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1 IMB - Institut de Mathématiques de Bordeaux 2 LFANT - Lithe and fast algorithmic number theory IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest

Abstract : We present an algorithm to compute the Euclidean minimum of an algebraic number field, which is a generalization of the algorithm restricted to the totally real case described by Cerri. With a practical implementation, we obtain unknown values of the Euclidean minima of algebraic number fields of degree up to 8 in any signature, especially for cyclotomic fields, and many new examples of norm-Euclidean or non-norm-Euclidean algebraic number fields. We also prove a result of independant interest concerning real quadratic fields whose Euclidean minimum is equal to 1.





Author: Pierre Lezowski -

Source: https://hal.archives-ouvertes.fr/



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