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

29 pages, 31 figures. Revised structure and better title, improved the W(G2,f) example

References in corpus (5)

• Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies
• A new scheme of integrability for (bi)Hamiltonian PDE
• Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
• Lambda: A Mathematica-package for operator product expansions in vertex algebras
• Dispersive deformations of the Hamiltonian structure of Euler's equations

Cited by in corpus (2)

• Computing with Hamiltonian operators
• Weakly nonlocal Poisson brackets: tools, examples, computations