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

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Pure Fields,ction 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.

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Goblet-Cells

Quartic Relative Extensions, in the extension field by using the relative power integral bases..In Sect. . we describe a relative analogue of the method of Sect. . to calculate relative power integral bases in relative quartic extensions. Applying this method in Sect. . we consider power integral bases in octic fields with qua

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Tables,ons. Recall that several examples are also given in the corresponding sections..In Sects. . and . we list the solutions of binomial Thue equations and binomial relative Thue equations, respectively..We made extensive computations in cubic, quartic, and sextic fields..The table of Sect. . gives all g

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D. J. Caballero-Garcia,A. Jimenez-MarrufoThe resolution of index form equations in cubic and quartic number fields is based on solving Thue equations. We give here an overview of the methods for solving these equations. We also consider binomial Thue equations that we shall apply in the sequel in pure quartic fields (Sect. .).

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Apoptosis

Thue Equations,The resolution of index form equations in cubic and quartic number fields is based on solving Thue equations. We give here an overview of the methods for solving these equations. We also consider binomial Thue equations that we shall apply in the sequel in pure quartic fields (Sect. .).

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