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This article deals with the determination of the Euclidean minimum M (K) of a totally real number field K of degree n ≥ 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 discrim-inants, most of which were previously unknown. Tables are given at(More)
In this article we study totally definite quaternion fields over the rational field and over quadratic number fields. We establish a complete list of all such fields which are Euclidean. Moreover, we prove that every field in this list is in fact norm-Euclidean. The proofs are both theoretical and algorithmic.
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