]. L. Alberti-2008, 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

E. Alonso, M. Becker, T. Roy, and . Wörmann, Multiplicities and Idempotents for Zerodimensional Systems, Algorithms in Algebraic Geometry and Applications, pp.1-20, 1996.

A. , ]. P. Aubry, D. Lazard, and M. M. Maza, On the theories of triangular sets, J. Symb. Comput, vol.28, pp.105-124, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01148870

A. , ]. P. Aubry, and M. M. Maza, Triangular sets for solving polynomial systems: a comparative implementation of four methods, J. Symb. Comput, vol.28, pp.125-154, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01148862

]. S. Basu, R. Pollack, and M. Roy, Algorithms in real algebraic geometry, Algorithms and Computation in Mathematics, vol.10, 2006.
DOI : 10.1007/978-3-662-05355-3

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

]. E. Berberich, P. Emeliyanenko, A. Kobel, and M. Sagraloff, Arrangement Computation for Planar Algebraic Curves Arxiv preprint http, Symbolic Numeric Computation -SNC, pp.17-132, 2011.

]. E. Berberich, P. Emeliyanenko, and M. Sagraloff, An Elimination Method for Solving Bivariate Polynomial Systems: Eliminating the Usual Drawbacks, Alenex, pp.14-132, 2011.
DOI : 10.1137/1.9781611972917.4

]. Berberich, M. Hemmer, M. Kerber, S. Lazard, L. Peñaranda et al., Algebraic Kernel, CGAL User and Reference Manual. CGAL Editorial Board, 4.3 édition, p.2013, 2013.
URL : https://hal.archives-ouvertes.fr/inria-00537545

F. Boulier, C. Chen, F. Lemaire, and M. M. Maza, Real Root Isolation of Regular Chains, Proceedings of the 2009 Asian Symposium on Computer Mathematics Math for Industry, pp.1-15, 2009.
DOI : 10.1007/978-3-662-43799-5_4

URL : https://hal.archives-ouvertes.fr/hal-00825036

]. Y. Bouzidi, S. Lazard, M. Pouget, and F. 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

]. Y. Bouzidi, S. Lazard, M. Pouget, and F. Rouillier, Rational univariate representations of bivariate systems and applications, Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation, ISSAC '13, p.2013, 2013.
DOI : 10.1145/2465506.2465519

URL : https://hal.archives-ouvertes.fr/hal-00802698

]. Y. Bouzidi, S. Lazard, M. Pouget, and F. Rouillier, Separating linear forms for bivariate systems, Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation, ISSAC '13, pp.41-106, 2013.
DOI : 10.1145/2465506.2465518

URL : https://hal.archives-ouvertes.fr/hal-00809425

]. W. Brown, On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors, Journal of the ACM, vol.18, issue.4, pp.478-504, 1971.
DOI : 10.1145/321662.321664

M. Burr, S. W. Choi, B. Galehouse, and C. Yap, Complete subdivision algorithms, II, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, ISSAC '08, p.17, 2008.
DOI : 10.1145/1390768.1390783

]. L. Busé, H. Khalil, and B. Mourrain, Resultant-Based Methods for Plane Curves Intersection Problems, In Computer Algebra in Scientific Computing (CASC) Lecture Notes in Computer Science, vol.3718, pp.75-92, 2005.
DOI : 10.1007/11555964_7

]. J. Canny, A new algebraic method for robot motion planning and real geometry, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987), pp.39-48, 1987.
DOI : 10.1109/SFCS.1987.1

]. J. Canny, Some algebraic and geometric computations in PSPACE, Proceedings of the twentieth annual ACM symposium on Theory of computing , STOC '88, pp.460-467, 1988.
DOI : 10.1145/62212.62257

F. Cazals, J. Faugère, M. Pouget, and F. Rouillier, Ridges and Umbilics of Polynomial Parametric Surfaces, pp.141-159, 2008.
DOI : 10.1007/978-3-540-72185-7_8

URL : https://hal.archives-ouvertes.fr/inria-00329762

]. C. Chen and M. M. Maza, Algorithms for computing triangular decompositions of polynomial systems, Proceeding of the 36th International Symposium on Symbolic and Algebraic Computation, pp.83-90, 2011.

]. Cheng, X. Gao, and C. K. Yap, Complete numerical isolation of real zeros in zero-dimensional triangular systems, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, pp.92-99, 2007.
DOI : 10.1145/1277548.1277562

]. Cheng, X. Gao, and J. Li, Root isolation for bivariate polynomial systems with local generic position method, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.103-110, 2009.
DOI : 10.1145/1576702.1576719

]. 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

]. G. Collins, The calculation of multivariate polynomial resultants, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, SYMSAC '71, pp.212-222, 1971.

