J. Berthomieu, J. Van-der-hoeven, and G. Lecerf, Relaxed algorithms for p-adic numbers, Journal de Th??orie des Nombres de Bordeaux, vol.23, issue.3
DOI : 10.5802/jtnb.777

URL : https://hal.archives-ouvertes.fr/hal-00486680

J. Berthomieu and R. Lebreton, Relaxed p-adic Hensel lifting for algebraic systems, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.59-66, 2012.
DOI : 10.1145/2442829.2442842

URL : https://hal.archives-ouvertes.fr/hal-00660566

S. [. Coppersmith and . 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

X. Dahan, X. Jin, M. Moreno-maza, and É. Schost, Change of order for regular chains in positive dimension, Theoretical Computer Science, vol.392, issue.1-3, pp.37-65, 2008.
DOI : 10.1016/j.tcs.2007.10.003

X. Dahan, M. Moreno-maza, É. Schost, W. Wu, and Y. Xie, Lifting techniques for triangular decompositions, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, pp.108-115, 2005.
DOI : 10.1145/1073884.1073901

X. Dahan, M. Moreno-maza, É. Schost, and Y. Xie, On the complexity of the D5 principle, Transgressive Computing, pp.149-168, 2006.
DOI : 10.1145/1113439.1113457

L. [. Fischer and . Stockmeyer, Fast on-line integer multiplication, Proceedings of the fifth annual ACM symposium on Theory of computing , STOC '73, pp.317-331, 1974.
DOI : 10.1145/800125.804037

. [. Granlund, GMP, the GNU multiple precision arithmetic library, 1991.

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

M. Giusti and J. Heintz, Algorithmes ??? disons rapides ??? pour la d??composition d???une vari??t?? alg??brique en composantes irr??ductibles et ??quidimensionnelles, MEGA, pp.169-194, 1991.
DOI : 10.1007/978-1-4612-0441-1_11

M. Giusti, J. Heintz, K. Hägele, J. E. Morais, L. M. Pardo et al., Lower bounds for diophantine approximations, Journal of Pure and Applied Algebra, vol.117, issue.118, pp.277-317, 1996.
DOI : 10.1016/S0022-4049(97)00015-7

G. [. Giusti, B. Lecerf, and . 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

T. [. Gianni and . Mora, Algebrric solution of systems of polynomirl equations using Groebher bases, Lecture Notes in Comput. Sci, vol.356, pp.247-257, 1987.
DOI : 10.1007/3-540-51082-6_83

]. F. Hen66 and . Hennie, On-line turing machine computations. Electronic Computers, IEEE Transactions, issue.1, pp.1535-1579, 1966.

J. Van-der-hoeven, G. Lecerf, and B. Mourrain, SVN Version 7058 Available from http, 2002.

J. Heintz, G. Matera, and A. Waissbein, On the Time-Space Complexity of Geometric Elimination Procedures, Applicable Algebra in Engineering, Communication and Computing, vol.11, issue.4, pp.239-296, 2001.
DOI : 10.1007/s002000000046

J. Van-der-hoeven, Relax, but Don???t be Too Lazy, Journal of Symbolic Computation, vol.34, issue.6, pp.479-542, 2002.
DOI : 10.1006/jsco.2002.0562

J. Van-der-hoeven, New algorithms for relaxed multiplication, Journal of Symbolic Computation, vol.42, issue.8, pp.792-802, 2007.
DOI : 10.1016/j.jsc.2007.04.004

J. Van-der-hoeven, From implicit to recursive equations, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00583125

]. E. Kal92 and . Kaltofen, On computing determinants of matrices without divisions, Proc. 1992 Internat. Symp. Symbolic Algebraic Comput. (ISSAC'92), pp.342-349, 1992.

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

]. S. Kat90 and . Katsura, Spin glass problem by the method of integral equation of the effective field, New Trends in Magnetism, pp.110-121, 1990.

E. Kaltofen and G. Villard, On the complexity of computing determinants, computational complexity, vol.13, issue.3-4, pp.91-130, 2004.
DOI : 10.1007/s00037-004-0185-3

]. D. Laz91 and . Lazard, A new method for solving algebraic systems of positive dimension, Applied algebra, algebraic algorithms, and errorcorrecting codes, pp.147-160, 1989.

M. [. Li, É. 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

J. F. Ritt, Differential algebra, 1966.
DOI : 10.1090/coll/033

]. F. Rou99 and . Rouillier, Solving zero-dimensional systems through the rational univariate representation, Appl. Algebra Engrg. Comm. Comput, vol.9, issue.5, pp.433-461, 1999.

É. Schost, Degree bounds and lifting techniques for triangular sets, Proceedings of the 2002 international symposium on Symbolic and algebraic computation , ISSAC '02, pp.238-245, 2002.
DOI : 10.1145/780506.780537

É. Schost, Complexity results for triangular sets, International Symposium on Symbolic and Algebraic Computation, pp.555-594, 2002.
DOI : 10.1016/S0747-7171(03)00095-6

]. A. Sto10 and . Stothers, On the Complexity of Matrix Multiplication, 2010.

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

]. S. Wat89 and . Watt, A fixed point method for power series computation, Symbolic and Algebraic Computation, pp.206-217, 1989.

]. W. Wu84 and . Wu, Basic principles of mechanical theorem proving in elementary geometries, J. Systems Sci. Math. Sci, vol.4, issue.3, pp.207-235, 1984.