J. D. Tulay-ayyildiz-akoglu, . Hauenstein, and . Szántó, Certifying solutions to overdetermined and singular polynomial systems over Q. CoRR, abs, 1408.

B. [. Alberti, J. Mourrain, and . Wintz, Topology and arrangement computation of semi-algebraic planar curves, Computer Aided Geometric Design, vol.25, issue.8, pp.631-651, 2008.
DOI : 10.1016/j.cagd.2008.06.009

URL : https://hal.archives-ouvertes.fr/inria-00343110

M. Burr, S. W. Choi, B. Galehouse, and C. K. Yap, Complete subdivision algorithms, II, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, ISSAC '08, pp.131-152, 2012.
DOI : 10.1145/1390768.1390783

C. Beltrán and A. Leykin, Robust Certified Numerical Homotopy Tracking, Foundations of Computational Mathematics, vol.25, issue.2, pp.1-43, 2013.
DOI : 10.1007/s10208-013-9143-2

S. [. Bouzidi, M. Lazard, F. Pouget, and . Rouillier, New bivariate system solver and topology of algebraic curves, 27th European Workshop on Computational Geometry -EuroCG, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00580431

L. Busé and B. Mourrain, Explicit factors of some iterated resultants and discriminants, Mathematics of Computation, vol.78, issue.265, pp.345-386, 2009.
DOI : 10.1090/S0025-5718-08-02111-X

Y. Bouzidi, Solving bivariate algebraic systems and topology of plane curves. Theses, 2014.
URL : https://hal.archives-ouvertes.fr/tel-00979707

S. J. Cheng, L. Lazard, M. Pe-naranda, F. Pouget, E. Rouillier et al., On the Topology of Real Algebraic Plane Curves, Mathematics in Computer Science, vol.41, issue.9, pp.113-137, 2010.
DOI : 10.1007/s11786-010-0044-3

URL : https://hal.archives-ouvertes.fr/inria-00517175

]. J. Ded06 and . Dedieu, Points fixes, zéros et la méthode de Newton, Mathématiques et Applications, 2006.

N. Delanoue and S. Lagrange, A numerical approach to compute the topology of the apparent contour of a smooth mapping from R 2 to R 2 . submitted to, Journal of Computational and Applied Mathematics, 2013.

M. Emeliyanenko and . Sagraloff, On the complexity of solving a bivariate polynomial system. CoRR, abs/1104, 2011.

A. Goldsztejn and L. Granvilliers, A new framework for sharp and efficient resolution of NCSP with manifolds of solutions, Constraints, vol.34, issue.2, pp.190-212, 2010.
DOI : 10.1007/s10601-009-9082-3

URL : https://hal.archives-ouvertes.fr/hal-00480819

M. Giusti, G. Lecerf, B. Salvy, and J. Yakoubsohn, On Location and Approximation of Clusters of Zeros: Case of Embedding Dimension One, Foundations of Computational Mathematics, vol.7, issue.1, pp.1-58, 2007.
DOI : 10.1007/s10208-004-0159-5

URL : https://hal.archives-ouvertes.fr/hal-00186739

J. D. Hauenstein and F. Sottile, Algorithm 921, ACM Transactions on Mathematical Software, vol.38, issue.4, pp.1-2820, 2012.
DOI : 10.1145/2331130.2331136

J. P. Jouanolou, Singularites Rationnelles Du Resultant, Algebraic geometry (Proc. Summer Meeting, pp.183-213, 1978.
DOI : 10.1007/BFb0066645

]. Kah03 and . Kahoui, An elementary approach to subresultants theory, J. Symb. Comput, vol.35, issue.3, pp.281-292, 2003.

]. R. Kea96, . Baker-kearfottkea97-]-r-baker, and . Kearfott, Rigorous global search : continuous problems. Nonconvex optimization and its applications Empirical evaluation of innovations in interval branch and bound algorithms for nonlinear systems, SIAM Journal on Scientific Computing, vol.18, issue.2, pp.574-594, 1996.

