Metadata-Version: 2.1
Name: numericalpoissongeometry
Version: 1.0.0
Summary: A Python Numeric module for (local) calculus on Poisson manifolds
Home-page: https://github.com/appliedgeometry/NumericalPoissonGeometry
Author: Miguel Evangelista-Alvarado, Jose C. Crispín Ruíz, Pablo Suárez-Serrato
Author-email: miguel.eva.alv@gmail.com, jcpanta@im.unam.mx, pablo@im.unam.mx
License: MIT
Description: [![Python](https://img.shields.io/pypi/pyversions/numericalpoissongeometry.svg?style=plastic)]()
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        <!--[![Documentation](https://img.shields.io/badge/api-reference-blue.svg)](https://colab.research.google.com/drive/1XYcaJQ29XwkblXQOYumT1s8_00bHUEKZ) -->
        
        ---
        # Numerical Poisson Geometry
        A Python module for (local) Poisson-Nijenhuis calculus on Poisson manifolds, with the following functions:
        
        | **num_bivector_field**        | **num_bivector_to_matrix**    | **num_poisson_bracket**           |
        | :---------------------------: | :---------------------------: | :------------------------------:  |
        | **num_hamiltonian_vf**        | **num_sharp_morphism**        | **num_coboundary_operator**       |
        | **num_modular_vf**            | **num_curl_operator**         | **num_one_forms_bracket**         |
        | **num_gauge_transformation**  | **num_linear_normal_form_R3** | **num_flaschka_ratiu_bivector**   |
        
        
        This repository accompanies our paper ['On Computational Poisson Geometry II: Numerical Methods'](https://arxiv.org/abs/2010.09785).
        
        <!-- For more information you can read the [wiki](https://github.com/mevangelista-alvarado/poisson_geometry/wiki) this project. or the our [documentation]()-->
        
        ## Motivation
        
        This project includes numerical methods that implementation parts of:
        
        * Miguel Evangelista-Alvarado, José C. Ruíz Pantaleón & P. Suárez-Serrato, <br/>
         [On Computational Poisson Geometry I: Symbolic Foundations](https://arxiv.org/pdf/1912.01746.pdf), <br/> 
           arXiv:1912.01746 [math.DG] (2019)
        
        
        ## 🚀
        <!--- #### Testing: --->
        <!-- Solo borrar esto
         * __Run our tutorial on Colab__ [English](https://colab.research.google.com/drive/1XYcaJQ29XwkblXQOYumT1s8_00bHUEKZ) / [Castellano](https://colab.research.google.com/drive/1F9I2TcrhSz0zRZSuALEWldxgw-AL6pOK)
           
         * __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 poissongeometry
              ```
           * Open python terminal to start:
              ```
              (venv_name) C:Users/dekstop/poisson$ python
              ```
           * Import PoissonGeometry class
              ```
              >>> from poisson.poisson import PoissonGeometry
              ```	 
        <!--  * Testing the class.
        	   For example we want convert a bivector to a matrix  <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/appliedgeometry/NumericalPoissonGeometry/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:
         * **José C. Ruíz Pantaleón** - [@jcrpanta](https://github.com/jcrpanta)
         * **Pablo Suárez Serrato** - [@psuarezserrato](https://github.com/psuarezserrato)
         * **Miguel Evangelista-Alvarado** - [@mevangelista-alvarado](https://github.com/mevangelista-alvarado)
        
        ## Thanks for citing our work if you use it! 🤓 ##
        @misc{evangelistaalvarado2020computational,<br/>
              title={On Computational Poisson Geometry II: Numerical Methods}, <br/>
              author={M. Evangelista-Alvarado and J. C. Ruíz-Pantaleón and P. Suárez-Serrato},<br/>
              year={2020},<br/>
              eprint={2010.09785},<br/>
              archivePrefix={arXiv},<br/>
              primaryClass={math.DG}<br/>
        }
        
        ## 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.
        
        ---
        
        <p align="center">
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          <img src="https://www.matem.unam.mx/++theme++im-theme-blue/images/logo_imunam.png">
        </p>
        
Platform: UNKNOWN
Classifier: Development Status :: 5 - Production/Stable
Classifier: Programming Language :: Python :: 3 :: Only
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Intended Audience :: Science/Research
Requires-Python: >=3.6
Description-Content-Type: text/markdown
