Computational class field theory

TL;DR

This paper discusses algorithms for explicitly computing abelian extensions of number fields, providing an algorithmic perspective on class field theory's intrinsic descriptions.

Contribution

It outlines the available algorithms for the explicit computation of abelian extensions, bridging theoretical class field theory with practical computational methods.

Findings

Algorithms for computing abelian extensions are summarized.

Explicit computational methods are connected to theoretical descriptions.

The paper highlights the algorithmic aspects of class field theory.

Abstract

Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such extensions.