Metadata-Version: 2.1
Name: PoissonGeometry
Version: 0.1
Summary: A Python class for (local) Poisson-Nijenhuis calculus on Poisson manifolds
Home-page: https://github.com/appliedgeometry/poisson_geometry
Author: Miguel Evangelista-Alvarado, Jose Ruiz, Pablo Suarez-Serrato
Author-email: miguel.eva.alv@gmail.com, jcpanta@im.unam.mx, pablo@im.unam.mx
License: MIT License
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Description-Content-Type: text/markdown
Requires-Dist: sympy
Requires-Dist: galgebra

# `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__           |                                |                      |

<!-- For more information you can read the [wiki](https://github.com/mevangelista-alvarado/poisson_geometry/wiki) this project. or the our [documentation]()-->

## 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](https://link.springer.com/article/10.1007/s11005-015-0792-8), 

 Lett. Math. Phys. 105, 1533-1550 (2015). 
 * P. Suárez-Serrato & J. Torres-Orozco. [Poisson structures on wrinkled fibrations](https://link.springer.com/article/10.1007/s40590-015-0072-8),

 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](https://link.springer.com/article/10.1007/s10455-019-09651-2),

 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](http://journalofsingularities.org/volume19/article2.html), 

 Journal of Singularities 19, 19-33(2019)

## 🚀
<!--- #### Testing: --->
 * __Run on Colab__ [English](https://colab.research.google.com/drive/1XYcaJQ29XwkblXQOYumT1s8_00bHUEKZ) / [Spanish](https://colab.research.google.com/drive/1SN6PS0auO-h3aCXIenblnwJIV-YpowtZ)

 * __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](https://gist.github.com/mevangelista-alvarado/8ee2fd663e7446e543fc04eacce0f303))
   * 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
      ```

	<!-- 
	* Testing the class.
	   For example we want convert to matriz the bivector <a href="https://www.codecogs.com/eqnedit.php?latex=$$\pi=x_{3}\frac{\partial}{\partial&space;x_{1}}\wedge\frac{\partial}{\partial&space;x_{2}}&space;-&space;x_{2}\frac{\partial}{\partial&space;x_{1}}\wedge\frac{\partial}{\partial&space;x_{3}}&space;&plus;&space;x_{1}\frac{\partial}{\partial&space;x_{2}}\wedge\frac{\partial}{\partial&space;x_{3}}$$" target="_blank"><img src="https://latex.codecogs.com/gif.latex?$$\pi=x_{3}\frac{\partial}{\partial&space;x_{1}}\wedge\frac{\partial}{\partial&space;x_{2}}&space;-&space;x_{2}\frac{\partial}{\partial&space;x_{1}}\wedge\frac{\partial}{\partial&space;x_{3}}&space;&plus;&space;x_{1}\frac{\partial}{\partial&space;x_{2}}\wedge\frac{\partial}{\partial&space;x_{3}}$$" title="$$\pi=x_{3}\frac{\partial}{\partial x_{1}}\wedge\frac{\partial}{\partial x_{2}} - x_{2}\frac{\partial}{\partial x_{1}}\wedge\frac{\partial}{\partial x_{3}} + x_{1}\frac{\partial}{\partial x_{2}}\wedge\frac{\partial}{\partial x_{3}}$$" /></a>
	   then <a href="https://www.codecogs.com/eqnedit.php?latex=\pi" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\pi" title="\pi" /></a> is equivalent to ```{(1,2): 'x3', (1,3): '-x2', (2,3): 'x1'}``` in this class.
	   ```
	   >>> from poisson import PoissonGeometry
	   >>> # We instantiate the Poisson class for dimension 3
	   >>> pg = PoissonGeometry(3)
	   >>> pg.bivector_to_matrix({(1,2): 'x3', (1,3): '-x2', (2,3): 'x1'})
	   Matrix([
	   [  0,  x3, -x2],
	   [-x3,   0,  x1],
	   [ x2, -x1,   0]])
	   ```

		This function has an option for output is in latex format string, for this, we change the flag latex_format to True (its default value is False) as shown below.

		```
		 >>> print(pg.bivector_to_matrix({(1,2): 'x3', (1,3): '-x2', (2,3): 'x1'}, latex_format=True))
		   \left[\begin{array}{ccc}0 & x_{3} & - x_{2}\\- x_{3} & 0 & x_{1}\\x_{2} & - x_{1} & 0\end{array}\right]
		```
		<!--For more information to how use this class you can read the [documentation]() or the our [wiki](https://github.com/mevangelista-alvarado/poisson_geometry/wiki)-->

<!--## TO DO
Calculate Poisson Cohomology with linear coefficients.-->

## 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](https://github.com/mevangelista-alvarado)
 * **Jose Ruíz Pantaleón** - [@jcrpanta](https://github.com/jcrpanta)
 * **Pablo Suárez Serrato** - [@psuarezserrato](https://github.com/psuarezserrato)

## Thanks for citing our work if you use it! 🤓 ##

<!-- 
## Do not forget.
* Comment to others about this project 📢
* Cite this project if you use it 🤓.
* Finally, if you know one of the authors, invite him a beer🍺.
---


