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Bibliography

Major publications by the team in recent years
  • 1L. Busé, M. Elkadi, B. Mourrain.

    Resultant over the residual of a complete intersection, in: J. of Pure and Applied Algebra, 2001, vol. 164, p. 35-57.
  • 2L. Busé, M. Elkadi, B. Mourrain.

    Using projection operators in computer aided geometric design, in: Topics in algebraic geometry and geometric modeling, Providence, RI, Contemp. Math., Amer. Math. Soc., Providence, RI, 2003, vol. 334, p. 321–342.
  • 3M. Elkadi, B. Mourrain.

    Algorithms for residues and Lojasiewicz exponents, in: J. of Pure and Applied Algebra, 2000, vol. 153, p. 27-44.
  • 4M. Elkadi, B. Mourrain.

    Introduction à la résolution des systèmes polynomiaux, Mathématiques et Applications, Springer, 2007, vol. 59.
  • 5Ioannis Z. Emiris, A. Galligo, H. Lombardi.

    Certified approximate univariate GCDs, in: J. Pure & Applied Algebra, Special Issue on Algorithms for Algebra, May 1997, vol. 117 & 118, p. 229–251.
  • 6Ioannis Z. Emiris, B. Mourrain.

    Matrices in elimination theory, in: J. Symbolic Computation, Special Issue on Elimination, 1999, vol. 28, p. 3–44.
  • 7A. Galligo, M. van Hoeij.

    Approximate bivariate factorization: a geometric viewpoint, in: SNC '07: Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation, New York, NY, USA, ACM, 2007, p. 1–10.
  • 8E. Hubert.

    Differential invariants of a Lie group action: syzygies on a generating set, in: Journal of Symbolic Computation, 2009, vol. 44, no 4, p. 382-416. [ DOI : 10.1016/j.jsc.2008.08.003 ]

    http://hal.inria.fr/inria-00178189/en
  • 9E. Hubert, I. Kogan.

    Rational Invariants of a Group Action. Construction and Rewriting, in: Journal of Symbolic Computation, 2007, vol. 42, no 1-2, p. 203-217. [ DOI : 10.1016/j.jsc.2006.03.005 ]

    http://hal.inria.fr/inria-00198847/en
  • 10B. Mourrain, V. Y. Pan.

    Multivariate polynomials, duality and structured Matrices, in: J. of Complexity, 2000, vol. 16, no 1, p. 110-180.
Publications of the year

Doctoral Dissertations and Habilitation Theses

  • 11E. Ba.

    Résultant déterminantiel et applications, Université de Nice Sophia-Antipolis, December 2011.
  • 12J. Brachat.

    Schémas de Hilbert et décompositions de tenseurs, Université de Nice Sophia-Antipolis, July 2011.

    http://hal.inria.fr/tel-00620047/en
  • 13L. Busé.

    Représentations matricielles en théorie de l'élimination et applications à la géométrie, Université de Nice Sophia-Antipolis, April 2011, Habilitation à Diriger des Recherches.

    http://hal.inria.fr/tel-00593603/en
  • 14T. Luu Ba.

    Représentation matricielle implicite de coubres et surface algériques et applications, Université de Nice Sophia-Antipolis, July 2011.

    http://hal.inria.fr/tel-00610499/en

Articles in International Peer-Reviewed Journal

  • 15E. Arrondo, A. Bernardi.

    On the variety parameterizing completely decomposable polynomials, in: Journal of Pure and Applied Algebra, 2011, vol. 215, no 3, p. 201-220. [ DOI : 10.1016/j.jpaa.2010.04.008 ]

    http://hal.inria.fr/hal-00645963/en
  • 16E. Ballico, A. Bernardi.

    Decomposition of homogeneous polynomials with low rank, in: Mathematische Zeitschrift, 2011, Online first p. [ DOI : 10.1007/s00209-011-0907-6 ]

    http://hal.inria.fr/hal-00645978/en
  • 17E. Ballico, A. Bernardi.

    On the X-rank with respect to linear projections of projective varieties, in: Mathematical News / Mathematische Nachrichten, 2011, vol. 284, no 17-18, p. 2133-2140, 10 pages. [ DOI : 10.1002/mana.200910275 ]

    http://hal.inria.fr/hal-00646117/en
  • 18E. Ballico, A. Bernardi.

    On the X-rank with respect to linearly normal curves, in: Collectanea Mathematica, 2011.

    http://hal.inria.fr/hal-00646161/en
  • 19E. Ballico, A. Bernardi.

    Symmetric tensor rank with a tangent vector: a generic uniqueness theorem, in: Proceedings of the American Mathematical Society, 2012.

    http://hal.inria.fr/hal-00645979/en
  • 20A. Bernardi, E. Carlini, M. V. Catalisano.

    Higher secant varieties of ℙ n ×ℙ m embedded in bi-degree (1,d)., in: Journal of Pure and Applied Algebra, 2011, vol. 215, no 12, p. 2853-2858. [ DOI : 10.1016/j.jpaa.2011.04.005 ]

    http://hal.inria.fr/hal-00645976/en
  • 21A. Bernardi, A. Gimigliano, M. Idà.

    Computing symmetric rank for symmetric tensors, in: Journal of Symbolic Computation, 2011, vol. 46, no 1, p. 34-53. [ DOI : 10.1016/j.jsc.2010.08.001 ]

    http://hal.inria.fr/hal-00645973/en
  • 22L. Busé, G. Chèze.

    On the total order of reducibility of a pencil of algebraic plane curves, in: Journal of Algebra, September 2011, vol. 341, no 1, p. 256-278. [ DOI : 10.1016/j.jalgebra.2011.06.006 ]

    http://hal.inria.fr/hal-00348561/en
  • 23L. Busé, G. Chèze, S. Najib.