]. R. Kra69 and . Krawczyk, Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing (Arch. Elektron. Rechnen), vol.4, pp.187-201, 1969.

Y. Lu, D. J. Bates, A. J. Sommese, C. W. Wamplerlc87-]-w, H. E. Lorensen et al., Finding all real points of a complex curve In Algebra, geometry and their interactions Marching cubes: A high resolution 3d surface construction algorithm, Contemp. Math. Amer. Math. Soc. SIGGRAPH Comput. Graph, vol.448, issue.21, pp.183-205163, 1987.

T. [. Lee, C. H. Li, and . Tsai, HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method, Computing, vol.38, issue.6, pp.109-133, 2008.
DOI : 10.1007/s00607-008-0015-6

B. [. Liang, J. Mourrain, and . Pavone, Subdivision Methods for the Topology of 2d and 3d Implicit Curves, Geometric modeling and algebraic geometry, pp.171-186, 2005.
DOI : 10.1007/978-3-540-72185-7_11

URL : https://hal.archives-ouvertes.fr/inria-00130216

A. Leykin, J. Verschelde, and A. Zhao, Newton's method with deflation for isolated singularities of polynomial systems, Theoretical Computer Science, vol.359, issue.1-3, pp.111-122, 2006.
DOI : 10.1016/j.tcs.2006.02.018

[. Mantzaflaris and B. Mourrain, Deflation and certified isolation of singular zeros of polynomial systems, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, pp.249-256, 2011.
DOI : 10.1145/1993886.1993925

URL : https://hal.archives-ouvertes.fr/inria-00556021

G. Moroz, Fast polynomial evaluation and composition Inria Nancy -Grand Est (Villers-l` es, 2013.

S. Bernard-mourrain, S. Pion, J. Schmitt, E. P. Técourt, N. Tsigaridas et al., Algebraic issues in Computational Geometry, Effective Computational Geometry for Curves and Surfaces, Mathematics and Visualization, pp.117-155, 2006.

]. A. Neu90 and . Neumaier, Interval methods for systems of equations / Arnold Neumaier, 1990.

T. Ojika, S. Watanabe, and T. Mitsui, Deflation algorithm for the multiple roots of a system of nonlinear equations, Journal of Mathematical Analysis and Applications, vol.96, issue.2, pp.463-479, 1983.
DOI : 10.1016/0022-247X(83)90055-0

G. [. Plantinga and . Vegter, Isotopic approximation of implicit curves and surfaces, Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing , SGP '04, pp.245-254, 2004.
DOI : 10.1145/1057432.1057465

J. Recknagel, Topology of planar singular curves resultant of two trivariate polynomials, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00927768

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-00544998

S. M. Rump, SOLVING ALGEBRAIC PROBLEMS WITH HIGH ACCURACY, Proc. of the symposium on A new approach to scientific computation, pp.51-120, 1983.
DOI : 10.1016/B978-0-12-428660-3.50010-0

H. Schichl and A. Neumaier, Exclusion Regions for Systems of Equations, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.383-408, 2005.
DOI : 10.1137/S0036142902418898

J. M. Snyder, Interval analysis for computer graphics, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, SIGGRAPH '92, pp.121-130, 1992.

V. Stahl, Interval Methods for Bounding the Range of Polynomials and Solving Systems of Nonlinear Equations, 1995.

N. [. Seidel and . Wolpert, On the exact computation of the topology of real algebraic curves, Proceedings of the twenty-first annual symposium on Computational geometry , SCG '05, pp.107-115, 2005.
DOI : 10.1145/1064092.1064111

[. Szafraniec, On the number of branches of a 1-dimensional semianalytic set. Kodai Math, J, vol.11, issue.1, pp.78-85, 1988.

J. Verschelde and A. Haegemans, Homotopies for solving polynomial systems within a bounded domain, Theoretical Computer Science, vol.133, issue.1, pp.165-185, 1994.
DOI : 10.1016/0304-3975(94)00064-6