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-:orphan:
-
-.. To get rid of WARNING: document isn't included in any toctree
-
-Simplex tree user manual
-========================
-Definition
-----------
-
-.. include:: simplex_tree_sum.inc
-
-A simplicial complex :math:`\mathbf{K}` on a set of vertices :math:`V = \{1, \cdots ,|V|\}` is a collection of
-simplices :math:`\{\sigma\}`, :math:`\sigma \subseteq V` such that
-:math:`\tau \subseteq \sigma \in \mathbf{K} \rightarrow \tau \in \mathbf{K}`. The dimension :math:`n=|\sigma|-1` of
-:math:`\sigma` is its number of elements minus `1`.
-
-A filtration of a simplicial complex is a function :math:`f:\mathbf{K} \rightarrow \mathbb{R}` satisfying
-:math:`f(\tau)\leq f(\sigma)` whenever :math:`\tau \subseteq \sigma`. Ordering the simplices by increasing filtration
-values (breaking ties so as a simplex appears after its subsimplices of same filtration value) provides an indexing
-scheme.
-
-
-Implementation
---------------
-
-There are two implementation of complexes. The first on is the Simplex_tree data structure.
-The simplex tree is an efficient and flexible data structure for representing general (filtered) simplicial complexes.
-The data structure is described in :cite`boissonnatmariasimplextreealgorithmica`.
-
-The second one is the Hasse_complex. The Hasse complex is a data structure representing explicitly all co-dimension 1
-incidence relations in a complex. It is consequently faster when accessing the boundary of a simplex, but is less
-compact and harder to construct from scratch.
-
-Example
--------
-
-.. testcode::
-
-   import gudhi
-   st = gudhi.SimplexTree()
-   if st.insert([0, 1]):
-       print("[0, 1] inserted")
-   if st.insert([0, 1, 2], filtration=4.0):
-       print("[0, 1, 2] inserted")
-   if st.find([0, 1]):
-       print("[0, 1] found")
-   result_str = 'num_vertices=' + repr(st.num_vertices())
-   print(result_str)
-   result_str = 'num_simplices=' + repr(st.num_simplices())
-   print(result_str)
-   print("skeleton(2) =")
-   for sk_value in st.get_skeleton(2):
-       print(sk_value)
-
-
-The output is:
-
-.. testoutput::
-
-    [0, 1] inserted
-    [0, 1, 2] inserted
-    [0, 1] found
-    num_vertices=3
-    num_simplices=7
-    skeleton(2) =
-    ([0, 1, 2], 4.0)
-    ([0, 1], 0.0)
-    ([0, 2], 4.0)
-    ([0], 0.0)
-    ([1, 2], 4.0)
-    ([1], 0.0)
-    ([2], 4.0)