A compendium on the cluster algebra and quiver package in sage

TL;DR

This paper presents a comprehensive Sage package for cluster algebras and quivers, designed to facilitate education, research, and experimentation with the theory through examples, data, and conjecture testing.

Contribution

It introduces a user-friendly Sage package that includes theoretical background, practical examples, and detailed data structures for cluster algebra research and education.

Findings

Accessible to undergraduates and researchers

Includes executable examples in Sage environment

Supports testing of conjectures and data gathering

Abstract

This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by gathering data, and by exhibiting and testing conjectures. In this compendium, we include the relevant theory to introduce the reader to cluster algebras assuming no prior background; this exposition has been written to be accessible to an interested undergraduate. Throughout this compendium, we include examples that the user can run in the sage notebook or command line, and then close with a detailed description of the data structures and methods in this package.