1998-2021 Publications

• 2021
  • D. Lazard : “Degree of a polynomial ideal and Bézout inequalities”, (2021)
• 2015
  • D. Lazard : “Mobile 4R and 5R loops”, (2015)
• 2011
  • A. Hashemi, D. Lazard : “Sharper complexity bounds for zero-dimensional Göbner bases and polynomial system solving”, International Journal of Algebra and Computation, vol. 21 (5), pp. 703-713, (World Scientific Publishing) (2011)
• 2010
  • D. Lazard : “CAD and topology of semi-algebraic sets”, Mathematics in Computer Science, vol. 4 (1), pp. 93-112, (Springer) (2010)
• 2009
  • D. Lazard : “Algebraic points in geometry and application to {CAD}”, International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS), vol. 22, COE Lecture Note, Fukuoka, Japan, (Kyushu University, Japan) (2009)
  • D. Lazard, S. McCallum : “Iterated Discriminants”, Journal of Symbolic Computation, vol. 44 (9), pp. 1176-1193, (Elsevier) (2009)
  • D. Lazard : “Theorem Proving in Geometry and Tools for Polynomial System Solving”, International Conference on Mathematics Mechanization (ICMM) in honor of professor Wen-Tsun Wu's nineties birthday, Beijing, China (2009)
  • F. Boulier, D. Lazard, F. Ollivier, M. Petitot : “Computing representations for radicals of finitely generated differential ideals”, Applicable Algebra in Engineering, Communication and Computing, vol. 20 (1), pp. 73-121, (Springer Verlag) (2009)
  • D. Lazard : “Thirty years of Polynomial System Solving, and now?”, Journal of Symbolic Computation, vol. 44 (3), pp. 222-231, (Elsevier) (2009)
  • H. Everett, Ch. Gillot, D. Lazard, S. Lazard, M. Pouget : “The Voronoi diagram of three arbitrary lines in R3”, 25^th European Workshop on Computational Geometry - EuroCG'09, Bruxelles, Belgium, pp. 297-300 (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
  • L. Dupont, D. Lazard, S. Lazard, S. Petitjean : “Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm”, Journal of Symbolic Computation, vol. 43 (3), pp. 168-191, (Elsevier) (2008)
  • L. Dupont, D. Lazard, S. Lazard, S. Petitjean : “Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils”, Journal of Symbolic Computation, vol. 43 (3), pp. 192-215, (Elsevier) (2008)
  • L. Dupont, D. Lazard, S. Lazard, S. Petitjean : “Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections”, Journal of Symbolic Computation, vol. 43 (3), pp. 216-232, (Elsevier) (2008)
• 2007
  • G. Nong, D. Lazard, F. Rouillier, X. Yong : “Using computer algebra to certify the global convergence of a numerical optimization process”, Mathematics in Computer Science, vol. 1 (2), pp. 291-304, (Springer) (2007)
  • D. Lazard, S. McCallum : “Iterated Discriminants”, MEGA 2007: Effective Methods in Algebraic Geometry, Strobl, Austria (2007)
  • D. Lazard, F. Rouillier : “Solving parametric polynomial systems”, Journal of Symbolic Computation, vol. 42 (6), pp. 636-667, (Elsevier) (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
  • D. Lazard : “Solving Kaltofen’s Challenge on Zolotarev’s Approximation Problem”, Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, Genova, Italy, pp. 196-203, (ACM) (2006)
  • N. Gu, D. Lazard, F. Rouillier, Y. Xiang : “Using Computer Algebra to Certify the Global Convergence of a Numerical Optimization Process”, Mathematical Aspects of Computer and Information Sciences, Beijing, China, pp. 100-112 (2006)
  • D. Lazard : “Computing with Parameterized Varieties”, chapter in Algebraic Geometry and Geometric Modelling, Mathematics and Visualization, pp. 53-69, (Springer), (ISBN: 978-3-540-332749) (2006)
• 2005
  • A. Hashemi, D. Lazard : “Almost polynomial Complexity for Zero-dimensional Grbner Bases”, ASCM 2005 - 7^th Asian Symposium on Computer Mathematics, Seoul, Korea, Republic of, pp. 16-21 (2005)
