Supervision : Daniel LAZARD
Co-supervision : MOURRAIN B.

Vers une résolution stable et rapide des équations algébriques

Phd defence : 12/16/2002

Jury members :

Daniel Lazard
Jean-Charles Faugère
Marc Guisti [Rapporteur]
Carlo Traverso [Rapporteur]
Anfré Galligo
Bernard Mourrain

2002-2014 Publications

• 2014
  • B. Mourrain, Ph. Trébuchet : “Toric Border Basis”, Proceedings of the 39^th International Symposium on Symbolic and Algebraic Computation (ISSAC), Kobe, Japan, pp. 343-350, (ACM New York, NY, USA) (2014)
• 2013
  • J.‑B. Lasserre, M. Laurent, B. Mourrain, Ph. Rostalski, Ph. Trébuchet : “Moment Matrices, Border Bases and Real Radical Computation”, Journal of Symbolic Computation, vol. 51, pp. 63-85, (Elsevier) (2013)
  • M. Abril Bucero, B. Mourrain, Ph. Trébuchet : “Unconstraint global polynomial optimization via Gradient Ideal”, (2013)
• 2012
  • B. Mourrain, Ph. Trébuchet : “Border basis representation of a general quotient algebra”, International Conference on Symbolic and Algebraic Computation (ISSAC), Grenoble, France, pp. 265-272, (ACM Press) (2012)
  • J. Van Der Hoeven, G. Lecerf, B. Mourrain, Ph. Trébuchet, J. Berthomieu, D. Diatta, A. Mantzaflaris : “Mathemagix”, ACM Communications in Computer Algebra, vol. 45 (3/4), pp. 186-188, (Association for Computing Machinery (ACM)) (2012)
• 2011
  • G. Benattar, Ph. Trébuchet : “Trend Analysis in Polls, Topics, Opinions and Answers”, (2011)
  • G. Pierron, J.‑L. Lamotte, Ph. Trébuchet : “Modélisation de calcul à partir d’arbres et génération automatique de codes optimisés pour les nouvelles architectures de calcul”, RenPar'20, Saint-Malo, France, pp. 1-8 (2011)
  • B. Mourrain, M. Laurent, J.‑B. Lasserre, Ph. Trébuchet : “Moment matrices, border bases and real radical computation”, MEGA2011, Stockholm, Sweden, pp. 1-23, (MEGA 2011) (2011)
  • B.‑M. Bui‑Xuan, J.‑F. Raymond, Ph. Trébuchet : “Implantation des algorithmes Oum-Seymour et Oum”, 13^es Journées Graphes et Algorithmes 2011, Lyon, France, pp. 1-23 (2011)
  • J. Van Der Hoeven, G. Lecerf, B. Mourrain, Ph. Trébuchet, J. Berthomieu, D. Diatta, A. Mantzaflaris : “Mathemagix, the quest of modularity and efficiency for symbolic and certified numeric computation”, ACM Communications in Computer Algebra, vol. 45 (3), pp. 186-188, (Association for Computing Machinery (ACM)) (2011)
• 2010
  • Ph. Trébuchet : “A new certified numerical algorithm for solving polynomial systems”, SCAN2010, Lyon, France, pp. 1-8 (2010)
• 2009
  • F. Jézéquel, Ch. Denis, Ph. Trébuchet : “Reliable numerical evaluation of eigenvalues involved in polynomial systems solving”, Computer-assisted proofs - tools, methods and applications, Dagstuhl, Germany (2009)
  • S. Graillat, Ph. Trébuchet : “A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system”, ISSAC'09 - Proceedings of the 2009 international symposium on Symbolic and algebraic computation, Seoul, Korea, Republic of, pp. 167-173, (ACM) (2009)
• 2008
  • B. Mourrain, Ph. Trébuchet : “Stable normal forms for polynomial system solving”, Theoretical Computer Science, vol. 409 (2), pp. 229-240, (Elsevier) (2008)
• 2007
  • A. Bonnecaze, Ph. Trébuchet : “Threshold signature for distributed time stamping scheme”, Annals of Telecommunications - annales des télécommunications, vol. 11-12, pp. 1353-1364, (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)
  • B. Mourrain, J.‑P. Pavone, Ph. Trébuchet, Elias P. Tsigaridas, J. Wintz : “SYNAPS: A library for dedicated applications in symbolic numeric computing,”, chapter in Software for algebraic geometry, vol. 148, IMA Volumes in Mathematics and its Applications., pp. 81-110, (Springer) (2007)
• 2006
  • Ph. Trébuchet : “Strong Bi-Homogeneous Bezout theorems and algebraic Geometry”, Elimination Theory and Applications, Luminy, France (2006)
  • Ph. Trébuchet : “Generalized Normal Forms for polynomial system solving”, Workshop on application of Groebner Bases, Linz, Austria (2006)
  • M. Safey El Din, Ph. Trébuchet : “Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry”, 46 pages (2006)
• 2005
  • B. Mourrain, Ph. Trébuchet : “Generalized normal forms and polynomial system solving”, ISSAC 2005 - International Symposium on Symbolic and Algebraic Computation, Beijing, China, pp. 253-260, (ACM New York, NY, USA) (2005)
• 2004
  • Ph. Trébuchet : “Generalized Normal Forms for Positive Dimensional Ideals”, 1^st International Conference on Polynomial System Solving, Paris, France (2004)
  • M. Safey El Din, Ph. Trébuchet : “Strong Bi-homogeneous Bézout’s Theorem and degree bounds for algebraic optimization”, (2004)
• 2002
  • O. Devillers, B. Mourrain, F. Preparata, Ph. Trébuchet : “Circular Cylinders by Four or Five Points in Space”, Discrete and Computational Geometry, vol. 29 (1), pp. 83-104, (Springer Verlag) (2002)
  • O. Grellier, P. Comon, B. Mourrain, Ph. Trébuchet : “Analytical Blind Channel Identification”, IEEE Transactions on Signal Processing, vol. 50 (9), pp. 2196-2207, (Institute of Electrical and Electronics Engineers) (2002)
  • G. Dos Reis, B. Mourrain, Ph. Trébuchet, F. Rouillier : “An environment for Symbolic and Numeric Computation”, International Congress of Mathematical Software - ICMS'2002, Beijing, China, pp. 239-249, (World Scientific) (2002)