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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computation of the Euclidean minimum of algebraic number fields
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by Pierre Lezowski PDF
Math. Comp. 83 (2014), 1397-1426 Request permission


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.
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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:
  • 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:
  • MathSciNet review: 3167464