TL;DR
This paper introduces a Python toolkit for symbolic computation in Poisson geometry, enabling calculations of gauge transformations and parametric bivectors on manifolds, advancing computational methods in this mathematical field.
Contribution
The paper presents a novel computational toolkit and algorithms for local Poisson-Nijenhuis calculus, with implementations and practical examples.
Findings
Python module $ extsf{PoissonGeometry}$ successfully implements the algorithms
Demonstrated gauge transformations of Poisson bivectors in 3D
Determined parametric Poisson bivectors in 4D
Abstract
We present a computational toolkit for (local) Poisson-Nijenhuis calculus on manifolds. Our python module 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.
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