Skip to main content

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

Project description

Python PyPI Documentation License GitHub last commit


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'.


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 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! 🤓

title={On Computational Poisson Geometry I: Symbolic Foundations},
author={M. A. Evangelista-Alvarado and J. C. Ruíz-Pantaleón and P. Suárez-Serrato},


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.

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

poissongeometry-1.0.2.tar.gz (19.2 kB view hashes)

Uploaded Source

Built Distribution

poissongeometry-1.0.2-py3-none-any.whl (18.0 kB view hashes)

Uploaded Python 3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page