    Noether's forms for the study of non-composite rational functions and their spectrum, in: Acta Arithmetica, 2011, vol. 147, no 3, p. 217-231. [ DOI : 10.4064/aa147-3-2 ]

    http://hal.inria.fr/inria-00395839/en
  • 24G. Chèze, A. Galligo, B. Mourrain, J.-C. Yakoubsohn.

    A Subdivision Method for Computing Nearest Gcd with Certification, in: Theoretical Computer Science, August 2011, vol. 412, no 35, p. 4493-4503. [ DOI : 10.1016/j.tcs.2011.04.018 ]

    http://hal.inria.fr/inria-00589062/en
  • 25A. Galligo, A. Poteaux.

    Computing monodromy via continuation methods on random Riemann surfaces, in: Theor. Comput. Sci., 2011, vol. 412, no 16, p. 1492-1507.
  • 26E. Hubert.

    Convolution Surfaces based on Polygons for Infinite and Compact Support Kernels, in: Graphical Models, January 2012. [ DOI : 10.1016/j.gmod.2011.07.001 ]

    http://hal.inria.fr/inria-00536840/en
  • 27I. Janovitz-Freireich, B. Mourrain, L. Ronayi, A. Szanto.

    On the Computation of Matrices of Traces and Radicals of Ideals, in: Journal of Symbolic Computation, January 2012, vol. 47, no 1, p. 102-122. [ DOI : 10.1016/j.jsc.2011.08.020 ]

    http://hal.inria.fr/inria-00354120/en
  • 28X. Jia, Y.-K. Choi, B. Mourrain, W. Wang.

    An Algebraic Approach to Continuous Collision Detection for Ellipsoids, in: Computer Aided Geometric Design, March 2011, vol. 28, no 3, p. 164-176. [ DOI : 10.1016/j.cagd.2011.01.004 ]

    http://hal.inria.fr/hal-00646511/en
  • 29A. Mantzaflaris, B. Mourrain, E. Tsigaridas.

    On Continued Fraction Expansion of Real Roots of Polynomial Systems, Complexity and Condition Numbers, in: Theoretical Computer Science, May 2011, vol. 412, no 22, p. 2312-2330. [ DOI : 10.1016/j.tcs.2011.01.009 ]

    http://hal.inria.fr/inria-00530756/en
  • 30G. Xu, B. Mourrain, R. Duvigneau, A. Galligo.

    Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis, in: Computer-Aided Design, August 2011. [ DOI : 10.1016/j.cad.2011.05.007 ]

    http://hal.inria.fr/inria-00539616/en
  • 31G. Xu, B. Mourrain, R. Duvigneau, A. Galligo.

    Parametrization of computational domain in isogeometric analysis: methods and comparison, in: Computer Methods in Applied Mechanics and Engineering, April 2011, vol. 200, no 23-24, p. 2021-2031. [ DOI : 10.1016/j.cma.2011.03.005 ]

    http://hal.inria.fr/inria-00530758/en

International Conferences with Proceedings

  • 32D. Bembe, A. Galligo.

    Virtual Roots of a Real Polynomial and Fractional Derivatives, in: International Symposium on Symbolic and Algebraic Computation (ISSAC), San Jose, United States, A. Leykin (editor), ACM Press, June 2011, p. 27-34, Deutsch-Französische-Hochschule École-Franco-Allemande.. [ DOI : 10.1145/1993886.1993897 ]

    http://hal.archives-ouvertes.fr/hal-00559950/en/
  • 33A. Bernardi, J. Brachat, P. Comon, B. Mourrain.

    Multihomogeneous Polynomial Decomposition using Moment Matrices, in: Proceedings of the 36th international symposium on Symbolic and algebraic computation (ISSAC 11), San Jose, United States, A. Leykin (editor), ACM Press, June 2011, p. 35-42. [ DOI : 10.1145/1993886.1993898 ]

    http://hal.inria.fr/inria-00638837/en
  • 34M. Hodorog, B. Mourrain, J. Schicho.

    An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities, in: 11th International Conference on Computational Science and Its Applications, Santander, Spain, B. Murgante, O. Gervasi, A. Iglesias, D. Taniar, B. Apduhan (editors), Lecture Notes in Computer Science, Springer, Heidelberg, September 2011, vol. 6784, p. 121-131. [ DOI : 10.1007/978-3-642-21931-3_10 ]

    http://hal.inria.fr/hal-00646566/en
  • 35A. Mantzaflaris, B. Mourrain.

    Deflation and Certified Isolation of Singular Zeros of Polynomial Systems, in: International Symposium on Symbolic and Algebraic Computation (ISSAC), San Jose, CA, United States, A. Leykin (editor), ACM New York, June 2011, p. 249-256. [ DOI : 10.1145/1993886.1993925 ]

    http://hal.inria.fr/inria-00556021/en
  • 36G. Xu, B. Mourrain, R. Duvigneau, A. Galligo.

    Variational Harmonic Method for Parameterization of Computational Domain in 2D Isogeometric Analysis, in: 12th International CAD/Graphics 2011 conference, Jinan, China, C. T. Ralph Martin (editor), September 2011.

    http://hal.inria.fr/inria-00585663/en
  • 37C. Zanni, E. Hubert, M.-P. Cani.

    Warp-based Helical Implicit Primitives, in: Shape Modeling International (SMI), Herzliya, Israel, N. Mitra, O. Sorkine, A. Shamir, A. Tal (editors), Computers & Graphics, June 2011, vol. 35, Issue 3, p. 517-523. [ DOI : 10.1016/j.cag.2011.03.027 ]

    http://hal.inria.fr/inria-00605339/en