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, 307 p.
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, n^o 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, n^o 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, n^o 1, p. 110-180.

Publications of the year

Articles in International Peer-Reviewed Journals

11E. Ballico, A. Bernardi.

A partial stratification of secant varieties of Veronese varieties via curvilinear subschemes, in: Sarajevo Journal of Mathematics, 2012, n^o 1, p. 33-52.

http://hal.inria.fr/inria-00610522
12E. Ballico, A. Bernardi.

Decomposition of homogeneous polynomials with low rank, in: Mathematische Zeitschrift, 2012, p. 1141-1149. [ DOI : 10.1007/s00209-011-0907-6 ]

http://hal.inria.fr/hal-00645978
13E. Ballico, A. Bernardi.

Symmetric tensor rank with a tangent vector: a generic uniqueness theorem, in: Proceedings of the American Mathematical Society, 2012, n^o 10, p. 3377-3384. [ DOI : 10.1090/S0002-9939-2012-11191-8 ]

http://hal.inria.fr/hal-00645979
14E. Ballico, A. Bernardi.

Tensor ranks on tangent developable of Segre varieties, in: Linear and Multilinear Algebra, August 2012. [ DOI : 10.1080/03081087.2012.716430 ]

http://hal.inria.fr/inria-00610362
15E. Ballico, A. Bernardi, M. V. Catalisano.

Higher secant varieties of $ℙ^{n} \times ℙ^{1}$ embedded in bi-degree $(a, b)$ , in: Communications in Algebra, October 2012, n^o 10, p. 3822-3840, 19 pages. [ DOI : 10.1080./00927872.2011.595748 ]

http://hal.inria.fr/hal-00646167
16E. Ballico, A. Bernardi, M. V. Catalisano, L. Chiantini.

Grassmann secants and linear systems of tensors., in: Linear Algebra and its Applications, 2013, p. 121-135. [ DOI : 10.1016/j.laa.2012.07.045 ]

http://hal.inria.fr/inria-00637780
17A. Bernardi, J. Brachat, P. Comon, B. Mourrain.

General Tensor Decomposition, Moment Matrices and Applications, in: Journal of Symbolic Computation, August 2012, to appear. [ DOI : 10.1016/j.jsc.2012.05.012 ]

http://hal.inria.fr/inria-00590965
18A. Bernardi, I. Carusotto.

Algebraic Geometry tools for the study of entanglement: an application to spin squeezed states, in: Journal of Physics A: Mathematical and Theoretical, 2012, p. 105304-105317. [ DOI : 10.1088/1751-8113/45/10/105304 ]

http://hal.inria.fr/inria-00618450
19A. Bernardi, K. Ranestad.

On the cactus rank of cubic forms, in: Journal of Symbolic Computation, 2013, p. 291-297. [ DOI : 10.1016/j.jsc.2012.08.001 ]

http://hal.inria.fr/inria-00630456
20L. Busé, C. D'Andrea.

Singular factors of rational plane curves, in: Journal of Algebra, 2012, vol. 357, p. 322-346.

http://hal.inria.fr/hal-00714544
21L. Busé, B. T. Luu.

The surface/surface intersection problem by means of matrix based representations, in: Computer Aided Geometric Design, 2012, vol. 29, n^o 8, p. 579-598. [ DOI : 10.1016/j.cagd.2012.04.002 ]

http://hal.inria.fr/inria-00620947
22D. Diatta, B. Mourrain, O. Ruatta.

On the isotopic meshing of an algebraic implicit surface, in: Journal of Symbolic Computation, August 2012, vol. 47, n^o 8, p. 903-925. [ DOI : 10.1016/j.jsc.2011.09.010 ]

http://hal.inria.fr/hal-00421214
23B. Dmitry, O. Min-Jae, K. Taewan, B. Mourrain.

On the problem of instability in the dimension of a spline space over a T-mesh, in: Computers & Graphics, August 2012, vol. 36, n^o 5, p. 507-513. [ DOI : 10.1016/j.cag.2012.03.005 ]

http://hal.inria.fr/hal-00742505
24M. Elkadi, A. Galligo, B. T. Luu.

Approximate GCD of several univariate polynomials, small degree perturbations, in: Journal of Symbolic Computation, 2012, vol. 47, n^o 4, p. 410-421. [ DOI : 10.1016/j.jsc.2011.09.005 ]

http://hal.inria.fr/inria-00528634
25I. Emiris, A. Mantzaflaris, B. Mourrain.

Voronoi Diagrams of Algebraic Distance Fields, in: Computer Aided Design, February 2013, vol. 45, n^o 2, p. 511-516. [ DOI : 10.1016/j.cad.2012.10.043 ]

http://hal.inria.fr/hal-00722406
26A. Galligo.

Deformation of Roots of Polynomials via Fractional Derivatives, in: Journal of Symbolic Computation, August 2012. [ DOI : 10.1016/j.jsc.2012.05.011 ]

http://hal.inria.fr/hal-00653770
27A. Galligo.

