Nous décrivons des algorithmes efficaces pour les opérations usuelles de la théorie algorithmique des corps de nombres, en vue d’applications à la théorie du corps de classes. En particulier, nous traitons l’arithmétique élémentaire, l’approximation et l’obtention d’uniformisantes, le problème du logarithme discret, et le calcul de corps de classes via un élément primitif. Tout ces algorithmes ont été implantés dans le système Pari/Gp .
We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the Pari/Gp system.
Mots clés : class field theory, algorithmic number theory
@article{JTNB_2004__16_1_19_0,
author = {Karim Belabas},
title = {Topics in computational algebraic number theory},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {19--63},
publisher = {Universit\'e Bordeaux 1},
volume = {16},
number = {1},
year = {2004},
doi = {10.5802/jtnb.433},
mrnumber = {2145572},
zbl = {1078.11071},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.433/}
}
TY - JOUR AU - Karim Belabas TI - Topics in computational algebraic number theory JO - Journal de théorie des nombres de Bordeaux PY - 2004 SP - 19 EP - 63 VL - 16 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.433/ DO - 10.5802/jtnb.433 LA - en ID - JTNB_2004__16_1_19_0 ER -
Karim Belabas. Topics in computational algebraic number theory. Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 19-63. doi : 10.5802/jtnb.433. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.433/
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