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+========================
+Simplex tree user manual
+========================
+Definition
+----------
+
+.. include:: simplex_tree_sum.rst
+
+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")
+   print("num_vertices=", st.num_vertices())
+   print("num_simplices=", st.num_simplices())
+   print("skeleton_tree(2) =")
+   for sk_value in st.get_skeleton_tree(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_tree(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)