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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)
We give examples of Generalized Euclidean but not norm-Euclidean number fields of degree greater than 2. In the same way we give examples of 2-stage Euclidean but not norm-Euclidean number fields of degree greater than 2. In both cases, no such examples were known.