T. A. Akoglu, J. D. Hauenstein, and A. Szanto, Certifying solutions to overdetermined and singular polynomial systems over Q, 1408.

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

H. Caprasse, J. Demaret, and E. , Schrüfer: Can EXCALC be used to Investigate High-Dimensional Cosmological Models with Non-Linear Lagrangians? ISSAC, pp.116-124, 1988.

R. M. Corless, P. M. Gianni, and B. M. Trager, A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots, Proceedings of the 1997 international symposium on Symbolic and algebraic computation , ISSAC '97, pp.133-140, 1997.
DOI : 10.1145/258726.258767

B. H. Dayton, T. Li, and Z. Zeng, Multiple zeros of nonlinear systems, Mathematics of Computation, vol.80, issue.276, pp.2143-2168, 2011.
DOI : 10.1090/S0025-5718-2011-02462-2

B. H. Dayton and Z. Zeng, Computing the multiplicity structure in solving polynomial systems, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, pp.116-123, 2005.
DOI : 10.1145/1073884.1073902

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

M. Giusti and J. Yakoubsohn, Multiplicity hunting and approximating multiple roots of polynomial systems, Contemp. Math, vol.604, pp.105-128, 2013.
DOI : 10.1090/conm/604/12070

S. Graillat and P. Trébuchet, A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.167-173, 2009.
DOI : 10.1145/1576702.1576727
URL : https://hal.archives-ouvertes.fr/hal-01294713

J. D. Hauenstein and C. Wampler, Isosingular Sets and Deflation, Foundations of Computational Mathematics, vol.46, issue.9, pp.371-403, 2013.
DOI : 10.1007/s10208-013-9147-y

W. Hao, A. J. Sommese, and Z. Zeng, Algorithm 931, ACM Transactions on Mathematical Software, vol.40, issue.1, 2013.
DOI : 10.1145/2513109.2513114

G. Lecerf, Quadratic newton iterarion for systems with multiplicity, Found. Comput. Math, issue.2, pp.247-293, 2002.

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

N. Li and L. Zhi, Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One, SIAM Journal on Numerical Analysis, vol.50, issue.1, pp.354-372, 2012.
DOI : 10.1137/110827247

F. S. Macaulay, The Algebraic Theory of Modular Systems, 1916.

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

M. G. Marinari, T. Mora, and H. Möller, Gröbner duality and multiplicities in polynomial system solving, ISSAC '95, pp.167-179, 1995.

H. M. Möller and H. J. Stetter, Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems, Numerische Mathematik, vol.70, issue.3, pp.311-329, 1995.
DOI : 10.1007/s002110050122

B. Mourrain, Isolated points, duality and residues, Journal of Pure and Applied Algebra, vol.117, issue.118, pp.117-118469, 1997.
DOI : 10.1016/S0022-4049(97)00023-6
URL : https://hal.archives-ouvertes.fr/inria-00125278

T. Ojika, Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations, Journal of Mathematical Analysis and Applications, vol.123, issue.1, pp.199-221, 1987.
DOI : 10.1016/0022-247X(87)90304-0

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

S. Pope and A. Szanto, Nearest multivariate system with given root multiplicities, Journal of Symbolic Computation, vol.44, issue.6, pp.606-625, 2009.
DOI : 10.1016/j.jsc.2008.03.005

H. J. Stetter, Analysis of zero clusters in multivariate polynomial systems, Proceedings of the 1996 international symposium on Symbolic and algebraic computation , ISSAC '96, pp.127-136, 1996.
DOI : 10.1145/236869.236919

C. Traverso, The posso test suite. with complement by D, Bini & B. Mourrain, 1993.

X. Wu and L. Zhi, Determining singular solutions of polynomial systems via symbolic???numeric reduction to geometric involutive forms, Journal of Symbolic Computation, vol.47, issue.3, pp.104-122, 2008.
DOI : 10.1016/j.jsc.2011.10.001

N. Yamamoto, Regularization of solutions of nonlinear equations with singular jacobian matrices, J. Inform. Proc, vol.7, issue.1, pp.16-21, 1984.

Z. Zeng, Computing multiple roots of inexact polynomials, Mathematics of Computation, vol.74, issue.250, pp.869-903, 2005.
DOI : 10.1090/S0025-5718-04-01692-8