On Computational Poisson Geometry I: Symbolic Foundations

M. A. Evangelista-Alvarado, J. C. Ruíz-Pantaleón, Pablo Suárez-Serrato

Abstract: We present a computational toolkit for (local) Poisson-Nijenhuis calculus on manifolds. Our python module $\textsf{PoissonGeometry}$ implements our algorithms, and accompanies this paper. We include two examples of how our methods can be used, one for gauge transformations of Poisson bivectors in dimension 3, and a second one that determines parametric Poisson bivector fields in dimension 4.