  • L. Dupont, D. Lazard, S. Lazard, S. Petitjean : “Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm”, (2005)
  • L. Dupont, D. Lazard, S. Lazard, S. Petitjean : “Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils”, (2005)
  • L. Dupont, D. Lazard, S. Lazard, S. Petitjean : “Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections”, (2005)
• 2004
  • D. Lazard, F. Rouillier : “Solving Parametric Polynomial Systems”, International Conference on Polynomial System Solving, Paris, France, pp. 53-55 (2004)
  • D. Lazard : “Solving Quintics by Radicals”, chapter in The Legacy of Niels Henrik Abel, pp. 207-225, (Springer-Verlag), (ISBN: 3-540-43826-2) (2004)
• 2003
  • L. Dupont, D. Lazard, S. Lazard, S. Petitjean : “Near-Optimal Parameterization of the Intersection of Quadrics”, 19^th Symposium on Computational Geometry - SoCG 2003, San Diego, United States, pp. 246-255, (ACM) (2003)
• 2002
  • I. Kotsireas, D. Lazard : “Central Configurations of the 5-Body Problem with Equal Masses in Three-Space”, Journal of Mathematical Sciences, vol. 108 (6), pp. 1119-1138, (Springer Verlag (Germany)) (2002)
• 2001
  • D. Lazard : “Solving systems of algebraic equations”, Sigsam Bulletin, vol. 35 (3), pp. 11-37, (Association for Computing Machinery) (2001)
  • L. Dupont, D. Lazard, S. Lazard, S. Petitjean : “Towards the Robust Intersection of Implicit Quadrics”, Workshop on Uncertainty in Geometric Computations, vol. 704, The Springer International Series in Engineering and Computer Science, Sheffield, United Kingdom, pp. 59-68, (Springer) (2001)
  • D. Lazard : “On the specification for solvers of polynomial systems”, 5^th Asian Symposium on Computer Mathematics - ASCM 2001, vol. 9, Lecture Notes Series on Computing, Matsuyama, Japan, pp. 66-75, (World Scientific) (2001)
  • D. Lazard : “Résolution numérique des systèmes algébriques par des techniques exactes : application à la mécanique céleste”, Congrès national de mathématiques appliquées et industrielles, SMAI 2001, Pompadour, France, pp. 159-160, (SMAI) (2001)
  • D. Lazard : “Optimality of the parameterization of quadrics and their intersections”, Journées de cloture Visi3D et CoSTIC, Paris, France (2001)
  • D. Lazard : “Systèmes d’équations algébriques et robots parallèles”, Journées nationales de la recherche en robotique - JNRR'2001, Presqu'île de Giens, France, pp. 6 p, (INRIA, Sophia Antipolis) (2001)
• 2000
  • D. Lazard : “Resolution of polynomial systems”, 4^th Asian Symposium on Computer Mathematics - ASCM 2000, vol. 8, Lecture Notes Series on Computing, Chiang Mai, Thailand, pp. 1-8, (World Scientific) (2000)
  • D. Lazard : “Calcul formel : tendances et progrès récents”, Revue des Sciences et Technologies de l'Information - Série TSI : Technique et Science Informatiques, vol. 19 (1-2-3), pp. 325-333, (Lavoisier) (2000)
• 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)
  • I. Kotsireas, D. Lazard : “Central configurations of the 5-body problem with equal masses in three-dimensional space”, “Записки научных семинаров ПОМИ” - Zapiski Nauchnykh. Seminarov POMI - Note des séminaires scientifiques du département de mathématiques de Saint-Pétersbourg de l'Institut Steklov, vol. 258 (4), pp. 292-317, (``Nauka'' S.-Peterburg. Otdel.) (1999)
  • F. Boulier, D. Lazard, F. Ollivier, M. Petitot : “Computing representations for radicals of finitely generated differential ideals”, (1999)
• 1998
  • D. Lazard : “Solving Quintics by Radicals”, (1998)
  • I. Kotsireas, D. Lazard : “Central configurations of the 5-body problem with equal masses in three dimensional space”, CASC'98 - International Workshop on Computer Algebra for Scientific Computing, St.Petersburg, Russian Federation (1998)