial and Applications”, Mathematics in Computer Science, vol. 1 (1), pp. 177-207, (Springer) (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) (2007)
  • M. Safey El Din : “Algorithmes efficaces en géométrie algébrique réelle”, Journées Nationales de Calcul Formel, Marseille, France, pp. 1-126 (2007)
  • H. Everett, D. Lazard, S. Lazard, M. Safey El Din : “The Voronoi Diagram of Three Lines”, Proceedings of the twenty-third annual symposium on Computational geometry, Gyeongju, Korea, Republic of, pp. 255-264, (ACM) (2007)
• 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, Beijing, China, pp. 61-84 (2006)
  • M. Safey El Din : “Critical Point Method: theory and practice using Grobner Bases”, Special Semester on Groebner Bases, Linz, Austria (2006)
  • M. Mezzarobba, M. Safey El Din : “Computing roadmaps in smooth real algebraic sets”, Transgressive Computing 2006, Granada, Spain, pp. 327-338 (2006)
  • M. Safey El Din, Ph. Trébuchet : “Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry”, 46 pages (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)
• 2004
  • M. Safey El Din : “Generalized Critical Values and Solving Polynomial Inequalities”, 1^st International Conference on Polynomial System Solving, Paris, France (2004)
  • M. Safey El Din, E. 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, (Springer Verlag) (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)
  • 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”, (2004)
  • M. Safey El Din, Ph. Trébuchet : “Strong Bi-homogeneous Bézout’s Theorem and degree bounds for algebraic optimization”, (2004)
• 2003
  • M. Safey El Din, E. 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, United States, 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, (Elsevier) (2002)
  • M. Safey El Din, E. Schost : “Properness defects of projections and computation of one point in each connected component of a real algebraic set”, (2002)
• 2001
  • M. Safey El Din : “Résolution réelle des systèmes polynomiaux en dimension positive”, thesis, phd defence 01/05/2001, supervision 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, (Elsevier) (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, (Elsevier) (2000)
  • Ph. Aubry, F. Rouillier, M. Safey El Din : “Real Solving for positive dimensional systems”, (2000)
  • F. Rouillier, M. Safey El Din, E. 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, Zurich, Switzerland, pp. 26-40, (Springer) (2000)
  • Ph. Aubry, F. Rouillier, M. Safey El Din : “Real Solving for Positive Dimensional Systems”, 20 pages (2000)