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

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Geoffrey Edwards,Marie-Josée Fortinbles. The resolution of such an equation can yield a difficult problem. The main goal of this chapter is to point out that in the quartic case the index form equation can be reduced to a cubic and some corresponding quartic Thue equations (see Sect. .). This means that in fact the index form equatio

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Marie-Josée Fortin,Geoffrey Edwards quintic fields. In the most interesting case, for totally real quintic fields with Galois group .., .., or .., this computation takes several hours, contrary to the cubic and quartic cases, where to solve the index form equation was the matter of seconds or at most some minutes. The general method

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Probabilistic Projection in Planningds to calculate generators of power integral bases in case the sextic field admits some additional property, making the index form equation easier. We have efficient algorithms for sextic fields having quadratic or cubic subfields (see Sects. 11.2 and 11.3). Investigating the structure of the index

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Roberto Casati,Achille C. Varzi 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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https://doi.org/10.1007/978-3-030-23865-0Algebraic Number Theory; Algorithmic Analysis; number theory; Diophantine equation; Diophantine equation

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