Local-to-global computation of integral bases without a previous factorization of the discriminant

TL;DR

This paper presents a method to compute integral bases of number fields using a local-to-global approach that avoids initial discriminant factorization, relying instead on successive splittings and minimal factorizations.

Contribution

It adapts Ore's old technique to compute integral bases without prior discriminant factorization, simplifying the process under mild assumptions.

Findings

Successfully computes integral bases without initial discriminant factorization

Yields successive splittings of the discriminant as a by-product

Requires only squarefree factorization of certain base factors to complete

Abstract

We adapt an old local-to-global technique of Ore to compute, under certain mild assumptions, an integral basis of a number field without a previous factorization of the discriminant of the defining polynomial. In a first phase, the method yields as a by-product successive splittings of the discriminant. When this phase concludes, it requires a squarefree factorization of some base factors of the discriminant to terminate.