Euclidean minima of totally real fields : Algorithmic determination.
Résumé
This article deals with the determination of the Euclidean minimum $ M(K)$ of a totally real number field $ K$ of degree $ n\geq 2$, using techniques from the geometry of numbers. Our improvements of existing algorithms allow us to compute Euclidean minima for fields of degree $ 2$ to $ 8$ and small discriminants, most of which were previously unknown. Tables are given at the end of this paper.