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+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       Clément Maria
+ *
+ *    Copyright (C) 2014 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_
+#define DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_
+
+// needs namespace for Doxygen to link on classes
+namespace Gudhi {
+
+
+/** \defgroup simplex_tree Filtered Complexes
+ * @{
+ * \author    Clément Maria
+ *
+ * A simplicial complex \f$\mathbf{K}\f$ on a set of vertices \f$V = \{1, \cdots ,|V|\}\f$ is a collection of
+ * simplices \f$\{\sigma\}\f$, \f$\sigma \subseteq V\f$ such that
+ * \f$\tau \subseteq \sigma \in \mathbf{K} \rightarrow \tau \in \mathbf{K}\f$. The dimension \f$n=|\sigma|-1\f$ of
+ * \f$\sigma\f$ is its number of elements minus \f$1\f$.
+ *
+ * A filtration of a simplicial complex is a function \f$f:\mathbf{K} \rightarrow \mathbb{R}\f$ satisfying
+ * \f$f(\tau)\leq f(\sigma)\f$ whenever \f$\tau \subseteq \sigma\f$. 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.
+ *
+ * \section filteredcomplexesimplementation Implementations
+ * \subsection filteredcomplexessimplextree Simplex tree
+ * 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
+ * \image html "Simplex_tree_representation.png" "Simplex tree representation"
+ * 
+ * \subsubsection filteredcomplexessimplextreeexamples Examples
+ * 
+ * Here is a list of simplex tree examples :
+ * \li <a href="_simplex_tree_2simple_simplex_tree_8cpp-example.html">
+ * Simplex_tree/simple_simplex_tree.cpp</a> - Simple simplex tree construction and basic function use.
+ *
+ * \li <a href="_simplex_tree_2simplex_tree_from_cliques_of_graph_8cpp-example.html">
+ * Simplex_tree/simplex_tree_from_cliques_of_graph.cpp</a> - Simplex tree construction from cliques of graph read in
+ * a file.
+ * 
+ * Simplex tree construction with \f$\mathbb{Z}/3\mathbb{Z}\f$ coefficients on weighted graph Klein bottle file:
+ * \code $> ./simplex_tree_from_cliques_of_graph ../../data/points/Klein_bottle_complex.txt 3 \endcode
+ * \code Insert the 1-skeleton in the simplex tree in 0.000404 s. 
+max_dim = 3
+Expand the simplex tree in 3.8e-05 s. 
+Information of the Simplex Tree: 
+Number of vertices = 10   Number of simplices = 98 \endcode
+ * 
+ * \li <a href="_simplex_tree_2example_alpha_shapes_3_simplex_tree_from_off_file_8cpp-example.html">
+ * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp</a> - Simplex tree is computed and displayed
+ * from a 3D alpha complex (Requires CGAL, GMP and GMPXX to be installed).
+ * 
+ * \li <a href="_simplex_tree_2graph_expansion_with_blocker_8cpp-example.html">
+ * Simplex_tree/graph_expansion_with_blocker.cpp</a> - Simple simplex tree construction from a one-skeleton graph with
+ * a simple blocker expansion method.
+ *
+ * \subsection filteredcomplexeshassecomplex Hasse complex
+ * 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.
+ * 
+ * @}
+ */
+
+}  // namespace Gudhi
+
+#endif  // DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_