Singularities of Differentiable Maps: Volume I: The Classification of Critical Points Caustics and Wave Fronts, 1988. ,
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
Bertini: Software for numerical algebraic geometry, 2013. ,
Computing the topology of a real algebraic plane curve whose defining equations are available only, Comput. Aided Geom. Design, issue.7, pp.30675-706, 2013. ,
On the Topology of Real Algebraic Plane Curves, Mathematics in Computer Science, vol.41, issue.9, pp.113-137, 2010. ,
DOI : 10.1016/j.jsc.2006.06.004
URL : https://hal.archives-ouvertes.fr/inria-00517175
Points fixes, zéros et la méthode de Newton, Mathématiques et Applications, 2006. ,
Bifurcations and catastrophes: geometry of solutions to nonlinear problems ,
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
A New Robust Algorithm to Trace Curves, Reliable Computing, vol.29, issue.9, pp.309-324, 2007. ,
DOI : 10.1007/978-1-4757-2495-0
An efficient method for analyzing the topology of plane real algebraic curves, Mathematics and Computers in Simulation, vol.42, pp.4-6571, 1996. ,
A Subdivision Solver for Systems of Large Dense Polynomials, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01293526
Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve, Proceedings of the 6th International Conferences on Mathematical Aspects of Computer and Information Sciences, MACIS'15, 2015. ,
DOI : 10.1007/978-3-319-32859-1_6
URL : https://hal.archives-ouvertes.fr/hal-01239447
A certified numerical algorithm for the topology of resultant and discriminant curves, Journal of Symbolic Computation, vol.80, issue.2, pp.285-306, 2017. ,
DOI : 10.1016/j.jsc.2016.03.011
URL : https://hal.archives-ouvertes.fr/hal-01402194
Rigorous global search: continuous problems. Nonconvex optimization and its applications, 1996. ,
XPMaps and Topological Segmentation - A Unified Approach to Finite Topologies in the Plane, International Conference on Discrete Geometry for Computer Imagery, pp.22-33, 2002. ,
DOI : 10.1007/3-540-45986-3_2
Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing (Arch. Elektron. Rechnen), vol.4, pp.187-201, 1969. ,
An Interval Step Control for Continuation Methods, SIAM Journal on Numerical Analysis, vol.31, issue.3, pp.892-914, 1994. ,
DOI : 10.1137/0731048
URL : http://interval.louisiana.edu/preprints/1989-simple-interval-step-control.pdf
Finding all real points of a complex curve, Algebra, geometry and their interactions, pp.183-205, 2007. ,
DOI : 10.1090/conm/448/08665
URL : http://www.math.colostate.edu/~bates/preprints/real_curves.pdf
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
Graphs on surfaces and their applications, 2013. ,
Parallel Robots, volume 74 of Solid Mechanics and its Applications ,
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
Introduction to interval analysis. Siam, 2009. ,
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
Interval methods for systems of equations, 1990. ,
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
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
Interval Methods for Bounding the Range of Polynomials and Solving Systems of Nonlinear Equations, 1995. ,
On singularities of mappings of euclidean spaces. i. mappings of the plane into the plane, Annals of Mathematics, vol.62, issue.3, pp.374-410, 1955. ,