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

2025/05/07 by István Gaál, Gaál, István
Computer Science · Mathematics · #11D25 #11R04 #11Y50 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.04293

openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials

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