]. D. Cox, J. Little, and D. Shea, Ideals, varieties, and algorithms. Undergraduate Texts in Mathematics, 1997.

]. D. Cox, J. Little, and D. Shea, Using algebraic geometry. Numeéro 185 de Graduate Texts in Mathematics, p.78, 2005.

]. D. Cox, J. Little, and D. Shea, Ideals, varieties, and algorithms. Undergraduate Texts in Mathematics, 2007.

]. Diatta, Calcul effectif de la topologie de courbes et surfaces algebriques reelles, p.78, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00438817

]. D. Diochnos, I. Z. Emiris, and E. P. Tsigaridas, On the asymptotic and practical complexity of solving bivariate systems over the reals, Journal of Symbolic Computation, vol.44, issue.7, pp.818-835, 2009.
DOI : 10.1016/j.jsc.2008.04.009

]. A. Eigenwillig, M. Kerber, and N. Wolpert, Fast and exact geometric analysis of real algebraic plane curves, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, pp.151-158, 2007.
DOI : 10.1145/1277548.1277570

]. 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

]. I. Emiris, B. Mourrain, and E. P. Tsigaridas, The DMM bound, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC '10, pp.243-250, 2010.
DOI : 10.1145/1837934.1837981

URL : https://hal.archives-ouvertes.fr/inria-00393833

H. Everett, S. Lazard, D. Lazard, and M. Safey-el-din, The Voronoi diagram of three lines, Proceedings of the twenty-third annual symposium on Computational geometry, SCG '07, pp.255-264, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00186085

]. W. Fulton and R. Weiss, Algebraic curves: an introduction to algebraic geometry, 1989.

]. W. Fulton, Algebraic curves: an introduction to algebraic geometry Personal reprint made available by the author, 2008.

]. J. Garloff and A. P. Smith, Investigation of a subdivision based algorithm for solving systems of polynomial equations, Nonlinear Analysis: Theory, Methods & Applications, vol.47, issue.1, 2000.
DOI : 10.1016/S0362-546X(01)00166-3

]. 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, M. Gonzalez-vega, and . Kahoui, An Improved Upper Complexity Bound for the Topology Computation of a Real Algebraic Plane Curve, Journal of Complexity, vol.12, issue.4, pp.527-544, 1996.
DOI : 10.1006/jcom.1996.0032

I. Vega and . Necula, Efficient topology determination of implicitly defined algebraic plane curves, Computer Aided Geometric Design, vol.19, issue.18, pp.17-131, 2002.

]. M. Kalkbrener, A Generalized Euclidean Algorithm for Computing Triangular Representations of Algebraic Varieties, Journal of Symbolic Computation, vol.15, issue.2, pp.143-167, 1993.
DOI : 10.1006/jsco.1993.1011

M. Sagraloff, A Worst-case Bound for Topology Computation of Algebraic Curves, CoRR, vol.abs, 1104.

M. Sagraloff, A worst-case bound for topology computation of algebraic curves, J. Symb. Comput, vol.47, issue.3, pp.239-258

]. D. Knuth, The analysis of algorithm, pp.269-274, 1971.

]. D. Lazard, Solving zero-dimensional algebraic systems, Journal of Symbolic Computation, vol.13, issue.2, pp.117-132, 1992.
DOI : 10.1016/S0747-7171(08)80086-7

URL : http://doi.org/10.1016/s0747-7171(08)80086-7

S. Lazard, L. M. Peñaranda, and E. P. Tsigaridas, Univariate Algebraic Kernel and Application to Arrangements, Lecture Notes in Computer Science, vol.5526, issue.130, pp.209-220, 2009.
DOI : 10.1007/978-3-642-02011-7_20

URL : https://hal.archives-ouvertes.fr/inria-00372234

]. R. Lebreton, E. Mehrabi, and É. Schost, On the complexity of solving bivariate systems, Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation, ISSAC '13, pp.251-258, 2013.
DOI : 10.1145/2465506.2465950

URL : https://hal.archives-ouvertes.fr/lirmm-00814992

]. T. Li, Numerical Solution of Polynomial Systems by Homotopy Continuation Methods, Handbook of Numerical Analysis, pp.209-304, 2003.
DOI : 10.1016/S1570-8659(02)11004-0

]. X. Li, M. Moreno-maza, R. Rasheed, and É. Schost, The modpn library, ACM SIGSAM Bulletin, vol.42, issue.3, pp.841-858, 2011.
DOI : 10.1145/1504347.1504374

]. T. Lickteig and M. Roy, Sylvester???Habicht Sequences and Fast Cauchy Index Computation, Journal of Symbolic Computation, vol.31, issue.3, pp.315-341, 2001.
DOI : 10.1006/jsco.2000.0427

]. H. Lombardi, Sous-Résultant, suite de Sturm, spécialisation, 1990.

