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diff --git a/cython/doc/simplex_tree_user.rst b/cython/doc/simplex_tree_user.rst deleted file mode 100644 index aebeb29f..00000000 --- a/cython/doc/simplex_tree_user.rst +++ /dev/null @@ -1,72 +0,0 @@ -: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) |