Solving index form equations in fields of degree 9 with cubic subfields
type: Item
instance of: scholarly article
title: Solving index form equations in fields of degree 9 with cubic subfields
zbMATH Open document ID: 0983.11077
published in: Journal of Symbolic Computation
publication date: 2002-04-23T00:00:00Z
review text: This paper gives a detailed description of an effective algorithm for solving index form equations in number fields of degree 9, which are composites of complex cubic fields with coprime discriminants. In view of a recent result by the author [Can. Math. Bull. 41, 158-165 (1998; Zbl 0951.11012)], the index form equation may be reduced to cubic relative Thue equations over the cubic subfields. The most difficult computational task is to solve these Thue equations. The main purpose of the paper is to show that the present approach is much more effective than the direct method, which reduces the index form equation to unit equations over the normal closure of the degree 9 field. At the end of the paper, the author describes his computational experience with three explicit examples.
Mathematics Subject Classification ID: 11Y50
Mathematics Subject Classification ID: 11D59
Mathematics Subject Classification ID: 11D57
zbMATH DE Number: 1513057
zbMATH Keywords: effective algorithm
zbMATH Keywords: index form equations
zbMATH Keywords: cubic relative Thue equations
author: István Gaál
reviewed by: Roelof J. Stroeker
MaRDI profile type: Publication
full work available at URL: jsco.1999.0356
OpenAlex ID: W2029447385
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DOI: 10.1006/JSCO.1999.0356
description: scientific article; zbMATH DE number 1513057