Merge pull request #66 from VincentRouvreau/small_fixes

Small fixes

17 files changed, 236 insertions, 226 deletions

diff --git a/src/cython/cython/simplex_tree.pyx b/src/cython/cython/simplex_tree.pyx
index 0ab97f80..ea99c940 100644
--- a/src/cython/cython/simplex_tree.pyx
+++ b/src/cython/cython/simplex_tree.pyx
@@ -405,7 +405,8 @@ cdef class SimplexTree:
         """This function ensures that each simplex has a higher filtration
         value than its faces by increasing the filtration values.
 
-        :returns: The filtration modification information.
+        :returns: True if any filtration value was modified,
+        False if the filtration was already non-decreasing.
         :rtype: bool
 
 
@@ -513,10 +514,9 @@ cdef class SimplexTree:
         return intervals_result
 
     def persistence_pairs(self):
-        """This function returns the persistence pairs of the simplicial
-        complex.
+        """This function returns a list of persistence birth and death simplices pairs.
 
-        :returns: The persistence intervals.
+        :returns: A list of persistence simplices intervals.
         :rtype:  list of pair of list of int
 
         :note: persistence_pairs function requires
diff --git a/src/cython/doc/alpha_complex_sum.inc b/src/cython/doc/alpha_complex_sum.inc
index 1680a712..806988bb 100644
--- a/src/cython/doc/alpha_complex_sum.inc
+++ b/src/cython/doc/alpha_complex_sum.inc
@@ -1,22 +1,20 @@
-=================================================================  ===================================  ===================================
-:Author: Vincent Rouvreau                                          :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-:Requires: CGAL :math:`\geq` 4.7.0                                 Eigen3
-=================================================================  ===================================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| .. figure::                                                    | Alpha_complex is a simplicial complex constructed from the finite      |
-|      ../../doc/Alpha_complex/alpha_complex_representation.png  | cells of a Delaunay Triangulation.                                     |
-|      :alt: Alpha complex representation                        |                                                                        |
-|      :figclass: align-center                                   | The filtration value of each simplex is computed as the square of the  |
-|                                                                | circumradius of the simplex if the circumsphere is empty (the simplex  |
-|      Alpha complex representation                              | is then said to be Gabriel), and as the minimum of the filtration      |
-|                                                                | values of the codimension 1 cofaces that make it not Gabriel           |
-|                                                                | otherwise. All simplices that have a filtration value strictly         |
-|                                                                | greater than a given alpha squared value are not inserted into the     |
-|                                                                | complex.                                                               |
-|                                                                |                                                                        |
-|                                                                | This package requires having CGAL version 4.7 or higher (4.8.1 is      |
-|                                                                | advised for better performance).                                       |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| :doc:`alpha_complex_user`                                      | :doc:`alpha_complex_ref`                                               |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
+   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------+
+   | .. figure::                                                    | Alpha complex is a simplicial complex constructed from the finite      | :Author: Vincent Rouvreau                     |
+   |      ../../doc/Alpha_complex/alpha_complex_representation.png  | cells of a Delaunay Triangulation.                                     |                                               |
+   |      :alt: Alpha complex representation                        |                                                                        | :Introduced in: GUDHI 2.0.0                   |
+   |      :figclass: align-center                                   | The filtration value of each simplex is computed as the square of the  |                                               |
+   |                                                                | circumradius of the simplex if the circumsphere is empty (the simplex  | :Copyright: GPL v3                            |
+   |                                                                | is then said to be Gabriel), and as the minimum of the filtration      |                                               |
+   |                                                                | values of the codimension 1 cofaces that make it not Gabriel           | :Requires: Eigen3 and CGAL :math:`\geq` 4.7.0 |
+   |                                                                | otherwise. All simplices that have a filtration value strictly         |                                               |
