Titlebook: Diophantine Equations and Power Integral Bases; New Computational Me István Gaál Book 20021st edition Birkh?user Boston 2002 Algebraic Numb

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Kenneth S. Alexander,Joseph C. Watkinsrties, makes the resolution of index form equations much easier. A special situation (which otherwise is frequent in numerical examples) is considered in Section 4.4, when the field . is the composite of its subfields. The general results on composite fields have several applications, see e.g., Sections 8.3, 10.2, 10.3.1 and 10.3.3.

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Sextic Fields,An analogue of the general method used for quintic fields, reducing the index form equation directly to unit equations, does not seem to be feasible in sextic fields.

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Introduction,s. As we shall see, this algorithmic problem is satisfactorily solved for lower degree number fields (especially for cubic and quartic fields) and there are efficient methods for certain classes of higher degree fields. Our algorithms enable us in many cases to describe all power integral bases also in . of certain number fields.

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Quartic Fields,ex form equation can be reduced to a cubic and some corresponding quartic Thue equations (see Section 6.1). This means that in fact the index form equations in quartic fields are not much harder to solve than in the cubic case.