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Computation of the Euclidean minimum of algebraic number fields

Pierre Lezowski 1, 2
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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00632997
Contributor : Pierre Lezowski Connect in order to contact the contributor
Submitted on : Monday, October 17, 2011 - 11:43:56 AM
Last modification on : Friday, December 3, 2021 - 12:20:06 PM
Long-term archiving on: : Wednesday, January 18, 2012 - 2:26:46 AM

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  • HAL Id : hal-00632997, version 1

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Pierre Lezowski. Computation of the Euclidean minimum of algebraic number fields. 2011. ⟨hal-00632997v1⟩

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