<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In our recent paper I. Gaál: Calculating “small” solutions of relative Thue equations, J. Experiment. Math. (to appear) we gave an efficient algorithm to calculate “small” solutions of relative Thue equations (where “small” means an upper bound of type 10<sup>500</sup> for the sizes of solutions). Here we apply this algorithm to calculating power integral bases in sextic fields with an imaginary quadratic subfield and to calculating relative power integral bases in pure quartic extensions of imaginary quadratic fields. In both cases the crucial point of the calculation is the resolution of a relative Thue equation. We produce numerical data that were not known before.</p></abstract>

In our recent paper I. Gaál: Calculating “small” solutions of relative Thue equations, J. Experiment. Math. (to appear) we gave an efficient algorithm to calculate “small” solutions of relative Thue equations (where “small” means an upper bound of type 10500 for the sizes of solutions). Here we apply this algorithm to calculating power integral bases in sextic fields with an imaginary quadratic subfield and to calculating relative power integral bases in pure quartic extensions of imaginary quadratic fields. In both cases the crucial point of the calculation is the resolution of a relative Thue equation. We produce numerical data that were not known before.

Calculating Power Integral bases by Solving Relative Thue Equations

University of Debrecen Mathematical Institute H–4010-Debrecen Pf.12. Hungary

University of Debrecen Mathematical Institute H-4010-Debrecen Pf.12. Hungary

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Calculating Power Integral bases by Solving Relative Thue Equations"}

In our recent paper I. Gaál: Calculating “small” solutions of relative Thue equations, J. Experiment. Math. (to appear) we gave an efficient algorithm to...

Calculating Power Integral bases by Solving Relative Thue Equations

Publié en ligne: 11 mars 2015

Pages: 79 - 92

Reçu: 14 sept. 2014

DOI: https://doi.org/10.2478/tmmp-2014-0020

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.