+   |                                                                | greater than a given alpha squared value are not inserted into the     |                                               |
+   |                                                                | complex.                                                               |                                               |
+   |                                                                |                                                                        |                                               |
+   |                                                                | This package requires having CGAL version 4.7 or higher (4.8.1 is      |                                               |
+   |                                                                | advised for better performance).                                       |                                               |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------+
+   | * :doc:`alpha_complex_user`                                    | * :doc:`alpha_complex_ref`                                                                                             |
+   +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/bottleneck_distance_sum.inc b/src/cython/doc/bottleneck_distance_sum.inc
index 030fad9e..41b9c5a3 100644
--- a/src/cython/doc/bottleneck_distance_sum.inc
+++ b/src/cython/doc/bottleneck_distance_sum.inc
@@ -1,15 +1,14 @@
-=================================================================  ===================================  ===================================
-:Author: François Godi                                             :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-:Requires: CGAL :math:`\geq` 4.8.0
-=================================================================  ===================================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+-----------------------------------------------------------------+----------------------------------------------------------------------+
-| .. figure::                                                     | Bottleneck distance measures the similarity between two persistence  |
-|      ../../doc/Bottleneck_distance/perturb_pd.png               | diagrams. It's the shortest distance b for which there exists a      |
-|      :figclass: align-center                                    | perfect matching between the points of the two diagrams (+ all the   |
-|                                                                 | diagonal points) such that any couple of matched points are at       |
-|      Bottleneck distance is the length of                       | distance at most b.                                                  |
-|      the longest edge                                           |                                                                      |
-+-----------------------------------------------------------------+----------------------------------------------------------------------+
-| :doc:`bottleneck_distance_user`                                 |                                                                      |
-+-----------------------------------------------------------------+----------------------------------------------------------------------+
+   +-----------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------------------------+
+   | .. figure::                                                     | Bottleneck distance measures the similarity between two persistence  | :Author: François Godi                        |
+   |      ../../doc/Bottleneck_distance/perturb_pd.png               | diagrams. It's the shortest distance b for which there exists a      |                                               |
+   |      :figclass: align-center                                    | perfect matching between the points of the two diagrams (+ all the   | :Introduced in: GUDHI 2.0.0                   |
+   |                                                                 | diagonal points) such that any couple of matched points are at       |                                               |
+   |      Bottleneck distance is the length of                       | distance at most b.                                                  | :Copyright: GPL v3                            |
+   |      the longest edge                                           |                                                                      |                                               |
+   |                                                                 |                                                                      | :Requires: CGAL :math:`\geq` 4.8.0            |
+   +-----------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------------------------+
+   | * :doc:`bottleneck_distance_user`                               |                                                                                                                      |
+   +-----------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/conf.py b/src/cython/doc/conf.py
index 4a54d4fd..ce08f679 100755
--- a/src/cython/doc/conf.py
+++ b/src/cython/doc/conf.py
@@ -125,7 +125,7 @@ html_theme_options = {
      "sidebarbgcolor": "#A1ADCD",
      "sidebartextcolor": "black",
      "sidebarlinkcolor": "#334D5C",
-     "body_max_width": "1200px",
+     "body_max_width": "100%",
 }
 
