S. Shreeram and . Abhyankar, Algebraic geometry for scientists and engineers, Mathematical Surveys and Monographs, vol.35, 1990.

F. Apéry and J. Jouanolou, ´ Elimination: le cas d'une variable. Collection Méthodes, 2006.

E. Brieskorn and H. Knörrer, Plane algebraic curves. Translated from the German by John Stillwell, 1986.

L. Busé, On the equations of the moving curve ideal of a rational algebraic plane curve, Journal of Algebra, vol.321, issue.8, pp.2317-2344, 2009.
DOI : 10.1016/j.jalgebra.2009.01.030

F. Chen, W. Wang, and Y. Liu, Computing singular points of plane rational curves, Journal of Symbolic Computation, vol.43, issue.2, pp.92-117, 2008.
DOI : 10.1016/j.jsc.2007.10.003

. Eng-wee, T. W. Chionh, and . Sederberg, On the minors of the implicitization Bézout matrix for a rational plane curve, Comput. Aided Geom. Design, vol.18, issue.1, pp.21-36, 2001.

M. Kahoui, D-resultant and subresultants, Proceedings of the American Mathematical Society, vol.133, issue.08, pp.2193-2199, 2005.
DOI : 10.1090/S0002-9939-05-07850-0

J. Gutierrez, R. Rubio, and J. Yu, D-resultant for rational functions, Proc. Amer, pp.2237-2246, 2002.

X. Jia and R. Goldman, Using Smith normal forms and ??-bases to compute all the singularities of rational planar curves, Computer Aided Geometric Design, vol.29, issue.6, 2009.
DOI : 10.1016/j.cagd.2012.02.001

H. Park, Effective computation of singularities of parametric affine curves, Journal of Pure and Applied Algebra, vol.173, issue.1, pp.49-58, 2002.
DOI : 10.1016/S0022-4049(02)00017-8

S. Pérez-díaz, Computation of the singularities of parametric plane curves, Journal of Symbolic Computation, vol.42, issue.8, pp.835-857, 2007.
DOI : 10.1016/j.jsc.2007.06.001

J. , R. Sendra, and F. Winkler, Symbolic parametrization of curves, J. Symbolic Comput, vol.12, issue.6, pp.607-631, 1991.
DOI : 10.1016/s0747-7171(08)80144-7
URL : http://doi.org/10.1016/s0747-7171(08)80144-7

J. , R. Sendra, and F. Winkler, Tracing index of rational curve parametrizations, Comput . Aided Geom. Design, vol.18, issue.8, pp.771-795, 2001.

N. Song, F. Chen, and R. Goldman, Axial moving lines and singularities of rational planar curves, Computer Aided Geometric Design, vol.24, issue.4, pp.200-209, 2007.
DOI : 10.1016/j.cagd.2007.02.002

P. Stadelmeyer, On the computational complexity of resolving curve singularities and related problems, 2000.

C. Robert and . Thompson, An inequality for invariant factors, Proc. Amer. Math. Soc, vol.86, issue.1, pp.9-11, 1982.

R. J. Walker, Algebraic Curves, Princeton Mathematical Series, vol.13, 1950.

I. Sophia-antipolis-méditerranée, 2004 route des Lucioles, B.P. 93 06902 Sophia Antipolis, France E-mail address: Laurent.Buse@inria.fr URL: http://www-sop.inria.fr/members/Laurent.Buse/ Departament d' ` Algebra i Geometria, p.8007