A. V. Aho, K. Steiglitz, and J. D. Ullman, Evaluating Polynomials at Fixed Sets of Points, SIAM Journal on Computing, vol.4, issue.4, pp.533-539, 1975.
DOI : 10.1137/0204045

P. Aubry and A. Valibouze, Using Galois Ideals for Computing Relative Resolvents, Journal of Symbolic Computation, vol.30, issue.6, pp.635-651, 2000.
DOI : 10.1006/jsco.2000.0376
URL : https://hal.archives-ouvertes.fr/inria-00099277

P. Aubry and A. Valibouze, Algebraic computation of resolvents without extraneous powers, European Journal of Combinatorics, vol.33, issue.7, 2012.
DOI : 10.1016/j.ejc.2012.03.003
URL : https://hal.archives-ouvertes.fr/hal-00624447

A. Bostan, Algorithmique efficace pour des opérations de base en Calcul formel, 2003.

A. Bostan, M. F. Chowdhury, J. Van-der-hoeven, and . Schost, Homotopy methods for multiplication modulo triangular sets, J. Symb. Comp, 2011.

A. Bostan, P. Flajolet, B. Salvy, and . Schost, Fast computation of special resultants, Journal of Symbolic Computation, vol.41, issue.1, pp.1-29, 2006.
DOI : 10.1016/j.jsc.2005.07.001
URL : https://hal.archives-ouvertes.fr/inria-00000960

A. Bostan and . Schost, Polynomial evaluation and interpolation on special sets of points, Journal of Complexity, vol.21, issue.4, pp.420-446, 2005.
DOI : 10.1016/j.jco.2004.09.009

D. G. Cantor and E. Kaltofen, On fast multiplication of polynomials over arbitrary algebras, Acta Informatica, vol.7, issue.7, pp.693-701, 1991.
DOI : 10.1007/BF01178683

D. Casperson and J. Mckay, Symmetric functions, m-sets, and Galois groups, Math. Comp, vol.63, issue.208, pp.749-757, 1994.
DOI : 10.2307/2153295

N. Chebotarev, Grundzüge des Galois'shen Theorie. P. Noordhoff Efficient computation of squarefree Lagrange resolvents, 1950.

D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, Proceedings of the nineteenth annual ACM conference on Theory of computing , STOC '87, pp.251-280, 1990.
DOI : 10.1145/28395.28396
URL : http://doi.org/10.1016/s0747-7171(08)80013-2

X. Dahan, M. Moreno-maza, ´. E. Schost, and Y. Xie, On the complexity of the D5 principle, TC'06, pp.149-168, 2006.
DOI : 10.1145/1113439.1113457

L. De-feo-andéand´andé and . Schost, Fast arithmetics in Artin-Schreier towers over finite fields, ISSAC'09, pp.127-134, 2009.

C. Durvye and G. Lecerf, A concise proof of the Kronecker polynomial system solver from scratch, Expositiones Mathematicae, vol.26, issue.2, pp.101-139, 2008.
DOI : 10.1016/j.exmath.2007.07.001
URL : https://hal.archives-ouvertes.fr/hal-00682083

J. C. Faugère, P. Gianni, D. Lazard, and T. Mora, Efficient Computation of Zero-dimensional Gr??bner Bases by Change of Ordering, Journal of Symbolic Computation, vol.16, issue.4, pp.329-344, 1993.
DOI : 10.1006/jsco.1993.1051

J. Faugère and C. Mou, Fast algorithm for change of ordering of zero-dimensional Gröbner bases with sparse multiplication matrices, ISSAC'11, pp.115-122, 2011.

J. Zur-gathen and J. Gerhard, Modern Computer Algebra, 2003.
DOI : 10.1017/CBO9781139856065

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

J. Heintz, T. Krick, S. Puddu, J. Sabia, and A. Waissbein, Deformation Techniques for Efficient Polynomial Equation Solving, Journal of Complexity, vol.16, issue.1, pp.70-109, 2000.
DOI : 10.1006/jcom.1999.0529
URL : http://doi.org/10.1006/jcom.1999.0529

J. König, Aus dem UngarischenübertragenUngarischen¨Ungarischenübertragen vom Verfasser, B. G. Teubner, 1903.

L. Kronecker, Grundzüge einer arithmetischen theorie des algebraischen grössen, J. reine angew. Math, vol.92, pp.1-122

J. Lagrange, Réflexions sur la résolution algébrique deséquations deséquations, Mémoires de l'Académie de Berlin, 1770.

F. Lehobey, Resolvent computations by resultants without extraneous powers, Proceedings of the 1997 international symposium on Symbolic and algebraic computation , ISSAC '97, pp.85-92, 1997.
DOI : 10.1145/258726.258756

X. Li, M. M. Maza, and W. Pan, Computations modulo regular chains, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.239-246, 2009.
DOI : 10.1145/1576702.1576736
URL : http://arxiv.org/abs/0903.3690

X. Li, M. Moreno-maza, and . Schost, Fast arithmetic for triangular sets, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, pp.891-907, 2009.
DOI : 10.1145/1277548.1277585

F. S. Macaulay, The algebraic theory of modular systems, 1994.

A. Poteaux and . Schost, On the complexity of computing with zero-dimensional triangular sets, Journal of Symbolic Computation, vol.50, 2011.
DOI : 10.1016/j.jsc.2012.05.008
URL : https://hal.archives-ouvertes.fr/hal-00825847

N. Rennert and A. Valibouze, Calcul de r??solvantes avec les modules de Cauchy, Experimental Mathematics, vol.21, issue.22, pp.351-366, 1999.
DOI : 10.1090/S0025-5718-1973-0327712-4
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.4002

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

A. Schönhage, The fundamental theorem of algebra in terms of computational complexity, 1982.

A. Schönhage and V. Strassen, Fast multiplication of large numbers, Computing, vol.150, issue.3-4, pp.281-292, 1971.
DOI : 10.1007/BF02242355

J. T. Schwartz, Fast Probabilistic Algorithms for Verification of Polynomial Identities, Journal of the ACM, vol.27, issue.4, pp.701-717, 1980.
DOI : 10.1145/322217.322225

V. Shoup, Fast Construction of Irreducible Polynomials over Finite Fields, Journal of Symbolic Computation, vol.17, issue.5, pp.371-391, 1994.
DOI : 10.1006/jsco.1994.1025

L. Soicher, The computation of the Galois groups, 1981.

A. Stothers, On the Complexity of Matrix Multiplication, 2010.

A. Valibouze, Fonctions sym??triques et changements de bases, EUROCAL'87, pp.323-332, 1989.
DOI : 10.1007/3-540-51517-8_135

V. and V. Williams, Breaking the Coppersmith-Winograd barrier, 2011.

K. Yokoyama, A modular method for computing the Galois groups of polynomials, Journal of Pure and Applied Algebra, vol.117, issue.118, pp.617-636, 1997.
DOI : 10.1016/S0022-4049(97)00030-3