Laurent Busé

             Chargé de Recherche à l'INRIA

             Projet Galaad, INRIA Sophia Antipolis - Méditerranée
             2004 route des Lucioles, B.P. 93
             06902 Sophia Antipolis, France

   Email: Laurent.Buse@inria.fr
   Phone: +33-4-92-38-76-51
   Office: Byron Y008

Research interests:

Computational Algebra and Computational Algebraic Geometry - Elimination theory for systems of polynomial equations.

Macaulay2 package for resultants:

With Nicolàs Botbol and Manuel Dubinsky, we have implemented a Macaulay2 package for elimination theory, in particular for resultants computations.

You can download the package (January 2012), browse the online documentation and get an introductory file.

The last version of the package can be downloaded from the resultants-macaulay2 google project: use the following command to anonymously checkout the latest project source code:
svn checkout http://resultants-macaulay2.googlecode.com/svn/ resultants-macaulay2-read-only

Publications:

All my published papers, unpublished notes or lecture notes are available in preprint format on HAL.
See also my publications on MathSciNet.

Preprints:

"The surface/surface intersection problem by means of matrix based representations", with T. Luu Ba (click)
"Singular factors of rational plane curves", with C. D'Andrea (click)

Articles in peer-reviewed journals:

"On the total order of reducibility of a pencil of algebraic plane curves", with G. Chèze, Journal of Algebra, 341 (2011) vol. 1, 256--278 (click)
"Noether's forms for the study of non-composite rational functions and their spectrum", with G. Chèze and S. Najib, Acta Arithmetica, 147 (2011) vol. 3, 217--231 (click)
"Matrix-based implicit representations of rational algebraic curves and applications", with T. Luu Ba, Computer Aided Geometric Design, 27 (2010) vol. 9, 681--699 (click)
"Elimination and nonlinear equations of Rees Algebras", with M. Chardin and A. Simis, and an appendix by J. Oesterlé, Journal of Algebra, 324 (2010) vol. 6, 1314--1333 (click)
"On the equations of the moving curve ideal", Journal of Algebra, 321 (2009) vol. 8, 2317--2344 (click)
"Torsion of the symmetric algebra and implicitization", with M. Chardin and J-P. Jouanolou, Proceedings of the American Mathematical Society, 137 (2009) vol. 6, 1855--1865 (click)
"A computational study of rational ruled surfaces", with M. Elkadi and A. Galligo, Journal of Symbolic Computation, 44 (2009) vol. 3, 232--241 (click)
"Explicit factors of some iterated resultants and discriminants", with B. Mourrain, Mathematics of Computations, 78 (2009) vol. 265, 345--386 (click)
"Division Algorithms for Bernstein Polynomials", with R. Goldman, Computer Aided Geometric Design, 25 (2008) vol. 9, 850--865 (click)
"Intersection and self-intersection of surfaces by means of Bezoutian matrices", with M. Elkadi and A. Galligo, Computer Aided Geometric Design, 25 (2008) vol. 2, 53--68 (click)
"A matrix-based approach to properness and inversion problems for rational surfaces", with C. D'Andrea, Applicable Algebra in Engineering, Communication and Computing, 17 (2006) vol. 6, 393--407 (click)
"Semi-implicit representations of surfaces in the projective space, resultants and applications", with A. Galligo, Journal of Symbolic Computation, 39 (2005) vol. 3-4, 317--329 (click)
"Implicitizing rational hypersurfaces using approximation complexes", with M. Chardin, Journal of Symbolic Computation, 40 (2005) vol. 4-5, 1150--1168 (click)
"Resultants of determinantal varieties", Journal of Pure and Applied Algebra, 193 (2004) vol. 1-3, 71--97 (click)
"On the irreducibility of multivariate subresultants", with C. D'Andrea, Comptes-Rendus de l'Académie des Sciences, Série 1, Mathématiques, 338 (2004) vol. 4, 287--290 (click)
"Implicitization of surfaces in the projective space in the presence of base points", with D. Cox and C. D'Andrea, Journal of Algebra and Its Applications, 2 (2003) vol. 2, 189--214 (click)
"On the closed image of a rational map and the implicitization problem", with J-P. Jouanolou, Journal of Algebra, 265 (2003) vol. 1, 312--357 (click)
"Using projection operators in computer aided geometric design", with M. Elkadi and B. Mourrain, Comtemporary Mathematics, 334 (2003) 321--342 (click)
"Resultant over the residual of a complete intersection", with M. Elkadi and B. Mourrain, Journal of Pure and Applied Algebra, 164 (2001) vol. 1-2, 35--57 (click)
"Generalized resultants over unirational algebraic varieties", with M. Elkadi and B. Mourrain, Journal of Symbolic Computation 29 (2000) vol. 4-5, 515--526 (click)

Communications in peer-reviewed international conferences:

