Newton polygons and p-integral bases

TL;DR

This paper employs Newton polygons, an old technique by Ore, to efficiently construct p-integral bases of number fields defined by p-regular equations, with applications to quartic fields.

Contribution

It introduces a method using Newton polygons to compute p-integral bases for p-regular equations, enhancing computational efficiency.

Findings

Constructed p-integral bases for p-regular equations

Applied method to quartic fields

Demonstrated computational efficiency

Abstract

Let p be a prime number. In this paper we use an old technique of Ore, based on Newton polygons, to construct in an efficient way p-integral bases of number fields defined by a p-regular equation. To illustrate the potential applications of this construction, we show how this result yields a computation of a p-integral basis of an arbitrary quartic field in terms of a defining equation.