## Computation of the Euclidean minimum of algebraic number fields

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**83**(2014), 1397-1426 Request permission

## 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 in 2007. 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. Then, we show how to apply the algorithm to study extensions of norm-Euclideanity.## References

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## Additional Information

**Pierre Lezowski**- Affiliation: Université de Bordeaux, IMB, CNRS, UMR 5251, F-33400 Talence, France –and– INRIA, LFANT, F-33400 Talence, France
- MR Author ID: 988126
- Email: pierre.lezowski@math.u-bordeaux1.fr
- Received by editor(s): August 17, 2011
- Received by editor(s) in revised form: May 2, 2012, and July 23, 2012
- Published electronically: July 19, 2013
- © Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**83**(2014), 1397-1426 - MSC (2010): Primary 11Y40; Secondary 11R04, 11A05, 13F07
- DOI: https://doi.org/10.1090/S0025-5718-2013-02746-9
- MathSciNet review: 3167464