On computational Poisson geometry I: Symbolic foundations

We present a computational toolkit for (local) Poisson-Nijenhuis calculus on manifolds. Our Python module $\textsf{PoissonGeometry}$ implements our algorithms and accompanies this paper. Examples of how our methods can be used are explained, including gauge transformations of Poisson bivector in dim...

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Bibliographic Details
Published inJournal of geometric mechanics Vol. 13; no. 4; p. 607
Main Authors Evangelista-Alvarado, Miguel Ángel, Ruíz-Pantaleón, José Crispín, Suárez-Serrato, Pablo
Format Journal Article
LanguageEnglish
Published 01.12.2021
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Summary:We present a computational toolkit for (local) Poisson-Nijenhuis calculus on manifolds. Our Python module $\textsf{PoissonGeometry}$ implements our algorithms and accompanies this paper. Examples of how our methods can be used are explained, including gauge transformations of Poisson bivector in dimension 3, parametric Poisson bivector fields in dimension 4, and Hamiltonian vector fields of parametric families of Poisson bivectors in dimension 6.
ISSN:1941-4889
1941-4897
DOI:10.3934/jgm.2021018