LEZOWSKI, Pierre

doi:10.1090/S0025-5718-2013-02746-9

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LEZOWSKI, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]

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Mathematics of Computation. 2014, vol. 83, p. 1397-1426

American Mathematical Society

Resumen en inglés

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.< Leer menos