 # Add any paths that contain custom themes here, relative to this directory.
diff --git a/src/cython/doc/cubical_complex_sum.inc b/src/cython/doc/cubical_complex_sum.inc
index 280ad0e0..6dcf8e48 100644
--- a/src/cython/doc/cubical_complex_sum.inc
+++ b/src/cython/doc/cubical_complex_sum.inc
@@ -1,15 +1,14 @@
-=================================================================  ===================================  ===================================
-:Author: Pawel Dlotko                                              :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-=================================================================  ===================================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+--------------------------------------------------------------------------+----------------------------------------------------------------------+
-| .. figure::                                                              | The cubical complex is an example of a structured complex useful in  |
-|      ../../doc/Bitmap_cubical_complex/Cubical_complex_representation.png | computational mathematics (specially rigorous numerics) and image    |
-|      :alt: Cubical complex representation                                | analysis.                                                            |
-|      :figclass: align-center                                             |                                                                      |
-|                                                                          |                                                                      |
-|      Cubical complex representation                                      |                                                                      |
-+--------------------------------------------------------------------------+----------------------------------------------------------------------+
-| :doc:`cubical_complex_user`                                              | * :doc:`cubical_complex_ref`                                         |
-|                                                                          | * :doc:`periodic_cubical_complex_ref`                                |
-+--------------------------------------------------------------------------+----------------------------------------------------------------------+
+   +--------------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------+
+   | .. figure::                                                              | The cubical complex is an example of a structured complex useful in  | :Author: Pawel Dlotko       |
+   |      ../../doc/Bitmap_cubical_complex/Cubical_complex_representation.png | computational mathematics (specially rigorous numerics) and image    |                             |
+   |      :alt: Cubical complex representation                                | analysis.                                                            | :Introduced in: GUDHI 2.0.0 |
+   |      :figclass: align-center                                             |                                                                      |                             |
+   |                                                                          |                                                                      | :Copyright: GPL v3          |
+   |                                                                          |                                                                      |                             |
+   +--------------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------+
+   | * :doc:`cubical_complex_user`                                            | * :doc:`cubical_complex_ref`                                                                       |
+   |                                                                          | * :doc:`periodic_cubical_complex_ref`                                                              |
+   +--------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/fileformats.rst b/src/cython/doc/fileformats.rst
index e205cc8b..345dfdba 100644
--- a/src/cython/doc/fileformats.rst
+++ b/src/cython/doc/fileformats.rst
@@ -5,6 +5,35 @@
 File formats
 ############
 
+OFF file format
+***************
+
+OFF files must be conform to format described here:
+http://www.geomview.org/docs/html/OFF.html
+
+OFF files are mainly used as point cloud inputs. Here is an example of 7 points
+in a 3-dimensional space. As edges and faces are not used for point set, there
+is no need to specify them (just set their numbers to 0):
+
+.. literalinclude:: ../../data/points/alphacomplexdoc.off
+
+.. centered:: ../../points/alphacomplexdoc.off
+
+For dimensions bigger than 3, the dimension can be set like here::
+
+    # Dimension is no more 3
+    nOFF
+    # dimension 4 - 7 vertices - 0 face - 0 edge
+    4 7 0 0
+    # Point set:
+    1.0 1.0  0.0 0.0
+    7.0 0.0  0.0 0.0
+    4.0 6.0  0.0 0.0
+    9.0 6.0  0.0 0.0
+    0.0 14.0 0.0 0.0
+    2.0 19.0 0.0 0.0
+    9.0 17.0 0.0 0.0
+
 Persistence Diagram
 *******************
 
diff --git a/src/cython/doc/index.rst b/src/cython/doc/index.rst
index 15cbe267..e379bc23 100644
--- a/src/cython/doc/index.rst
+++ b/src/cython/doc/index.rst
@@ -6,80 +6,73 @@ GUDHI Python module documentation
      :alt: Gudhi banner
      :figclass: align-center
 
-Introduction
-************
-
-The Python interface for the Gudhi library (Geometry Understanding in Higher
-Dimensions) is a generic open source
-`Python module <http://gudhi.gforge.inria.fr/python/latest/>`_, for
-Computational Topology and Topological Data Analysis
-(`TDA <https://en.wikipedia.org/wiki/Topological_data_analysis>`_).
-The GUDHI library intends to help the development of new algorithmic solutions
-in TDA and their transfer to applications. It provides robust, efficient,
-flexible and easy to use implementations of state-of-the-art algorithms and
-data structures.
-
-The current release of the GUDHI library includes:
+Complexes
+*********
 
-* Data structures to represent, construct and manipulate simplicial complexes.
-* Simplification of simplicial complexes by edge contraction.
-* Algorithms to compute persistent homology and bottleneck distance.
+Cubical complexes
+=================
 
-We refer to :cite:`gudhilibrary_ICMS14` for a detailed description of the
-design of the library.
+.. include:: cubical_complex_sum.inc
 