Budan Tables of Real Univariate Polynomials, in: Journal of Symbolic Computation, 2013. [ DOI : 10.1016/j.jsc.2012.11.004 ]

http://hal.inria.fr/hal-00653756
28A. Galligo, L. Miclo.

On the cut-off phenomenon for the transitivity of randomly generated subgroups, in: Random Structures & Algorithms, March 2012, vol. 40, n^o 2, p. 189-219, 38 pages.

http://hal.inria.fr/hal-00384188
29E. Hubert, M.-P. Cani.

Convolution Surfaces based on Polygonal Curve Skeletons., in: Journal of Symbolic Computation, June 2012, vol. 47, n^o 6, p. 680-699. [ DOI : 10.1016/j.jsc.2011.12.026 ]

http://hal.inria.fr/inria-00429358
30E. Hubert.

Convolution Surfaces based on Polygons for Infinite and Compact Support Kernels, in: Graphical Models, January 2012, vol. 74, n^o 1, p. 1-13. [ DOI : 10.1016/j.gmod.2011.07.001 ]

http://hal.inria.fr/inria-00536840
31I. 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, n^o 1, p. 102-122. [ DOI : 10.1016/j.jsc.2011.08.020 ]

http://hal.inria.fr/inria-00354120
32J.-B. Lasserre, M. Laurent, B. Mourrain, P. Rostalski, P. Trébuchet.

Moment Matrices, Border Basis and Real Radical Computation, in: Journal of Symbolic Computation, July 2012. [ DOI : 10.1016/j.jsc.2012.03.007 ]

http://hal.inria.fr/hal-00651759
33B. Mourrain.

On the dimension of spline spaces on planar T-meshes, in: Mathematics of Computation, November 2012.

http://hal.inria.fr/inria-00533187
34B. Mourrain, N. Villamizar.

Homological techniques for the analysis of the dimension of triangular spline spaces, in: Journal of Symbolic Computation, March 2013, vol. 50, p. 564-577. [ DOI : 10.1016/j.jsc.2012.10.002 ]

http://hal.inria.fr/hal-00742636
35G. Xu, B. Mourrain, R. Duvigneau, A. Galligo.

A New Error Assessment Method in Isogeometric Analysis of 2D Heat Conduction Problems, in: Advanced Science Letters, May 2012, vol. 10, n^o 1, p. 508-512. [ DOI : 10.1166/asl.2012.3321 ]

http://hal.inria.fr/hal-00742955
36G. Xu, B. Mourrain, R. Duvigneau, A. Galligo.

Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications, in: Computer-Aided Design, February 2013, vol. 45, n^o 2, p. 395-404. [ DOI : 10.1016/j.cad.2012.10.022 ]

http://hal.inria.fr/hal-00685002

Articles in National Peer-Reviewed Journals

37L. Busé.

Intersection entre courbes et surfaces rationnelles au moyen des représentations implicites matricielles, in: Revue Electronique Francophone d'Informatique Graphique (REFIG), 2012, vol. 6, n^o 1, p. 27-37.

http://hal.inria.fr/hal-00687050

International Conferences with Proceedings

38M. E. Alonso, A. Galligo.

A Root Isolation Algorithm for Sparse Univariate Polynomials, in: International Conference on Symbolic and Algebraic Computation (ISSAC), Grenoble, France, J. van der Hoeven, M. van Hoeij (editors), ACM Press, July 2012, p. 35-42, 8 double pages..

http://hal.inria.fr/hal-00762295
39E. Hubert, G. Labahn.

Rational invariants of scalings from Hermite normal forms, in: International Conference on Symbolic and Algebraic Computation (ISSAC), Grenoble, France, J. van der Hoeven, M. van Hoeij (editors), ISSAC Proceedings, ACM Press, 2012, p. 219-226.

http://hal.inria.fr/hal-00657991
40B. Mourrain, P. Trébuchet.

Border basis representation of a general quotient algebra, in: International Conference on Symbolic and Algebraic Computation (ISSAC), Grenoble, France, ACM Press, July 2012, p. 265-272.

http://hal.inria.fr/hal-00709962

Scientific Books (or Scientific Book chapters)

41E. Hubert.

Algebraic and Differential Invariants, in: Foundations of Computational Mathematics, Budapest 2011, F. Cucker, T. Krick, A. Pinkus, A. Szanto (editors), London Mathematical Society Lecture Note Series, Cambridge Universtiy Press, November 2012, vol. 403, p. 168-190.

http://hal.inria.fr/hal-00763310

Internal Reports

42L. Blanchard, R. Duvigneau, B. Mourrain.

Automated Generation of Geometric Models for a Bulbous Trawler Ship, Inria, July 2012, n^o RR-8011.

http://hal.inria.fr/hal-00714791

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