Monogenity in totally complex sextic fields, revisited

TL;DR

This paper introduces a simple, efficient method for calculating generators of power integral bases in certain sextic number fields, significantly improving previous techniques and applicable to infinite families.

Contribution

Develops a new, streamlined algorithm for finding power integral bases in sextic fields containing a real cubic and a complex quadratic field, enhancing computational efficiency.

Findings

Method successfully applied to infinite parametric families.

Significant reduction in computational complexity.

Enhanced accuracy over previous methods.

Abstract

In addition to rather complicated general methods it is interesting and valuable to develop fast efficient methods for calculating generators of power integral bases in special types of number fields. We consider sextic fields containing a real cubic and a complex quadratic fields. We develop a very simple and very efficient method to calculate generators of power integral bases in this type of fields. Our method can be applied to infinite families of number fields, as well. We substantially improve the former methods. Our algorithm is illustrated with detailed examples, involving infinite parametric families.