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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Index Form Equations in General,rties, 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., Sect

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Relative Power Integral Bases,situation. The algorithms for determining generators of relative power integral bases will be applied for finding generators of integral bases in higher degree fields having subfields. It is easy to see that if an element generates a power integral basis, then it also generates a relative power inte

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Some Higher Degree Fields,g; for sextic fields a general algorithm does not seem to be feasible, we developed methods for determining power integral bases only in sextic fields having subfields. The case of number fields of degree seven seems to be complicated, since these fields can not have subfields. Special number fields

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Tables, algorithms enables us to list the generators of power integral bases for all number fields with small discriminants. We give the data usually in increasing order of discriminants. These data complete other number field data contained in similar tables. Recall, that in the more complicated fields, w

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