MasterPVA and WAlg: Mathematica packages for Poisson vertex algebras and classical affine $\mathcal{W}$-algebras

TL;DR

This paper introduces Mathematica packages MasterPVA, MasterPVAmulti, and WAlg designed for computing lambda-brackets in Poisson vertex algebras and classical affine W-algebras, facilitating research in infinite-dimensional Hamiltonian systems.

Contribution

The paper presents new computational tools that automate lambda-bracket calculations in Poisson vertex and W-algebras, enhancing research capabilities in mathematical physics.

Findings

Successfully implemented packages with explicit examples.

Streamlined calculations of lambda-brackets in complex algebras.

Facilitated research in Hamiltonian systems and W-algebras.

Abstract

We give an introduction to the Mathematica packages "MasterPVA" and "MasterPVAmulti used to compute lambda-brackets in Poisson vertex algebras, which play an important role in the theory of infinite-dimensional Hamiltonian systems. As an application, we give an introduction to the Mathematica package "WAlg" aimed to compute the lambda-brackets among the generators of classical affine W-algebras. The use of these packages is shown by providing some explicit examples.