Enumerating orders in number fields

TL;DR

This paper introduces a tree structure to systematically enumerate all orders within a number field, including those of bounded index and over specific orders, facilitating comprehensive analysis.

Contribution

It presents a novel tree-based method for enumerating all orders in a number field, extending to bounded index and specific base orders.

Findings

Efficient enumeration of orders in algebraic number fields.

Framework applicable to orders of bounded index and over given orders.

Provides a systematic approach to explore the structure of orders.

Abstract

We arrange the orders in an algebraic number field in a tree. This tree can be used to enumerate all orders of bounded index in the maximal order as well as the orders over some given order.