============================================================================
simplicial: simplicial complexes, homology, topology and persistent homology
============================================================================

:Date:   2021-01-13 (updated 2023-12-13)



What for 
========

Simplified package for understanding how to compute homology, persistent
homology and how to visualize simplicial 
complexes and alike.

.. warning::
 Work in progress (very much) 


 
INSTALL:
--------


First install (download, or exec)

.. code-block:: guess

  $ wget https://www.dlfer.xyz/var/simplicial.py

from a shell, or

  >>> !wget https://www.dlfer.xyz/var/simplicial.py

from a jupyter notebook cell). Check it first if it is safe. 


.. automodule:: simplicial

CONTENT:
========
   
.. autoclass:: simplicial.SimplicialComplex 
   :members: 

.. autoclass:: simplicial.SimplicialMap
   :members: 


.. autofunction:: simplicial.simplicial_sphere

.. autofunction:: simplicial.join_of_complexes

.. autofunction:: simplicial.cartesian_product

.. autofunction:: simplicial.connected_sum

.. autofunction:: simplicial.disjoint_union   

.. autofunction:: simplicial.display_2d

.. autofunction:: simplicial.display_3d

.. autofunction:: simplicial.view

.. autofunction:: simplicial.boundary_operators   

.. autofunction:: simplicial.betti_numbers    


.. autofunction:: simplicial.sign_ordered

.. autofunction:: simplicial.homology

.. autofunction:: simplicial.homology_of_map

.. autofunction:: simplicial.persistent_homology

.. autoclass:: Point
   :members:   

.. autoclass:: Embed
   :members:


OTHER:
------

.. autofunction:: simplicial.subsets

.. autofunction:: simplicial.EPchar

.. autofunction:: simplicial.dim

.. autofunction:: simplicial.dims_c

FOR MATRICES:
-------------

.. autofunction:: simplicial.row_echelon_form

.. autofunction:: simplicial.LDR

.. autofunction:: simplicial.shift_Z

   

DOWNLOAD
========

 - :download:`simplicial.py <soft/simplicial.py>`