On Computational Poisson Geometry II: Numerical Methods

Abstract

We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and modular vector fields, compute the image under the coboundary and trace operators, the Lie bracket of differential 1-forms, gauge transformations, and normal forms of Lie-Poisson structures on $\mathbf{R}^{3}$. The complexity of each of our methods is calculated, and we include experimental verifications on examples in dimensions two and three.