E. Becker, T. Mora, M. G. Marinari, and C. Traverso, The shape of the Shape Lemma, Proceedings of the international symposium on Symbolic and algebraic computation , ISSAC '94, pp.129-133, 1994.
DOI : 10.1145/190347.190382

W. Bosma, J. Cannon, and C. Playoust, The Magma Algebra System I: The User Language, Journal of Symbolic Computation, vol.24, issue.3-4, pp.3-4235, 1997.
DOI : 10.1006/jsco.1996.0125

A. Bostan, B. Salvy, and E. Schost, Fast Algorithms for Zero-Dimensional Polynomial Systems using Duality, Applicable Algebra in Engineering, Communication and Computing, vol.14, issue.4, pp.239-272, 2003.
DOI : 10.1007/s00200-003-0133-5

URL : https://hal.archives-ouvertes.fr/inria-00072296

J. Dumas, T. Gautier, M. Giesbrecht, P. Giorgi, B. Hovinen et al., LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA, Mathematical Software, pp.40-50, 2002.
DOI : 10.1142/9789812777171_0005

D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, 1995.

J. Faugère, P. Gaudry, L. Huot, and G. Renault, Polynomial systems solving by fast linear algebra, 2013.

J. Faugère, A new efficient algorithm for computing Gröbner bases without reduction to zero (F5), Proceedings of the 2002 international symposium on Symbolic and algebraic computation, ISSAC '02, pp.75-83, 2002.

J. Faugère, P. Gaudry, L. Huot, and G. Renault, Using Symmetries in the Index Calculus for Elliptic Curves Discrete Logarithm, Journal of Cryptology, vol.32, issue.1, pp.1-41
DOI : 10.1007/s00145-013-9158-5

J. 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, L. Huot, A. Joux, G. Renault, and V. Vitse, Symmetrized summation polynomials: Using small order torsion points to speed up elliptic curve index calculus, 2014, To appear in the proceedings of the 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2014.

J. Faugère and C. Mou, Fast algorithm for change of ordering of zero-dimensional Gröbner bases with sparse multiplication matrices, ISSAC '11: Proceedings of the 2011 international symposium on Symbolic and algebraic computation, pp.1-8, 2011.

J. Faugère and C. Mou, Sparse FGLM algorithms, Journal of Symbolic Computation, vol.80, 2013.
DOI : 10.1016/j.jsc.2016.07.025

A. Galligo, A propos du th??or??me de pr??paration de weierstrass, 1973.
DOI : 10.1090/S0002-9947-1968-0217093-3

P. Gianni and T. Mora, Algebraic solution of systems of polynomial equations using Gröbner bases, Applied Algebra, Algebraic Algorithms and Error Correcting Codes, Proceedings of AAECC-5, pp.247-257, 1989.

E. Jonckheere and C. Ma, A simple Hankel interpretation of the Berlekamp-Massey algorithm, Linear Algebra and its Applications, vol.125, pp.65-76, 1989.
DOI : 10.1016/0024-3795(89)90032-3

W. Keller-gehrig, Fast algorithms for the characteristics polynomial, Theoretical Computer Science, vol.36, pp.309-317, 1985.
DOI : 10.1016/0304-3975(85)90049-0

Y. N. Lakshman, On the complexity of computing a Gröbner basis for the radical of a zero dimensional ideal, Proceedings of the twenty-second annual ACM symposium on Theory of computing, STOC '90, pp.555-563, 1990.

D. Lazard, Gr??bner bases, Gaussian elimination and resolution of systems of algebraic equations, Computer Algebra, pp.146-156, 1983.
DOI : 10.1007/3-540-12868-9_99

J. Massey, Shift-register synthesis and bch decoding. Information Theory, IEEE Transactions on, vol.15, issue.1, pp.122-127, 1969.

G. Moreno-socías, Degrevlex Gr??bner bases of generic complete intersections, Journal of Pure and Applied Algebra, vol.180, issue.3, pp.263-283, 2003.
DOI : 10.1016/S0022-4049(02)00297-9

A. Morgan, Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems, Society for Industrial and Applied Mathematics, 2009.

B. Mourrain and V. Y. Pan, Asymptotic acceleration of solving multivariate polynomial systems of equations, Proceedings of the thirtieth annual ACM symposium on Theory of computing , STOC '98, pp.488-496, 1998.
DOI : 10.1145/276698.276862

H. Orman, The oakley key determination protocol, 1998.
DOI : 10.17487/rfc2412

K. Pardue, Nonstandard Borel-Fixed Ideals, 1994.

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.

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. Strassen, Gaussian elimination is not optimal, Numerische Mathematik, vol.13, issue.4, pp.354-356, 1969.
DOI : 10.1007/BF02165411

V. and V. Williams, Multiplying matrices faster than coppersmith-winograd, Proceedings of the 44th symposium on Theory of Computing, STOC '12, pp.887-898, 2012.
DOI : 10.1145/2213977.2214056

D. H. Wiedemann, Solving sparse linear equations over finite fields, IEEE Transactions on Information Theory, vol.32, issue.1, pp.54-62, 1986.
DOI : 10.1109/TIT.1986.1057137