@incollection{XUPS_2005____89_0, author = {Karim Belabas}, title = {L{\textquoteright}algorithmique de~la~th\'eorie~alg\'ebrique des nombres}, booktitle = {Th\'eorie algorithmique des nombres et \'equations diophantiennes}, series = {Journ\'ees math\'ematiques X-UPS}, pages = {89--162}, publisher = {Les \'Editions de l{\textquoteright}\'Ecole polytechnique}, year = {2005}, doi = {10.5802/xups.2005-02}, mrnumber = {2224342}, zbl = {1121.11080}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/xups.2005-02/} }
TY - JOUR AU - Karim Belabas TI - L’algorithmique de la théorie algébrique des nombres JO - Journées mathématiques X-UPS PY - 2005 SP - 89 EP - 162 PB - Les Éditions de l’École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/xups.2005-02/ DO - 10.5802/xups.2005-02 LA - fr ID - XUPS_2005____89_0 ER -
%0 Journal Article %A Karim Belabas %T L’algorithmique de la théorie algébrique des nombres %J Journées mathématiques X-UPS %D 2005 %P 89-162 %I Les Éditions de l’École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/xups.2005-02/ %R 10.5802/xups.2005-02 %G fr %F XUPS_2005____89_0
Karim Belabas. L’algorithmique de la théorie algébrique des nombres. Journées mathématiques X-UPS, Théorie algorithmique des nombres et équations diophantiennes (2005), pp. 89-162. doi : 10.5802/xups.2005-02. https://proceedings.centre-mersenne.org/articles/10.5802/xups.2005-02/
[1] L. M. Adleman; H. W. Lenstra Finding irreducible polynomials over finite fields, Proceedings of the eighteenth annual ACM symposium on Theory of Computing (Berkeley, CA) (STOC ’86), Association for Computing Machinery, New York, NY, 1986, pp. 350-355 | DOI
[2] Manindra Agrawal; Neeraj Kayal; Nitin Saxena Primes is in P, Ann. of Math. (2), Volume 160 (2004) no. 2, pp. 781-793 | DOI | MR | Zbl
[3] A. V. Aho; J. E. Hopcroft; J. D. Ullman The design and analysis of computer algorithms, Addison-Wesley, 1975
[4] E. Bach Explicit bounds for primality testing and related problems, Math. Comput., Volume 55 (1990) no. 191, pp. 355-380 | DOI | MR | Zbl
[5] Bernard Beauzamy Products of polynomials and a priori estimates for coefficients in polynomial decompositions : a sharp result, J. Symbolic Comput., Volume 13 (1992) no. 5, pp. 463-472 | DOI | MR | Zbl
[6] Karim Belabas Topics in computational algebraic number theory, J. Théor. Nombres Bordeaux, Volume 16 (2004), pp. 19-63 | DOI | Numdam | MR | Zbl
[7] Karim Belabas; Mark van Hoeij; Jürgen Klüners; Allan Steel Factoring polynomials over global fields, J. Théor. Nombres Bordeaux, Volume 21 (2009) no. 1, pp. 15-39 http://jtnb.cedram.org/item?id=JTNB_2009__21_1_15_0 | DOI | Numdam | MR | Zbl
[8] E. R. Berlekamp Factoring polynomials over large finite fields, Math. Comput., Volume 24 (1970), pp. 713-735 | DOI | MR | Zbl
[9] J. Buchmann; H. W. Lenstra Approximating rings of integers in number fields, J. Théor. Nombres Bordeaux, Volume 6 (1994) no. 2, pp. 221-260 | DOI | MR | Zbl
[10] H. Cohen; H. W. Lenstra Heuristics on class groups of number fields, Number theory (Noordwijkerhout 1983) (Lect. Notes in Math.), Volume 1068, Springer, Berlin, 1984, pp. 33-62 | MR | Zbl
[11] H. Cohen; J. Martinet Études heuristiques des groupes de classes des corps de nombres, J. reine angew. Math., Volume 404 (1990), pp. 39-76 | Zbl
[12] Henri Cohen A course in computational algebraic number theory, Graduate Texts in Math., 138, Springer-Verlag, Berlin, 1993 | DOI
[13] H. Davenport; H. Heilbronn On the density of discriminants of cubic fields (II), Proc. Roy. Soc. London Ser. A, Volume 322 (1971), pp. 405-420 | MR | Zbl