-Data structures
-***************
+Simplicial complexes
+====================
 
 Alpha complex
-=============
+-------------
 
 .. include:: alpha_complex_sum.inc
 
-Cover complexes
-===============
+Rips complex
+-------------
+
+.. include:: rips_complex_sum.inc
 
-.. include:: nerve_gic_complex_sum.rst
+Witness complex
+---------------
 
-Cubical complex
+.. include:: witness_complex_sum.inc
+
+Cover complexes
 ===============
 
-.. include:: cubical_complex_sum.inc
+.. include:: nerve_gic_complex_sum.inc
 
-Rips complex
-============
+Data structures and basic operations
+************************************
 
-.. include:: rips_complex_sum.inc
+Data structures
+===============
 
 Simplex tree
-============
+------------
 
 .. include:: simplex_tree_sum.inc
 
+Topological descriptors computation
+***********************************
+
+Persistence cohomology
+======================
+
+.. include:: persistent_cohomology_sum.inc
+
+Manifold reconstruction
+***********************
+
 Tangential complex
 ==================
 
 .. include:: tangential_complex_sum.inc
 
-Witness complex
-===============
-
-.. include:: witness_complex_sum.inc
 
-
-Toolbox
-*******
+Topological descriptors tools
+*****************************
 
 Bottleneck distance
 ===================
 
 .. include:: bottleneck_distance_sum.inc
 
-Persistence cohomology
-======================
-
-.. include:: persistent_cohomology_sum.inc
-
 Persistence graphical tools
 ===========================
 
diff --git a/src/cython/doc/nerve_gic_complex_sum.inc b/src/cython/doc/nerve_gic_complex_sum.inc
new file mode 100644
index 00000000..0e606fe1
--- /dev/null
+++ b/src/cython/doc/nerve_gic_complex_sum.inc
@@ -0,0 +1,16 @@
+.. table::
+   :widths: 30 50 20
+
+   +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------+
+   | .. figure::                                                    | Nerves and Graph Induced Complexes are cover complexes, i.e.           | :Author: Mathieu Carrière          |
+   |      ../../doc/Nerve_GIC/gicvisu.jpg                           | simplicial complexes that provably contain topological information     |                                    |
+   |      :alt: Graph Induced Complex of a point cloud.             | about the input data. They can be computed with a cover of the data,   | :Introduced in: GUDHI 2.3.0        |
+   |      :figclass: align-center                                   | that comes i.e. from the preimage of a family of intervals covering    |                                    |
+   |                                                                | the image of a scalar-valued function defined on the data.             | :Copyright: GPL v3                 |
+   |                                                                |                                                                        |                                    |
+   |                                                                |                                                                        | :Requires: CGAL :math:`\geq` 4.8.1 |
+   |                                                                |                                                                        |                                    |
+   |                                                                |                                                                        |                                    |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------+
+   | * :doc:`nerve_gic_complex_user`                                | * :doc:`nerve_gic_complex_ref`                                                                              |
+   +----------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/nerve_gic_complex_sum.rst b/src/cython/doc/nerve_gic_complex_sum.rst
deleted file mode 100644
index 523c119f..00000000
--- a/src/cython/doc/nerve_gic_complex_sum.rst
+++ /dev/null
@@ -1,15 +0,0 @@
-=================================================================  ===================================  ===================================
-:Author: Mathieu Carrière                                          :Introduced in: GUDHI 2.3.0          :Copyright: GPL v3
-:Requires: CGAL :math:`\geq` 4.8.1
-=================================================================  ===================================  ===================================
-
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| .. figure::                                                    | Nerves and Graph Induced Complexes are cover complexes, i.e.           |
-|      ../../doc/Nerve_GIC/gicvisu.jpg                           | simplicial complexes that provably contain topological information     |
-|      :alt: Graph Induced Complex of a point cloud.             | about the input data. They can be computed with a cover of the data,   |
-|      :figclass: align-center                                   | that comes i.e. from the preimage of a family of intervals covering    |
-|                                                                | the image of a scalar-valued function defined on the data.             |
-|      Graph Induced Complex of a point cloud.                   |                                                                        |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| :doc:`nerve_gic_complex_user`                                  | :doc:`nerve_gic_complex_ref`                                           |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
diff --git a/src/cython/doc/nerve_gic_complex_user.rst b/src/cython/doc/nerve_gic_complex_user.rst
index 44f30e1a..9101f45d 100644
--- a/src/cython/doc/nerve_gic_complex_user.rst
+++ b/src/cython/doc/nerve_gic_complex_user.rst
@@ -7,14 +7,13 @@ Cover complexes user manual
 Definition
 ----------
 
