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Numerical Poisson Geometry

A Python module for (local) Poisson-Nijenhuis calculus on Poisson manifolds, with the following functions:

num_bivector_field	num_bivector_to_matrix	num_poisson_bracket
num_hamiltonian_vf	num_sharp_morphism	num_coboundary_operator
num_modular_vf	num_curl_operator	num_one_forms_bracket
num_gauge_transformation	num_linear_normal_form_R3	num_flaschka_ratiu_bivector

This repository accompanies our paper 'On Computational Poisson Geometry II: Numerical Methods'.

Motivation

This project includes numerical methods that implementation parts of:

• Miguel Evangelista-Alvarado, José C. Ruíz Pantaleón & P. Suárez-Serrato, (2021)
  On Computational Poisson Geometry I: Symbolic Foundations,
  Journal of Geometric Mechanics, Vol 13, Issue 4.

🚀

Bugs & Contributions

Our issue tracker is at https://github.com/appliedgeometry/NumericalPoissonGeometry/issues. Please report any bugs that you find. Or, even better, if you are interested in our project you can fork the repository on GitHub and create a pull request.

Licence 📄

MIT licence

Authors ✒️

This work is developed and maintained by:

• José C. Ruíz Pantaleón - @jcrpanta
• Pablo Suárez Serrato - @psuarezserrato
• Miguel Evangelista-Alvarado - @mevangelista-alvarado

Thanks for citing our work if you use it! 🤓

@articleInfo{ERS2021,
	title = {On computational Poisson geometry II: Numerical methods},
	journal = {Journal of Computational Dynamics},
	volume = {8},
	number = {3},
	pages = {273-307}
	year = {2021},
	issn = {2158-2491},
	doi = {10.3934/jcd.2021012},
	url = {https://www.aimsciences.org/article/id/6aacf722-3708-40d1-9e7b-770f289551ed},
	author = {Miguel Ángel Evangelista-Alvarado and José Crispín Ruíz-Pantaleón and Pablo Suárez-Serrato},
	keywords = {Poisson structures, Hamiltonian dynamics, Poisson–Nijenhuis calculus, numerical methods, Python}
}

Acknowledgments

This work was partially supported by the grants CONACyT, “Programa para un Avance Global e Integrado de la Matemática Mexicana” CONACyT-FORDECYT 26566 and "Aprendizaje Geométrico Profundo" UNAM-DGAPA-PAPIIT-IN104819. JCRP wishes to also thank CONACyT for a postdoctoral fellowship held during the production of this work.

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