PUBLICATIONS
-
S. Hahmann, A. Belyaev, L. Busé, G. Elber, B. Mourrain, and C. Roessl,
- ``Shape Interrogation - A State of the Art,'', 2007
- to appear in {\em Shape analysis and structuring}, De Floriani, L. and
Spagnuolo, M. (ed.), Springer Verlag.
-
B. Mourrain,
- ``Pythagore's dilemma, Symbolic-Numeric Computation and the Border Basis
Method,'', 2006
- to appear in {\em Symbolic-Numeric Computation}, {Wang, Dongming and Zhi,
Li-Hon} (ed.), Birkh{\"a}user.
-
J.D. Boissonnat, D. Cohen-Steiner, B. Mourrain, G. Rote, and G. Vegter,
- ``Meshing of Surfaces,'', pp. 459--478
- Mathematics and Visualisation. Springer-Verlag, 2006.
-
B. Mourrain, S. Pion, S. Schmitt, J.P. Técourt, E. Tsigaridas, and Wolpert N.,
- ``Algebraic Issues in Computational Geometry,'', pp. 459--478
- Mathematics and Visualisation. Springer-Verlag, 2006.
-
M. Elkadi, B. Mourrain, and R. Piene, editors,
- ``Algebraic Geometry and Geometric Modeling,''
- Mathematics of Visualisation. Springer, 2006.
-
M. Elkadi and B. Mourrain,
- ``Introduction à la résolution des systèmes d'équations algébriques,'',
2006
- to appear,{59, Mathématiques et Applications, Springer-Verlag}.
-
Chen Liang, B. Mourrain, and J.P. Pavone,
-
``Subdivision methods for 2d and 3d implicit curves,''
- In Computational Methods for Algebraic Spline Surfaces.
Springer-Verlag, 2006
- To appear.
-
Ioannis Z. Emiris, Bernard Mourrain, and Elias P. Tsigaridas,
- ``Real Algebraic Numbers:
Complexity Analysis and Experimentations,''
- Research Report 5897, INRIA, Avril 2006.
-
B. Mourrain, N.G. Pavlidis, D.K. Tasoulis, and M. Vrahatis,
- ``Determining the Number of Real Roots of Polynomials through Neural
Networks,''
- Computers and Mathematics with Applications, 39:527--536,
2006.
-
B. Mourrain,
- ``Les logiciels libres comme publication scientifique d'un nouveau
type,'', 2005
- Gazette des Mathématiciens, SMF.
-
L. Busé, H. Khalil, and B. Mourrain,
-
``Resultant-Based Method for Plane Curves Intersection Problems,''
- In Proc.\ of the conf. Computer Algebra in Scientifc Computing,
volume 3718 of LNCS, pp. 75-92. Springer, 2005.
-
B. Mourrain and J.-P. Pavone,
- ``Subdivision methods for
solving polynomial equations,''
- Technical Report 5658, {INRIA} Sophia-Antipolis, 2005.
-
B. Mourrain and Ph. Trébuchet,
-
``Generalised normal forms and polynomial system solving,''
- In M. Kauers, editor, Proc.\ Intern.\ Symp.\ on Symbolic and Algebraic
Computation, pp. 253-260. New-York, ACM Press., 2005.
-
B. Mourrain and J.-P. Técourt,
-
``Computing the Topology of Real Algebraic Surface,''
- In MEGA electronic proceedings, 2005.
-
B. Mourrain, F. Rouillier, and M.-F. Roy,
- ``Bernstein's
basis and real root isolation,'', pp. 459--478
- Mathematical Sciences Research Institute Publications. Cambridge
University Press, 2005.
-
B. Mourrain,
-
``Bezoutian and quotient ring structure,''
- J. of Symbolic Comput., 39:397-415, 2005.