]. W. 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

]. K. Mehlhorn and M. Sagraloff, A Deterministic Descartes Algorithm for Real Polynomials, 2008.

]. K. Mehlhorn, M. Sagraloff, and P. Wang, From approximate factorization to root isolation with application to cylindrical algebraic decomposition, Journal of Symbolic Computation, vol.66, issue.153, p.27, 1301.
DOI : 10.1016/j.jsc.2014.02.001

]. R. Moore, M. J. Cloud, and R. B. Kearfott, Introduction to interval analysis. SIAM e-books, Society for Industrial and Applied Mathematics, 2009.

]. B. Mourrain and J. P. Pavone, Subdivision methods for solving polynomial equations, Polynomial System Solving in honor of Daniel Lazard, pp.292-306, 2009.
DOI : 10.1016/j.jsc.2008.04.016

URL : https://hal.archives-ouvertes.fr/inria-00070350

. Mpfr and . Mpfr, MPFR: a library for multiple-precision floating-point computations, mpfr.org

]. A. Neumaier, Interval methods for systems of equations. Cambridge Middle East Library, 1990.

D. N. Diatta, B. Mourrain, and O. Ruatta, On the computation of the topology of a non-reduced implicit space curve, ISSAC'08: Proceedings of the twenty-first International Symposium on Symbolic and algebraic computation, pp.47-54, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00218271

]. L. Peñaranda, Géometrie algorithmique non linéaire et courbes algébriques planaires, 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. Renegar, On the Worst-Case Arithmetic Complexity of Approximating Zeros of Systems of Polynomials, SIAM Journal on Computing, vol.18, issue.2, pp.350-370, 1989.
DOI : 10.1137/0218024

]. W. Rheinboldt, Methods for solving systems of nonlinear equations, CBMS-NSF Regional Conference Series in Applied Mathematics . Society for Industrial and Applied Mathematics, 1998.
DOI : 10.1137/1.9781611970012

]. F. Rouillier, Solving Zero-Dimensional Systems Through the Rational Univariate Representation, Applicable Algebra in Engineering, Communication and Computing, vol.9, issue.5, pp.433-461, 1999.
DOI : 10.1007/s002000050114

URL : https://hal.archives-ouvertes.fr/inria-00073264

]. 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

]. Roy, Basic algorithms in real algebraic geometry and their complexity : from Strum theorem to the existential theory of reals. Lectures on Real Geometry in memoriam of Mario Raimondo, Gruyter Expositions in Mathematics, vol.23, pp.1-67, 1996.

]. S. Rump, SOLVING ALGEBRAIC PROBLEMS WITH HIGH ACCURACY, 1983.
DOI : 10.1016/B978-0-12-428660-3.50010-0

]. M. Sagraloff, When Newton meets Descartes, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.297-304, 2012.
DOI : 10.1145/2442829.2442872

]. 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

]. E. Sherbrooke and N. M. Patrikalakis, Computation of the solutions of nonlinear polynomial systems, Computer Aided Geometric Design, vol.10, issue.5, pp.379-405, 1993.
DOI : 10.1016/0167-8396(93)90019-Y

]. A. Strzebonski and E. P. Tsigaridas, Univariate real root isolation in multiple extension fields, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.343-350, 2012.
DOI : 10.1145/2442829.2442878

URL : https://hal.archives-ouvertes.fr/hal-00776074

]. J. Verschelde, Polynomial homotopy continuation with PHCpack, ACM SIGSAM Bulletin, vol.44, issue.3/4, 2010.
DOI : 10.1145/1940475.1940524

]. J. Zur-gathen, J. Gerhard, and U. K. Cambridge, Modern computer algebra, pp.39-55, 0118.
DOI : 10.1017/CBO9781139856065

]. D. Wang, Elimination methods. Texts & Monographs in Symbolic Computation, 2001.
DOI : 10.1007/978-3-7091-6202-6

URL : https://hal.archives-ouvertes.fr/inria-00100616