poissongeometry 0.1

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

PoissonGeometry

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

sharp_morphism	lichnerowicz_poisson_operador	modular_vf
poisson_bracket	bivector_to_matrix	jacobiator
hamiltonian_vf	is_homogeneaos_unimodular	one_forms_bracket
isomorphic_lie_poisson_R3	linear_normal_form_R3	gauge_transformation
flaschka_ratiu_bivector	is_poisson_tensor	is_in_kernel
is_casimir	is_poisson_vf	is_poisson_par
curl_operator

Motivation

Some of the functions in this class have been used to obtain the results in the following publications.

• 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 on Colab English / Spanish

• 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 -r requirements.txt
    

  • Open the python terminal to start:

    (venv_name) C:Users/dekstop/poisson$ python
    

Bugs & Contributions

Our issue tracker is at https://github.com/mevangelista-alvarado/poisson_geometry/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 Ruíz Pantaleón - @jcrpanta
• Pablo Suárez Serrato - @psuarezserrato

Thanks for citing our work if you use it! 🤓