The QuiverTools package for SageMath and Julia

TL;DR

QuiverTools is a software package in SageMath and Julia that facilitates the study of quivers, their moduli spaces, and related geometric and algebraic computations, aiding researchers in representation theory.

Contribution

It introduces a versatile software tool with new features for analyzing quivers, including stability checks, decompositions, and intersection theory computations.

Findings

Supports computation of subdimension vectors and canonical decompositions

Enables checking of (semi)stability and enumeration of Harder-Narasimhan types

Includes intersection theory calculations on quiver moduli

Abstract

We introduce QuiverTools, a new software package, available in both a SageMath and Julia version, to study quivers and their moduli spaces of representations. Its key features are the computation of general subdimension vectors, leading to canonical decompositions, and checking the existence of (semi)stable representations, as well as the enumeration of Harder-Narasimhan types and related calculations for Teleman quantization. Computations related to intersection theory on quiver moduli are also implemented.