[14] J.-P. Demailly Analyse numérique et équations différentielles, Presses Universitaires de Grenoble, 1996
[15] Jordan S. Ellenberg; Akshay Venkatesh The number of extensions of a number field with fixed degree and bounded discriminant, Ann. of Math. (2), Volume 163 (2006) no. 2, pp. 723-741 | DOI | MR | Zbl
[16] David Ford; Sebastian Pauli; Xavier-François Roblot A fast algorithm for polynomial factorization over , J. Théor. Nombres Bordeaux, Volume 14 (2002) no. 1, pp. 151-169 | DOI | MR | Zbl
[17] Joachim von zur Gathen; Jürgen Gerhard Modern computer algebra, Cambridge University Press, Cambridge, 2013 | DOI
[18] Xavier Gourdon Algorithmique du théorème fondamental de l’algèbre (1993) no. 1852 (Rapport de recherche)
[19] J. L. Hafner; K. S. McCurley A rigorous subexponential algorithm for computation of class groups, J. Amer. Math. Soc., Volume 2 (1989) no. 4, pp. 837-850 | DOI | MR | Zbl
[20] H. Hasse Zahlentheorie, Akademie-Verlag GmbH, 1949
[21] Peter Henrici Applied and computational complex analysis, Wiley-Interscience, New York, 1974 (Volume 1 : Power series—integration—conformal mapping—location of zeros)
[22] Mark van Hoeij Factoring polynomials and the knapsack problem, J. Number Theory, Volume 95 (2002) no. 2, pp. 167-189 | DOI | MR | Zbl
[23] J. C. Lagarias; H. L. Montgomery; A. M. Odlyzko A bound for the least prime ideal in the Chebotarev density theorem, Invent. Math., Volume 54 (1979) no. 3, pp. 271-296 | DOI | MR | Zbl
[24] J. C. Lagarias; A. M. Odlyzko Effective versions of the Chebotarev density theorem, Algebraic number fields : -functions and Galois properties (Proc. Sympos., Durham, 1975), Academic Press, London, 1977, pp. 409-464 | Zbl
[25] Serge Lang Algebraic number theory, Graduate Texts in Math., 110, Springer-Verlag, New York, 1994 | DOI
[26] The development of the number field sieve (A. K. Lenstra; H. W. Lenstra, eds.), Lect. Notes in Math., 1554, Springer-Verlag, Berlin, 1993 | DOI | Zbl
[27] A. K. Lenstra; H. W. Lenstra; L. Lovász Factoring polynomials with rational coefficients, Math. Ann., Volume 261 (1982) no. 4, pp. 515-534 | DOI | MR | Zbl
[28] H. W. Lenstra Algorithms in algebraic number theory, Bull. Amer. Math. Soc. (N.S.), Volume 26 (1992) no. 2, pp. 211-244 | DOI | MR | Zbl
[29] M. Mignotte An inequality about factors of polynomials, Math. Comput., Volume 28 (1974), pp. 1153-1157 | DOI | MR | Zbl
[30] Phong Q. Nguyen; Damien Stehlé Floating-point LLL revisited, Advances in cryptology—EUROCRYPT 2005 (Lect. Notes in Comput. Sci.), Volume 3494, Springer, Berlin, 2005, pp. 215-233 | DOI | MR | Zbl
[31] J. Oesterlé Le problème de Gauss sur le nombre de classes, Enseign. Math., Volume 34 (1988), pp. 43-67 | MR | Zbl
[32] C. H. Papadimitriou Computational complexity, Addison-Wesley, 1994
[33] F. Rouillier; P. Zimmermann Efficient isolation of polynomial’s real roots, J. Comput. Appl. Math., Volume 162 (2003) no. 1, pp. 33-50 | DOI | MR | Zbl
[34] René Schoof Four primality testing algorithms, Algorithmic number theory : lattices, number fields, curves and cryptography (Math. Sci. Res. Inst. Publ.), Volume 44, Cambridge Univ. Press, Cambridge, 2008, pp. 101-126 | MR | Zbl
[35] Samir Siksek The modular approach to Diophantine equations, Explicit methods in number theory (Panoramas & Synthèses), Volume 36, Société Mathématique de France, Paris, 2012, pp. 151-179 | MR | Zbl
[36] P. Stevenhagen; H. W. Lenstra Chebotarëv and his density theorem., Math. Intelligencer, Volume 18 (1996) no. 2, pp. 26-37 | DOI | Zbl
[37] A. Storjohann Algorithms for matrix canonical forms, Ph. D. Thesis, ETH Zurich (2000)
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