. Auzinger and . Stetter, An Elimination Algorithm for the Computation of All Zeros of a System of Multivariate Polynomial Equations, Int. Series of Numerical Math, vol.86, pp.11-30, 1998.
DOI : 10.1007/978-3-0348-6303-2_2

B. Buchberger, G. Collins, and R. Loos, Computer algebra symbolic and algebraic computation, ACM SIGSAM Bulletin, vol.16, issue.4, 1982.
DOI : 10.1145/1089310.1089312

S. Basu, R. Pollack, and M. Roy, Algorithms in real algebraic geometry, Algorithms and Computations in Mathematics, vol.10, 2003.
DOI : 10.1007/978-3-662-05355-3

URL : https://hal.archives-ouvertes.fr/hal-01083587

]. B. Buc85 and . Buchberger, Gröbner bases : an algorithmic method in polynomial ideal theory. Recent trends in multidimensional systems theory, 1985.

F. Cazals, J. Faugere, M. Pouget, and F. Rouillier, The implicit structure of ridges of a smooth parametric surface, Computer Aided Geometric Design, vol.23, issue.7, 2005.
DOI : 10.1016/j.cagd.2006.04.002

URL : https://hal.archives-ouvertes.fr/inria-00071237

D. Cox, J. Little, and D. Shea, Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra. Undergraduate texts in mathematics, 1992.

]. G. Col75 and . Collins, Quantifier elimination for real closed fields by cylindrical algebraic decomposition, Springer Lecture Notes in Computer Science, vol.33, issue.33, pp.515-532, 1975.

M. [. Cazals and . Pouget, Topology driven algorithms for ridge extraction on meshes, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00070481

]. Fau99 and . Faugère, A new efficient algorithm for computing gröbner bases ( f 4 ), Journal of Pure and Applied Algebra, vol.139, issue.1-3, pp.61-88, 1999.

[. Faugère, A new efficient algorithm for computing gröbner bases without reduction to zero f 5, International Symposium on Symbolic and Algebraic Computation Symposium -ISSAC 2002, 2002.

J. C. Faugère, P. Gianni, D. Lazard, and T. Mora, Efficient Computation of Zero-dimensional Gr??bner Bases by Change of Ordering, Journal of Symbolic Computation, vol.16, issue.4, pp.329-344, 1993.
DOI : 10.1006/jsco.1993.1051

G. Gatellier, A. Labrouzy, B. Mourrain, and J. Técourt, Computing the topology of 3- dimensional algebraic curves, Computational Methods for Algebraic Spline Surfaces, pp.27-44, 2004.

M. Giusti, G. Lecerf, and B. Salvy, A Gr??bner Free Alternative for Polynomial System Solving, Journal of Complexity, vol.17, issue.1, pp.154-211, 2001.
DOI : 10.1006/jcom.2000.0571

L. Gonzalez-vega and I. Necula, Efficient topology determination of implicitly defined algebraic plane curves, Computer Aided Geometric Design, vol.19, issue.9, 2002.
DOI : 10.1016/S0167-8396(02)00167-X

J. Keyser, M. Ouchi, and . Rojas, The exact rational univariate representation for detecting degeneracies, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2005.

]. D. Laz83 and . Lazard, Gröbner bases, gaussian elimination, and resolution of systems of algebraic equations, EUROCAL' 83 European Computer Algebra Conference, pp.146-156, 1983.

]. R. Mor90 and . Morris, Symmetry of Curves and the Geometry of Surfaces: two Explorations with the aid of Computer Graphics, 1990.

]. R. Mor96 and . Morris, The sub-parabolic lines of a surface, Mathematics of Surfaces VI, IMA new series 58, pp.79-102, 1996.

P. [. Mourrain and . Trébuchet, Generalized normal forms and polynomial system solving, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, 2005.
DOI : 10.1145/1073884.1073920

URL : https://hal.archives-ouvertes.fr/inria-00070537

T. Maekawa, F. Wolter, and N. Patrikalakis, Umbilics and lines of curvature for shape interrogation, Computer Aided Geometric Design, vol.13, issue.2, pp.133-161, 1996.
DOI : 10.1016/0167-8396(95)00018-6

]. I. Por01 and . Porteous, Geometric Differentiation, 2001.

]. F. Rou99 and . Rouillier, Solving zero-dimensional systems through the rational univariate representation, Journal of Applicable Algebra in Engineering, Communication and Computing, vol.9, issue.5, pp.433-461, 1999.

F. [. Revol and . Rouillier, Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library, Reliable Computing, vol.2, issue.3, pp.1-16, 2005.
DOI : 10.1007/s11155-005-6891-y

URL : https://hal.archives-ouvertes.fr/inria-00100985

P. [. Rouillier and . Zimmermann, Efficient isolation of polynomial's real roots, Journal of Computational and Applied Mathematics, vol.162, issue.1, pp.33-50, 2003.
DOI : 10.1016/j.cam.2003.08.015

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex

I. De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399