-.. include:: nerve_gic_complex_sum.rst
+.. include:: nerve_gic_complex_sum.inc
 
 Visualizations of the simplicial complexes can be done with either
 neato (from `graphviz <http://www.graphviz.org/>`_),
 `geomview <http://www.geomview.org/>`_,
 `KeplerMapper <https://github.com/MLWave/kepler-mapper>`_.
-Input point clouds are assumed to be
-`OFF files <http://www.geomview.org/docs/html/OFF.html>`_.
+Input point clouds are assumed to be OFF files (cf. :doc:`fileformats`).
 
 Covers
 ------
diff --git a/src/cython/doc/persistence_graphical_tools_sum.inc b/src/cython/doc/persistence_graphical_tools_sum.inc
index 5577cf99..b412de56 100644
--- a/src/cython/doc/persistence_graphical_tools_sum.inc
+++ b/src/cython/doc/persistence_graphical_tools_sum.inc
@@ -1,12 +1,14 @@
-=================================================================  ===================================  ===================================
-:Author: Vincent Rouvreau                                          :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-:Requires: matplotlib                                              numpy                                scipy
-=================================================================  ===================================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+-----------------------------------------------------------------+-----------------------------------------------------------------------+
-| .. figure::                                                     | These graphical tools comes on top of persistence results and allows  |
-|      img/graphical_tools_representation.png                     | the user to build easily persistence barcode, diagram or density.     |
-|                                                                 |                                                                       |
-+-----------------------------------------------------------------+-----------------------------------------------------------------------+
-|  :doc:`persistence_graphical_tools_user`                        | :doc:`persistence_graphical_tools_ref`                                |
-+-----------------------------------------------------------------+-----------------------------------------------------------------------+
+   +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+
+   | .. figure::                                                     | These graphical tools comes on top of persistence results and allows  | :Author: Vincent Rouvreau                     |
+   |      img/graphical_tools_representation.png                     | the user to build easily persistence barcode, diagram or density.     |                                               |
+   |                                                                 |                                                                       | :Introduced in: GUDHI 2.0.0                   |
+   |                                                                 |                                                                       |                                               |
+   |                                                                 |                                                                       | :Copyright: GPL v3                            |
+   |                                                                 |                                                                       |                                               |
+   |                                                                 |                                                                       | :Requires: matplotlib, numpy and scipy        |
+   +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+
+   | * :doc:`persistence_graphical_tools_user`                       | * :doc:`persistence_graphical_tools_ref`                                                                              |
+   +-----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/persistent_cohomology_sum.inc b/src/cython/doc/persistent_cohomology_sum.inc
index a26df1dc..20ca073c 100644
--- a/src/cython/doc/persistent_cohomology_sum.inc
+++ b/src/cython/doc/persistent_cohomology_sum.inc
@@ -1,27 +1,26 @@
-=================================================================  ===================================  ===================================
-:Author: Clément Maria                                             :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-=================================================================  ===================================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+-----------------------------------------------------------------+-----------------------------------------------------------------------+
-| .. figure::                                                     | The theory of homology consists in attaching to a topological space   |
-|      ../../doc/Persistent_cohomology/3DTorus_poch.png           | a sequence of (homology) groups, capturing global topological         |
-|      :figclass: align-center                                    | features like connected components, holes, cavities, etc. Persistent  |
-|                                                                 | homology studies the evolution -- birth, life and death -- of these   |
-|      Rips Persistent Cohomology on a 3D                         | features when the topological space is changing. Consequently, the    |
-|      Torus                                                      | theory is essentially composed of three elements: topological spaces, |
-|                                                                 | their homology groups and an evolution scheme.                        |
-|                                                                 |                                                                       |
-|                                                                 | Computation of persistent cohomology using the algorithm of           |
-|                                                                 | :cite:`DBLP:journals/dcg/SilvaMV11` and                               |
-|                                                                 | :cite:`DBLP:journals/corr/abs-1208-5018` and the Compressed           |
-|                                                                 | Annotation Matrix implementation of                                   |
