T. A. Akoglu, J. D. Hauenstein, and ´. A. Szántó, Certifying solutions to overdetermined and singular polynomial systems over Q, 2014.

L. Alberti, B. Mourrain, and J. 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

D. J. Bates, J. D. Hauenstein, A. J. Sommese, and C. W. Wampler, Bertini: Software for numerical algebraic geometry, 2013.

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

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

Y. Bouzidi, S. Lazard, M. Pouget, F. Rouillier, M. En-burr et al., New bivariate system solver and topology of algebraic curves Complete subdivision algorithms ii: Isotopic meshing of singular algebraic curves, 27th European Workshop on Computational Geometry -EuroCG, pp.131-152, 2011.

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

J. Cheng, S. Lazard, L. Peñaranda, M. Pouget, F. 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

R. M. Corless, G. M. Diaz-toca, M. Fioravanti, L. Gonzalez-vega, I. F. Rua et al., Computing the topology of a real algebraic plane curve whose defining equations are available only ???by values???, Computer Aided Geometric Design, vol.30, issue.7, pp.675-706, 2013.
DOI : 10.1016/j.cagd.2013.04.003

D. Cox, J. Little, and D. O-'shea, Using Algebraic Geometry, 2005.
DOI : 10.1007/978-1-4757-6911-1

J. 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 <mml:math altimg="si17.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> to <mml:math altimg="si18.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>, Journal of Computational and Applied Mathematics, vol.271, pp.267-284, 2014.
DOI : 10.1016/j.cam.2014.03.032

P. Emeliyanenko and M. Sagraloff, On the complexity of solving a bivariate polynomial system, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.154-161, 2012.
DOI : 10.1145/2442829.2442854

M. Giusti, G. Lecerf, B. Salvy, J. Yakoubsohn, and . Feb, 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.1-28, 2012.
DOI : 10.1145/2331130.2331136

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

M. E. Kahoui, An elementary approach to subresultants theory, Journal of Symbolic Computation, vol.35, issue.3, pp.281-292, 2003.
DOI : 10.1016/S0747-7171(02)00135-9

URL : http://doi.org/10.1016/s0747-7171(02)00135-9

R. B. Kearfott, Rigorous global search: continuous problems. Nonconvex optimization and its applications, 1996.
DOI : 10.1007/978-1-4757-2495-0

R. B. Kearfott, 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, 1997.
DOI : 10.1137/S1064827594266131

R. Krawczyk, Newton-algorithms for evaluation of roots with error bounds, Computing, vol.47, issue.3, pp.187-201, 1969.
DOI : 10.1007/BF02234767

T. Lee, T. Li, and C. 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

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

C. Liang, B. Mourrain, and J. Pavone, Subdivision methods for 2d and 3d implicit curves. In: Geometric modeling and algebraic geometry, pp.171-186, 2008.
DOI : 10.1007/978-3-540-72185-7_11

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

L. Lin and C. Yap, Adaptive Isotopic Approximation of Nonsingular Curves: the Parameterizability and Nonlocal Isotopy Approach, Discrete & Computational Geometry, vol.26, issue.2, pp.760-795, 2011.
DOI : 10.1007/s00454-011-9345-9

W. E. Lorensen and H. E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, ACM SIGGRAPH Computer Graphics, vol.21, issue.4, pp.163-169, 1987.
DOI : 10.1145/37402.37422

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.3930

Y. Lu, D. J. Bates, A. J. Sommese, and C. W. Wampler, Finding all real points of a complex curve, In: Algebra, geometry and their interactions. Contemp. Math. Amer. Math. Soc, vol.448448, pp.183-20508665, 2007.
DOI : 10.1090/conm/448/08665

A. 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

B. Martin, A. Goldsztejn, L. Granvilliers, and C. Jermann, Certified Parallelotope Continuation for One-Manifolds, SIAM Journal on Numerical Analysis, vol.51, issue.6, pp.3373-3401, 2013.
DOI : 10.1137/130906544

URL : https://hal.archives-ouvertes.fr/hal-01408525

R. E. Moore and S. T. Jones, Safe Starting Regions for Iterative Methods, SIAM Journal on Numerical Analysis, vol.14, issue.6, pp.1051-1065, 1977.
DOI : 10.1137/0714072

G. Moroz, Fast polynomial evaluation and composition, Inria Nancy -Grand Est, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00846961

B. Mourrain, S. Pion, S. Schmitt, J. Técourt, E. P. Tsigaridas et al., Algebraic Issues in Computational Geometry, Effective Computational Geometry for Curves and Surfaces. Mathematics and Visualization, pp.117-155, 2006.
DOI : 10.1007/978-3-540-33259-6_3

D. H. Myszka, A. P. Murray, and C. W. Wampler, Computing the Branches, Singularity Trace, and Critical Points of Single Degree-of-Freedom, Closed-Loop Linkages, Journal of Mechanisms and Robotics, vol.6, issue.1, 2013.
DOI : 10.1115/1.4025752

A. Neumaier, T. Ojika, S. Watanabe, and T. Mitsui, Interval methods for systems of equations URL http://www.loc.gov/catdir/toc/cam041/89070812 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.

L. M. Peñaranda, Non-linear computational geometry for planar algebraic curves. Theses, Université Nancy II. URL https, 2010.

S. Plantinga and G. 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. Bachelor's Thesis. URL http, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00927768

N. Revol and F. 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

F. Rouillier and P. 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

S. M. Rump, SOLVING ALGEBRAIC PROBLEMS WITH HIGH ACCURACY, 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

R. Seidel and N. 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

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.
DOI : 10.1145/133994.134024

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.7431

V. Stahl, Interval methods for bounding the range of polynomials and solving systems of nonlinear equations, 1995.

Z. Szafraniec, On the number of branches of a $1$-dimensional semianalytic set, Kodai Mathematical Journal, vol.11, issue.1, pp.78-85, 1988.
DOI : 10.2996/kmj/1138038822

J. Van-der-hoeven, Reliable homotopy continuation, Tech. rep, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00589948

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