-
L. Alberti, G. Comte, and B. Mourrain,
-
``Meshing implicit algebraic surfaces: the smooth case,''
- In L.L. Schumaker M. Maehlen, K. Morken, editor, Mathematical Methods
for Curves and Surfaces: Tromso'04, pp. 11-26. Nashboro, 2005.
-
B. Mourrain, J.-P. Técourt, and M. Teillaud,
- ``On the
computation of an arrangement of quadrics in 3D,''
- Computational Geometry; Theory and Applications, 30:145-164,
2005.
-
B. Mourrain and J.P.. Técourt,
- ``Isotopic meshing of a
real algebraic surface,''
- Technical Report 5508, {INRIA} Sophia-Antipolis, 2005.
-
B. Mourrain and Ph. Trébuchet,
- ``Generalised normal forms
and polynomial system solving,''
- Technical Report 5471, {INRIA} Sophia-Antipolis, 2005.
-
M. Elkadi and B. Mourrain,
- ``Symbolic-n%
umeric tools for solving polynomial equations and applications,'',
volume 14 of Algorithms and Computation in Mathematics, pp. 125-168
- Springer, 2005.
-
Franck Aries, B. Mourrain, and J.-P. Técourt,
-
``Quadratically Parametrized Surfaces: Algorithms and Applications,''
- In Geometric Modeling and Computing: Seattle, pp. 1-20. Nashboro
Press, 2004.
-
B. Mourrain, J.-P. Técourt, and M. Teillaud,
- ``On the computation of an arrangement of quadrics in 3D,''
- Comput. Geom. Theory Appl., (30):145--164, 2005
- Special issue, 19th European Workshop on Computational Geometry, Bonn.
-
G. Gatellier, A. Labrouzy, B. Mourrain, and J.-P. Técourt,
-
``Computing the topology of 3-dimensional algebraic curves,''
- In Computational Methods for Algebraic Spline Surfaces, pp. 27-44.
Springer-Verlag, 2005.
-
L. Alberti, G. Comte, and B. Mourrain,
- ``Meshing implicit
algebraic surfaces: the smooth case,''
- Technical Report 5405, {INRIA} Sophia-Antipolis, 2004.
-
G. Gatellier, A. Labrouzy, B. Mourrain, and J.P. Técourt,
- ``Computing the toplogy of
three dimensional algebaric curves,''
- Technical Report 5194, {INRIA} Sophia-Antipolis, 2004.
-
B. Mourrain, F. Rouillier, and M.-F. Roy,
- ``Bernstein's basis and
real root isolation,''
- Technical Report 5149, {INRIA} Rocquencourt, 2004
- Submitted for journal publication.
-
M. Elkadi and B. Mourrain,
-
``Residue and implicitization problem for rational surfaces,''
- Appl. Algebra Eng. Comm. Comput., 14(5), 2004.
-
Ioannis Z. Emiris, Bernard Mourrain, and Victor Y. Pan,
- ``Guest editors of the special Issue Algebraic and numerical algorithms,''
- Theoret. Comput. Sci., 315(2-3):307--308, 2004.
-
B. Mourrain,
- ``Bezoutian and quotient ring structure,''
- In MEGA electronic prooceedings, 2003.
-
Laurent Busé, Lionel Deschamps, André Galligo, and Bernard Mourrain,
- ``On convertion methods between different representations of surfaces,''
- Technical Report ECG-TR-302109-01, {INRIA} Sophia-Antipolis, 2003.
-
Bernard Mourrain, Jean-Pierre Técourt, and Dimitri Zinoviev,
- ``Computing robustly the intersection of two algebraically defined
surfaces,''
- Technical Report ECG-TR-242108-01, {INRIA} Sophia-Antipolis, 2003.
-
Gabriel Dos Reis, Bernard Mourrain, and Jean-Pierre Tecourt,
- ``On the Representations of 3D surfaces,''
- Technical Report ECG-TR-242106-01, {INRIA} Sophia-Antipolis, 2003.
