Ensembles triangulaires de pôlynomes et résolution de systèmes algébriques. Implantation en Axiom

1997-2020 Publications

• 2020
  • Ph. Aubry, J. Marrez, A. Valibouze : “Computing real solutions of fuzzy polynomial systems”, Fuzzy Sets and Systems, vol. 399, pp. 55-76, (Elsevier) (2020)
• 2019
  • Ph. Aubry, J. Marrez, A. Valibouze : “The Real Transform: Computing Positive Solutions of Fuzzy Polynomial Systems”, 11^th International Conference on Fuzzy Computation Theory and Applications, vol. 1: FCTA, Proceedings of the 11^th International Joint Conference on Computational Intelligence, Vienna, Austria, pp. 351-359, (SciTePress - Science and Technology Publications) (2019)
• 2018
  • Ph. Aubry, J. Marrez, A. Valibouze : “Résolution réelle de systèmes polynomiaux flous”, (2018)
  • J. Marrez, Ph. Aubry, A. Valibouze : “Étude et implantation d’une méthode algébrique pour résoudre des systèmes à coefficients flous”, Journées Nationales de Calcul Formel 2018, Luminy, France (2018)
• 2017
  • Ph. Aubry, J. Marrez, A. Valibouze : “Computing real solutions of polynomial fuzzy systems”, (2017)
• 2012
  • Ph. Aubry, A. Valibouze : “Algebraic Computation of resolvents without extraneous powers”, European Journal of Combinatorics, vol. 33 (7), pp. 1369-1385, (Elsevier) (2012)
  • Ph. Aubry, A. Valibouze : “Parallel computation of resolvents by multimodular techniques and decomposition formula”, International Journal of Algebra and Computation, vol. 22 (5), pp. 1-21, (World Scientific Publishing) (2012)
  • T. Zhao, D. Wang, H. Hong, Ph. Aubry : “Real Solution Formulas of Cubic and Quartic Equations Applied to Generate Dynamic Diagrams with Inequality Constraints”, 27^th Annual ACM Symposium on Applied Computing (SAC 2012), Trento, Italy, pp. 94-101 (2012)
• 2011
  • A. Valibouze, Ph. Aubry : “Décomposition et calcul parallèle de la Résolvante de Lagrange”, 2^e Colloque franco-maghrébin de Calcul formel, Iles de Kerkennah, Tunisia (2011)
• 2010
  • Ph. Aubry, A. Valibouze : “Parallel computation of Lagrange resolvents by multi-resolvents”, Parallel Computer Algebra 2010, vol. 15 (4), TSU, Ser. Natural & Technical Sciences, Tambov, Russian Federation, pp. 1328-1341 (2010)
  • Ph. Aubry, A. Valibouze : “Calcul algébrique efficace de résolvantes relatives”, Journées Nationales du Calcul Formel 2010, Luminy, France (2010)
• 2009
  • Ph. Aubry, A. Valibouze : “Calcul algébrique efficace de résolvantes relatives”, (2009)
• 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)
• 2001
  • Ph. Aubry, D. Wang : “Reasoning about Surfaces Using Differential Zero and Ideal Decomposition”, Automated Deduction in Geometry, vol. 2061, Lecture Notes in Computer Science, Zurich, Switzerland, pp. 154-174, (Springer Berlin Heidelberg) (2001)
• 2000
  • Ph. Aubry, A. Valibouze : “Using Galois ideals for computing relative resolvents”, Journal of Symbolic Computation, vol. 30 (6), pp. 635-651, (Elsevier) (2000)
  • Ph. Aubry, F. Rouillier, M. Safey El Din : “Real Solving for positive dimensional systems”, (2000)
  • Ph. Aubry, F. Rouillier, M. Safey El Din : “Real Solving for Positive Dimensional Systems”, 20 pages (2000)
• 1999
  • Ph. Aubry : “Ensembles triangulaires de pôlynomes et résolution de systèmes algébriques. Implantation en Axiom”, thesis, phd defence 01/13/1999, supervision Lazard, D. (1999)
  • Ph. Aubry, A. Valibouze : “Galois ideals and relative resolvents”, Workshop on Galois Theory, Dagstuhl, Germany (1999)
  • Ph. Aubry, D. Lazard, M. Moreno Maza : “On the theories of triangular sets”, Journal of Symbolic Computation, vol. 28 (1-2), pp. 105-124, (Elsevier) (1999)
  • Ph. Aubry, M. Moreno Maza : “Triangular Sets for Solving Polynomial Systems: a Comparative Implementation of Four Methods”, Journal of Symbolic Computation, vol. 28 (1-2), pp. 125-154, (Elsevier) (1999)
• 1998
  • Ph. Aubry, A. Valibouze : “Using Galois ideals for computing relative resolvents”, MEGA'98, Saint Malo, France (1998)
  • Ph. Aubry, A. Valibouze : “Computing characteristic polynomials associated to some quotient rings”, (1998)
• 1997
  • Ph. Aubry, M. Moreno Maza : “Triangular sets for solving polynomial systems :a comparison of four methods”, (1997)