A Python module for (local) Poisson-Nijenhuis calculus on Poisson manifolds
Project description
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:
-
L. C. Garcia-Naranjo, P. Suárez-Serrato & R. Vera,
Poisson Structures on Smooth 4-Manifolds,
Lett. Math. Phys. 105, 1533-1550 (2015) -
P. Suárez-Serrato & J. Torres-Orozco,
Poisson Structures on Wrinkled Fibrations,
Bol. Soc.Mat. Mex. 22, 263-280 (2016) -
P. Suárez-Serrato, J. Torres Orozco, & R. Vera,
Poisson and Near-Symplectic Structures on Generalized Wrinkled Fibrations in Dimension 6,
Ann. Glob. Anal. Geom. (2019) 55, 777-804 (2019) -
M. Evangelista-Alvarado, P. Suárez-Serrato, J. Torres-Orozco & R. Vera,
On Bott-Morse Foliations and their Poisson Structures in Dimension 3,
Journal of Singularities 19, 19-33 (2019)
🚀
-
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:
- Miguel Evangelista Alvarado - @mevangelista-alvarado
- Jose C. Ruíz Pantaleón - @jcrpanta
- Pablo Suárez Serrato - @psuarezserrato
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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