-
Bernard Mourrain, Jean-Pierre Técourt, and Monique Teillaud,
- ``Predicates for the Sweeping of an Arrangement of Quadrics in 3D,''
- Technical Report ECG-TR-242205-01, {INRIA} Sophia-Antipolis, 2003.
-
Olivier Devillers, Bernard Mourrain, Franco P. Preparata, and Philippe
Trebuchet,
- ``Circular Cylinders by Four or Five Points in Space,''
- Discrete and Computational Geometry, 29:83--104, 2003.
-
L. Busé, M. Elkadi, and B. Mourrain,
- ``Using projection operators in Computer Aided Geometric Design,''
- In Topics in Algebraic Geometry and Geometric Modeling,, pp.
321-342. Contemporary Mathematics, 2003.
-
B. Mourrain, Y. V. Pan, and O. Ruatta,
- ``Accelerated solution of multivariate polynomial systems of equations,''
- SIAM J. Comput., 32(2):435--454, 2003.
-
I. Emiris, B. Mourrain, and Y. V. Pan,
- ``Ed. of the special issue on Algebraic and Numerical Algorithms,''
- volume 315 of Theoretical Computer Science. 2004.
-
Bernard Mourrain, Jean-Pierre Técourt, and Dimitri Zinoviev,
- ``Computing robustly the intersection of two algebraically defined
surfaces,''
- Technical Report ECG-TR-242108-01, {INRIA} Sophia-Antipolis, 2003.
-
B. Mourrain, J.P. Técourt, and M. Teillaud,
- ``Algebraic methods for dealing with 3D implicit quadrics,''
- Technical Report ECG-TR-182105-02, INRIA Sophia-Antipolis, 2002.
-
J.C. Faugère, B. Mourrain, and F. Rouillier,
- ``Outils de
calcul symbolique numérique collaboratif,'', septembre 2002
- CDROM contenant les supports de cours et des logiciels pour le calcul
linéaire, algébrique, symbolique et numérique (cgal, gb, giac, givaro,
gmp, linbox, mpfr, mupad, ntl, pari, rs, synaps, texmacs, scilab, udx).
-
B. Mourrain and Ph. Trébuchet,
- ``Algebraic methods for numerical solving,''
- Technical Report ECG-TR-122102-02, INRIA Sophia-Antipolis, 2002.
-
G. Dos Reis, B. Mourrain, F. Rouillier, and Ph. Trébuchet,
- ``An environment for Symbolic and Numeric Computation,''
- Technical Report ECG-TR-122102-03, INRIA Sophia-Antipolis, 2002.
-
B. Mourrain, M.N. Vrahatis, and J.C. Yakoubsohn,
- ``On the complexity of isolating real roots and computing with certainty
the topological degree,''
- Technical Report ECG-TR-122102-04, INRIA Sophia-Antipolis, 2002.
-
B. Mourrain,
-
``An introduction to algebraic and geometric methods for solving polynomial
equations,''
- Technical Report ECG-TR-122102-01, INRIA Sophia-Antipolis, 2002.
-
B. Mourrain and Ph. Trébuchet,
- ``Algebraic methods for numerical solving,''
- Analele Universitatii di Timisoara, XXXIX:149--169, 2001.
-
B. Mourrain and Ph. Trébuchet,
- ``Algebraic methods for numerical solving,''
- In Proc. of the 3rd International Workshop on Symbolic and Numeric
Algorithms for Scientific Computing'01 (Timisoara, Romania), pp. 42-57,
2002.
-
G. Dos Reis, B. Mourrain, R. Rouillier, and Ph. Trébuchet,
- ``An
environment for Symbolic and Numeric Computation,''
- In Proc. of the International Conference on Mathematical Software
2002, World Scientific, pp. 239--249, 2002.
-
B. Mourrain and O. Ruatta,
-
``Relation between roots and coefficients, interpolation and application to
system solving,''
- J. of Symbolic Computation, 33(5):679-699, 2002.
