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A Python module for (local) Poisson-Nijenhuis calculus on Poisson manifolds

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Python PyPI Documentation License GitHub last commit


PoissonGeometry

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

poisson_bracket hamiltonian_vf lichnerowicz_poisson_operator
modular_vf curl_operator flaschka_ratiu_bivector
sharp_morphism bivector_to_matrix jacobiator
one_forms_bracket gauge_transformation is_unimodular_homogeneous *
linear_normal_form_R3 isomorphic_lie_poisson_R3 is_in_kernel *
is_poisson_tensor * is_casimir * is_poisson_vf *
is_poisson_pair *

Remark. We have indicated with an asterisk (*) the six methods whose implementations require testing whether a symbolic expression is zero. These are naturally limited by theoretical computational constraints.

This repository accompanies our paper 'On Computational Poisson Geometry I: Symbolic Foundations'.

Motivation

Some of the functions in this module have been used to obtain the results in these articles:

🚀

  • Run our tutorial on Colab English / Castellano

  • Run on your local machine

    • Clone this repository on your local machine.
    • Open a terminal with the path where you clone this repository.
    • Create a virtual environment,(see this link)
    • Install the requirements:
      (venv_name) C:Users/dekstop/poisson$ pip install poissongeometry
      
    • Open python terminal to start:
      (venv_name) C:Users/dekstop/poisson$ python
      
    • Import PoissonGeometry module:
      >>> from poisson.poisson import PoissonGeometry
      

Bugs & Contributions

Our issue tracker is at https://github.com/appliedgeometry/poissongeometry/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:

Thanks for citing our work if you use it! 🤓

@misc{evangelistaalvarado2019computational,
title={On Computational Poisson Geometry I: Symbolic Foundations},
author={M. A. Evangelista-Alvarado and J. C. Ruíz-Pantaleón and P. Suárez-Serrato},
year={2019},
eprint={1912.01746},
archivePrefix={arXiv},
primaryClass={math.DG}
}

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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