doc/python/cohomology-persistence.rst
 author Camille Wormser Wed, 12 Aug 2009 07:16:35 -0700 branch dev changeset 162 eec482c29319 parent 146 4e27f1f7c169 child 166 1f3d54b2315b permissions -rw-r--r--
Removing unused parameter names in order to avoid warnings -> no warning anymore in zigzag-persistence

:class:CohomologyPersistence class
====================================

The :ref:rips-pairwise-cohomology illustrates the use of :class:CohomologyPersistence.

.. class:: CohomologyPersistence

.. method:: __init__(prime)

Initializes :class:CohomologyPersistence with the given prime; from
this point on all the computation will be performed with coefficients
coming from :math:\mathbb{Z}/prime \mathbb{Z}.

Adds a simplex with the given boundary to the complex, i.e.
:math:K_{i+1} = K_i \cup \sigma and boundary = :math:\partial \sigma.
If a new class is born as a result of the addition, birth is stored with
it for future reference.

:returns: a pair (i, d). The first element is the index i.
It is the internal representation of the newly added simplex,
and should be used later for removal or when constructing the
boundaries of its cofaces. In other words, boundary must
consist of these indices.  The second element d is the death
element. It is None if a birth occurred, otherwise it
contains the value passed as birth to
:meth:~CohomologyPersistence.add when the class that just
died was born.

.. method:: __iter__()

Iterator over the live cocycles stored in
:class:CohomologyPersistence. The returned elements are of the type
:class:Cocycle below.

.. class:: Cocycle

.. attribute:: birth

The birth value associated with the cocycle. It is passed to
:class:CohomologyPersistence in method
:meth:~CohomologyPersistence.add.

.. method:: __iter__()

Iterator over the individual nodes (simplices) of the cocycle, each of type
:class:CHSNode.

.. class:: CHSNode

.. attribute:: si

The index of the simplex, of type :class:CHSimplexIndex.

.. attribute:: coefficient

Coefficient in :math:\mathbb{Z}/prime \mathbb{Z} associated with the
simplex.

.. class:: CHSimplexIndex

.. attribute:: order

The count associated with the simplex when it is inserted into
:class:CohomologyPersistence.