The Kronecker-Vahlen theorem fails in real quadratic norm-Euclidean fields

The present paper is devoted to methods of the automatic verifying of the Kronecker-Vahlen theorem on the shortest length of the Euclidean algorithm in algebraic number fields with the infinite group of units. We provide explicit methods to prove that the Kronecker-Vahlen theorem fails in certain al...

Full description

Saved in:
Bibliographic Details
Published in:Journal of symbolic computation 2021-05, Vol.104, p.134-141
Main Authors: Vaskouski, Maksim, Kondratyonok, Nikita
Format: Article
Language:English
Subjects:
Division chain
Euclidean minimum
Norm-Euclidean quadratic number field
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The present paper is devoted to methods of the automatic verifying of the Kronecker-Vahlen theorem on the shortest length of the Euclidean algorithm in algebraic number fields with the infinite group of units. We provide explicit methods to prove that the Kronecker-Vahlen theorem fails in certain algebraic number field. In particular, we give a complete solution of the problem for quadratic norm-Euclidean number fields.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2020.04.009