Calculating generators of power integral bases in sextic fields with a quadratic subfield: the general case
Istv\'an Ga\'al
TL;DR
This paper extends algorithms for finding generators of power integral bases in sextic fields with quadratic subfields to the general case, overcoming technical challenges and broadening applicability.
Contribution
It develops a comprehensive method for calculating generators in the most general sextic field cases with quadratic subfields.
Findings
Extended algorithms successfully handle the general case
Overcame key technical difficulties in the computation process
Broadened the scope of power integral basis determination
Abstract
In some previous works we gave algorithms for determining generators of power integral basis in sextic fields with a quadratic subfield, under certain restrictions. The purpose of the present paper is to extend those methods to the general case, when the relative integral basis of the sextic field over the quadratic subfield is of general form. This raises several technical difficulties, that we consider here.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation · Cryptography and Residue Arithmetic