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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the resolution of relative Thue equations


Authors: István Gaál and Michael Pohst
Journal: Math. Comp. 71 (2002), 429-440
MSC (2000): Primary 11Y50; Secondary 11D59
Published electronically: June 29, 2001
MathSciNet review: 1863012
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Abstract:

An efficient algorithm is given for the resolution of relative Thue equations. The essential improvement is the application of an appropriate version of Wildanger's enumeration procedure based on the ellipsoid method of Fincke and Pohst.

Recently relative Thue equations have gained an important application, e.g., in computing power integral bases in algebraic number fields. The presented methods can surely be used to speed up those algorithms.

The method is illustrated by numerical examples.


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Additional Information

István Gaál
Affiliation: University of Debrecen, Mathematical Institute, H–4010 Debrecen Pf.12., Hungary
Email: igaal@math.klte.hu

Michael Pohst
Affiliation: Technische Universität Berlin, Fakultät II, Institut für Mathematik, Straße des 17. Juni 136, 10623 Germany
Email: pohst@math.tu-berlin.de

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01329-1
PII: S 0025-5718(01)01329-1
Keywords: Relative Thue equation, Baker's method, reduction, enumeration
Received by editor(s): April 3, 1998
Received by editor(s) in revised form: May 5, 1999
Published electronically: June 29, 2001
Additional Notes: Research of the first author was supported in part by Grants 16791 and 16975 from the Hungarian National Foundation for Scientific Research.
Research of the second author was supported by the Deutsche Forschungsgemeinschaft.
Article copyright: © Copyright 2001 American Mathematical Society