Isomorphisms of Algebraic Number Fields

TL;DR

This paper introduces a new, efficient algorithm for determining all isomorphisms between algebraic number fields, especially effective when only one isomorphism exists.

Contribution

The paper presents a novel method for identifying all isomorphisms between algebraic number fields, improving efficiency over previous approaches.

Findings

Algorithm successfully finds all isomorphisms in tested cases.

Efficiency increases when the number of isomorphisms is one.

Method outperforms existing techniques in specific scenarios.

Abstract

Let $\mathbb{Q}(\alpha)$ and $\mathbb{Q}(\beta)$ be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, $\mathbb{Q}(\beta) \rightarrow \mathbb{Q}(\alpha)$. The algorithm is particularly efficient if the number of isomorphisms is one.