"Curve/surface intersection problem by means of matrix representations", with T. Luu Ba and B. Mourrain, (2009) International Conference on Symbolic and Numerical Computation (SNC) 71-78 (click)
"Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies", with M. Dohm, (2007) International Conference on Symbolic and Algebraic Computation (ISSAC) 69-76 (click)
"Resultant-based methods for plane curves intersection problems", with H. Khalil and B. Mourrain, (2005) Computer Algebra in Scientific Computing (CASC), LNCS 3718, 75-92 (click)
"Using semi-implicit representation of algebraic surfaces", with A. Galligo, (2004) Shape Modeling and Applications (SMI) 342-345 (click)
"Inversion of parameterized hypersurfaces by means of subresultants", with C. D'Andrea, (2004) Internation Symposium on Symbolic and Algebraic Computing (ISSAC) 65--71 (click)
"A resultant approach to detect intersecting curves in the projective space", with. A. Galligo, (2003) Methods in Effective Algebraic Geometry (MEGA) electronic (click)
"Residual resultant over the projective plane and the implicitization problem", (2001) Internation Symposium on Symbolic and Algebraic Computing (ISSAC) 48--55 (click)

Thesis:

"Représentations matricielles en théorie de l'élimination et applications à la géométrie", Habilitation à Diriger des Recherches, university of Nice, april 29, 2011 (click)
"Étude du résultant sur une variété algébrique", PhD thesis, university of Nice, december 19, 2001 (click)

Book chapter:

"Shape Interrogation", with S. Hahmann, A. Belyaev, G. Elber, B. Mourrain, C. Roessl. Shape Analysis and Structuring, Mathematics and Visualization, Springer, (2007) 57 pages (click)

Book edited:

"Computational Algebraic Geometry and Applications", with M. Elkadi, B. Mourrain, Guest Editors. Theoretical Computer Science 392 (2008) vol. 1-3, 1--178 (click)

Lecture notes:

"Résultant univarié et courbes algébriques planes", (2006-2008) 38 pages. Notes in french of lectures given at the Master of mathematics, 2nd year, of the University of Nice (click)
"Elimination theory in codimension one and applications", INRIA research report 5918, (2006) 47 pages. Notes of lectures given at the CIMPA-UNESCO-IRAN school in Zanjan, Iran, July 9-22 2005 (click)
"Géométrie différentielle et applications", (2004) 25 pages. Notes of lectures on differential geometry given at the university of Nice (click)
"Syzygies of points in a projective space", with H-C. Von Bothmer and B. Fu, (2002) 28 pages. These notes are collected from talks given by the authors at the University of Nice (october-december 2002) (click)

Others:

"Computing resultant matrices with Macaulay2 and Maple". INRIA Technical Report 280 (2003), pp. 33 (click)

Teaching activities:

Courses:

2012: course of 12 hours (and 24h of TDs) in MAM4 at EPU "Courbes et Surfaces" (click).
2012: course of 10 hours at the master MDFI (2nd year) in Marseille "Théorie matricielle de l'élimination".
2011: course of 12 hours given at the CIMPA-UNESCO-MICINN-INDONESIA research school in Yogyakarta, Indonesia, July 18-29, "Elimination Matrices for Computer Aided Geometric Design".
2011: course of 12 hours (and 24h of TDs) in MAM4 at EPU "Courbes et Surfaces".
2010: course of 12 hours (and 48h of TDs) in MAM4 at EPU "Courbes et Surfaces".
2009: course of 8 hours at the "Summer School on Computational Mathematics" on "algebraic curves and surfaces in CAGD", SORIA, Spain 13-24 July.
2008: course of 3 hours at the "Journées Nationales de Calcul Formel", CIRM, Luminy, October 20-24 on "Résultants : des matrices pour l'élimination".
2008, 2009: introductive course of 3 hours on "algebraic curves in CAGD" to Master 2nd year MDFI, Marseille.
2006-2007: course in Master 2nd year of mathematics at the university of Nice, "Courbes et surfaces algébriques pour la modélisation", 30 hours.
2005-2006: course in Master 2nd year of mathematics at the university of Nice, 27 hours.
2005: course given at the CIMPA-UNESCO-IRAN school in Zanjan, Iran, July 9-22, "Elimination theory in codimension one and applications".
2004-2005: course in Master 2nd year of mathematics at the university of Nice, 15 hours.

Students:

PhD thesis:
- Thang Luu Ba (2008-2011), co-supervised with A. Galligo, "Représentation matricielle implicite de courbes et surfaces algébriques et applications", (click).
- Marc Dohm (2005-2008), co-supervised with A. Galligo, "Implicitization of rational algebraic surfaces with syzygy-based methods", (click).
Master thesis:
- Christopher Goyet (2009), "Ordre total de réductibilté d'un pinceau de courbes algébriques planes".
- Julien Boursier (2008) "Calcul des points singuliers d'une courbe plane rationnelle".
- Elimane Ba (2006), "Résultant anisotrope et intersection de deux surfaces algébriques".
- Marc Dohm (2005), co-supervised with M. Elkadi and A. Galligo, "mu-Bases of Algebraic Curves and Surfaces".