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

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.

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.

@article{JTNB_1991__3_2_351_0,
     author = {Cohen, Henri and Diaz y Diaz, Francisco},
     title = {A polynomial reduction algorithm},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {351--360},
     publisher = {Universit\'e Bordeaux I},
     volume = {3},
     number = {2},
     year = {1991},
     doi = {10.5802/jtnb.55},
     zbl = {0758.11053},
     mrnumber = {1149802},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_1991__3_2_351_0/}
}
Henri Cohen; Francisco Diaz Y Diaz. A polynomial reduction algorithm. Journal de Théorie des Nombres de Bordeaux, Tome 3 (1991) no. 2, pp. 351-360. doi : 10.5802/jtnb.55. https://jtnb.centre-mersenne.org/item/JTNB_1991__3_2_351_0/

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