A polynomial reduction algorithm
Journal de Théorie des Nombres de Bordeaux, Volume 3 (1991) no. 2, pp. 351-360.

The algorithm described in this paper is a practical approach to the problem of giving, for each number field K a polynomial, as canonical as possible, a root of which is a primitive element of the extension K/. Our algorithm uses the LLL algorithm to find a basis of minimal vectors for the lattice of n determined by the integers of K under the canonical map.

L’algorithme que nous décrivons dans ce papier est une approche pratique de la représentation d’un corps de nombre K par la racine d’un polynôme aussi canonique que possible. Nous utilisons l’algorithme LLL pour trouver une base de petits vecteurs pour le réseau de n image des entiers de K par le plongement canonique.

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     title = {A polynomial reduction algorithm},
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Henri Cohen; Francisco Diaz Y Diaz. A polynomial reduction algorithm. Journal de Théorie des Nombres de Bordeaux, Volume 3 (1991) no. 2, pp. 351-360. doi : 10.5802/jtnb.55. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.55/

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