-
B. Mourrain, Y. V. Pan, and O. Ruatta,
- ``Asymptotic acceleration of solving multivariate polynomial systems of
equations,''
- In Proceedings of Smale fest 2000, Foundations of Computational
Mathematics, pp. 267-294. World Scientific, NewJersey, London, Singapore,
Hong Kong, 2002.
-
B. Mourrain, M. Vrahatis, and J.C. Yakoubsohn,
- ``On the
Complexity of Isolating Real Roots and Computing with Certainty the
Topological Degree,''
- J. of Complexity, 18(2):612--640, 2002.
-
B. Mourrain,
- ``An introduction to algebraic
methods for solving polynomial equations,'', 2000
- Tutorial.
-
O. Devillers, A. Fronville, B. Mourrain, and M. Teillaud,
- ``Algebraic Methods and Arithmetic Filtering for Exact Predicates on
Circle Arcs,''
- Computational Geometry: Theory and Applications,
22:119--142, 2002.
-
O. Grellier, P. Comon, B. Mourrain, and Ph. Trébuchet,
- ``Analytical Blind Channel Identification,''
- IEEE Trans. on Signal Processing, 50(9):2196--2207, 2002.
-
B. Mourrain,
- ``Ed. of the proc.\ Intern.\ Symp.\ on Symbolic and Algebraic
Computation, Univ. Western Ontario, Canada,''
- New-York, ACM Press., 2001.
-
D. Bondyfalat, B. Mourrain, and T. Papadopoulo,
- ``Using Scene Constraints during the Calibration Procedure,''
- volume 2, pp. 124--130. IEEE Computer Society Press., 2001.
-
B. Mourrain, M. Vrahatis, and J.C. Yakoubsohn,
- ``Isolation of real roots
and computation of the topological degree,''
- Rapport de Recherche 4300, INRIA, Octobre 2001.
-
O. Devillers, B. Mourrain, F. Preparata, and Ph. Trébuchet,
- ``On circular cylinders by
four or five points in space,''
- Rapport de Recherche 4195, INRIA, 2001.
-
Y.J. Choie, B. Mourrain, and P. Solé,
- ``Rankin
Cohen brackets and Invariant Theory,''
- J. of Algebraic Combinatorics, 13(1):5-13, Jan. 2001.
-
L. Busé, M. Elkadi, and B. Mourrain,
-
``Resultant over the residual of a complete intersection,''
- J. of Pure and Applied Algebra, 164:35-57, 2001.
-
I.Z. Emiris, B. Mourrain, V.P. Plagianakos, and M.N. Vrahatis,
- ``Sign Methods for Enumerating Solutions of Nonlinear Algebraic Systems,''
- In Hellenic European Conf.\ Computer Math.\ \& Appl., pp. 469--473,
Athens, Greece, September 2001.
-
B. Mourrain and H. Prieto,
- ``A framework for Symbolic
and Numeric Computations,''
- Rapport de Recherche 4013, INRIA, 2000.
-
B. Mourrain and Ph. Trébuchet,
-
``Solving projective complete intersection faster,''
- In C. Traverso, editor, Proc.\ Intern.\ Symp.\ on Symbolic and
Algebraic Computation, pp. 231-238. New-York, ACM Press., 2000.
-
A. Fronville, O. Devillers, M. Teillaud, and B. Mourrain,
- ``Algebraic Methods and Arithmetic Filtering for Exact Predicates on
Circle Arcs,''
- In Proc. 16th ACM Symp. on Comp. Geometry, Hong Kong, Chine, 2000.
-
L. Busé, M. Elkadi, and B. Mourrain,
-
``Generalized resultant over unirational algebraic varieties,''
- J. of Symbolic Computation, 29:515-526, 2000.
-
D. Bondyfalat, B. Mourrain, and V. Y. Pan,
-
``Computation of a specified root of a polynomials system of equations using
eigenvector,''
- Lin. Alg. and its Appl., 319:193-209, 2000.
