Titlebook: Diophantine Equations and Power Integral Bases; Theory and Algorithm István Gaál Book 2019Latest edition Springer Nature Switzerland AG 201

外形

Spatial Tensions in Urban Designn properties, makes the resolution of index form equations much easier. In the numerical examples the field . is often the composite of its subfields. This special case is considered in Sect. .. The general results on composite fields have several applications, see for example Sects. ., ., ., and ..

方舟

Probabilistic Projection in Planningction of the integral basis in . allows us to give conditions on the monogenity of .. We follow the presentation of Gaál and Remete (J Number Theory 173:129–146, 2017). We consider pure cubic, quartic, sextic, and octic fields in detail.

寬容

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商議

A Computational Model for the Insect Brain determine generators of power integral bases. 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 cas

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起草

Geoffrey Edwards,Marie-Josée Fortin..Finally, in Sect. . we show that index form equations in pure quartic fields lead to binomial Thue equations..Interesting tables about the distribution of minimal indices and about the average behavior of minimal indices of quartic fields can be found in the tables of Sects. . and ., respectively.

察覺

Probabilistic Projection in Planninge show some interesting applications of the results of Sect. . on composite fields. We close the chapter by investigating power integral bases in the infinite parametric family of simplest sextic fields (Sect. 11.5).

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名義上

https://doi.org/10.1007/978-94-017-3046-4mber fields up to discriminants 10. and 10., respectively, with all possible generators of power integral bases are given in Sects. . and ., respectively. Monogenity data are given in a large number of further quartic fields in Sect. ...The five totally real cyclic sextic fields with smallest discri