Computing upper cluster algebras

TL;DR

This paper introduces computational techniques for presenting upper cluster algebras, focusing on algorithms that work effectively when the algebra is totally coprime and finitely generated, with practical examples included.

Contribution

It provides new methods for computing presentations of upper cluster algebras that are suitable for computer implementation and guaranteed to succeed under certain conditions.

Findings

Techniques successfully produce presentations for upper cluster algebras.

Methods are effective when the algebra is totally coprime and finitely generated.

Several examples demonstrate the applicability of the methods.

Abstract

This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is totally coprime and finitely generated. We include several examples of presentations produced by these methods.