Calculating Power Integral Bases by Solving Relative Thue Equations
نویسندگان
چکیده
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.
منابع مشابه
On the resolution of relative Thue equations
An efficient algorithm is given for the resolution of relative Thue equations. The essential improvement is the application of an appropriate version of Wildanger’s enumeration procedure based on the ellipsoid method of Fincke and Pohst. Recently relative Thue equations have gained an important application, e.g., in computing power integral bases in algebraic number fields. The presented method...
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