Topics in computational algebraic number theory
Journal de Théorie des Nombres de Bordeaux, Volume 16 (2004) no. 1, pp. 19-63.

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.

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 .

Received:
Published online:
DOI: 10.5802/jtnb.433
Classification: 11Y40
Keywords: class field theory, algorithmic number theory
Karim Belabas 1

1 Mathématiques–Bâtiment 425 Université Paris–Sud F–91405 Orsay Cedex
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Karim Belabas. Topics in computational algebraic number theory. Journal de Théorie des Nombres de Bordeaux, Volume 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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