-
M. Elkadi and B. Mourrain,
- ``Algorithms for residues and Lojasiewicz exponents,''
- J. of Pure and Applied Algebra, 153:27-44, 2000.
-
H. Hirukawa, B.Mourrain, and Y. Papegay,
-
``A Symbolic-Numeric Silhouette Algorithm,''
- In Proceedings of 2000 IEEE International conference on RObotics
Systems. IEEE Robotics Society, 2000.
-
A. Fronville, O. Devillers, M. Teillaud, and B. Mourrain,
- ``Algebraic Methods and
Arithmetic Filtering for Exact Predicates on Circle Arcs,''
- Rapport de Recherche 3826, INRIA, 1999.
-
I.Z. Emiris, B. Mourrain, V.P. Plagianakos, and M.N. Vrahatis,
- ``Robust Methods for Counting, Localizing and Computing with Certainty
Simple Zeros of Analytic Functions,''
- In Proc. 5th Intern. Symp. Orthogonal Polyn., Spec. Functions \&
Appl., Patras, Greece, 1999
- toappear.
-
D. Bondyfalat, B. Mourrain, and T. Papadopoulo,
- ``An
Application of Automatic Theorem Proving in Computer Vision,''
- In X.-S. Gao, D. Wang, and L. Yang, editors, Automated Deduction in
Geometry, number 1669 in LNAI, pp. 207-231. Springer-Verlag, Berlin
Heidelberg, 1999.
-
I.Z. Emiris, B. Mourrain, and M.N. Vrahatis,
- ``Sign Methods for Counting
and Computing Real Roots of Algebraic Systems,''
- Rapport de Recherche 3669, INRIA, 1999.
-
M. Elkadi and B. Mourrain,
- ``A
new algorithm for the geometric decomposition of a variety,''
- In S. Dooley, editor, Proc. Intern. Symp. on Symbolic and Algebraic
Computation, pp. 9-16. ACM Press, New-York, 1999.
-
B. Mourrain and V. Y. Pan,
-
``Multivariate Polynomials, Duality and Structured Matrices,''
- J. of Complexity, 16(1):110-180, 2000.
-
B. Mourrain and V. Y. Pan,
- ``Lifting/descending processes for polynomial zeros,''
- J. of Complexity, 16:265-273, 2000.
-
B. Mourrain,
- ``A
new criterion for normal form algorithms,''
- In M. Fossorier, H. Imai, Shu Lin, and A. Poli, editors, Proc.
AAECC, volume 1719 of LNCS, pp. 430-443. Springer, Berlin, 1999.
-
A. Bonnecaze, B. Mourrain, and P. Solé,
- ``Jacobi Polynomials, Type II codes, and designs,''
- Designs, Codes and Cryptography, 16:215-234, 1999.
-
I.Z. Emiris and B. Mourrain,
- ``Computer
Algebra Methods for Studying and Computing Molecular Conformations,''
- Algorithmica, Special Issue on Algorithms for Computational
Biology, 25:372--402, 1999.
-
I.Z. Emiris and B. Mourrain,
-
``Matrices in Elimination Theory,''
- J. of Symbolic Computation, 28(1\&2):3-44, 1999.
-
P. Comon, O. Grellier, and B. Mourrain,
- ``Blind
Channel Identification with MSK inputs,''
- In Asilomar Conference, Pacific Grove, California, November 1-4
1998
- Invited session.
-
B. Mourrain,
- ``An
introduction to linear algebra methods for solving polynomial
equations,''
- In E.A. Lipitakis, editor, HERCMA'98, pp. 179-200, 1999.
-
M. Elkadi and B. Mourrain,
- ``Some applications of
Bezoutians in Effective Algebraic Geometry,''
- Rapport de Recherche 3572, INRIA, Sophia Antipolis, 1998.
-
B. Mourrain and V. Y. Pan,
-