Calculating generators of power integral bases in sextic fields with a real quadratic subfield

TL;DR

This paper presents an efficient algorithm for computing generators of power integral bases in sextic fields with real quadratic subfields, leveraging integer arithmetic to improve computational speed.

Contribution

It introduces a novel algorithm specifically designed for sextic fields with real quadratic subfields, enhancing the efficiency of calculating power integral bases.

Findings

Integer arithmetic significantly speeds up calculations.

The algorithm effectively handles sextic fields with real quadratic subfields.

Insights into generators of power integral bases in unit-generated number fields.

Abstract

We discuss the problem of calculating generators of power integral bases in sextic fields, especially focusing on the case of sextic fields with real quadratic subfields. Our main purpose is to describe an efficient algorithm for calculating generators of power integral bases. We show that appropriately using integer arithmetics speeds up the calculations considerably. Our experiences lead to some interesting general statements on generators of power integral bases in number fields generated by a unit.