-|                                                                 | :cite:`DBLP:conf/esa/BoissonnatDM13`.                                 |
-|                                                                 |                                                                       |
-+-----------------------------------------------------------------+-----------------------------------------------------------------------+
-|  :doc:`persistent_cohomology_user`                              | Please refer to each data structure that contains persistence         |
-|                                                                 | feature for reference:                                                |
-|                                                                 |                                                                       |
-|                                                                 | * :doc:`simplex_tree_ref`                                             |
-|                                                                 | * :doc:`cubical_complex_ref`                                          |
-|                                                                 | * :doc:`periodic_cubical_complex_ref`                                 |
-+-----------------------------------------------------------------+-----------------------------------------------------------------------+
+   +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+
+   | .. figure::                                                     | The theory of homology consists in attaching to a topological space   | :Author: Clément Maria                        |
+   |      ../../doc/Persistent_cohomology/3DTorus_poch.png           | a sequence of (homology) groups, capturing global topological         |                                               |
+   |      :figclass: align-center                                    | features like connected components, holes, cavities, etc. Persistent  | :Introduced in: GUDHI 2.0.0                   |
+   |                                                                 | homology studies the evolution -- birth, life and death -- of these   |                                               |
+   |      Rips Persistent Cohomology on a 3D                         | features when the topological space is changing. Consequently, the    | :Copyright: GPL v3                            |
+   |      Torus                                                      | theory is essentially composed of three elements: topological spaces, |                                               |
+   |                                                                 | their homology groups and an evolution scheme.                        |                                               |
+   |                                                                 |                                                                       |                                               |
+   |                                                                 | Computation of persistent cohomology using the algorithm of           |                                               |
+   |                                                                 | :cite:`DBLP:journals/dcg/SilvaMV11` and                               |                                               |
+   |                                                                 | :cite:`DBLP:journals/corr/abs-1208-5018` and the Compressed           |                                               |
+   |                                                                 | Annotation Matrix implementation of                                   |                                               |
+   |                                                                 | :cite:`DBLP:conf/esa/BoissonnatDM13`.                                 |                                               |
+   |                                                                 |                                                                       |                                               |
+   +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+
+   |  * :doc:`persistent_cohomology_user`                            | Please refer to each data structure that contains persistence                                                         |
+   |                                                                 | feature for reference:                                                                                                |
+   |                                                                 |                                                                                                                       |
+   |                                                                 | * :doc:`simplex_tree_ref`                                                                                             |
+   |                                                                 | * :doc:`cubical_complex_ref`                                                                                          |
+   |                                                                 | * :doc:`periodic_cubical_complex_ref`                                                                                 |
+   +-----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/rips_complex_sum.inc b/src/cython/doc/rips_complex_sum.inc
index ea26769a..e8e505e2 100644
--- a/src/cython/doc/rips_complex_sum.inc
+++ b/src/cython/doc/rips_complex_sum.inc
@@ -1,17 +1,16 @@
-=====================================================================  ===========================  ===================================
-:Author: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse    :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-=====================================================================  ===========================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| .. figure::                                                    | Rips complex is a simplicial complex constructed from a one skeleton   |
-|      ../../doc/Rips_complex/rips_complex_representation.png    | graph.                                                                 |
-|      :figclass: align-center                                   |                                                                        |
-|                                                                | The filtration value of each edge is computed from a user-given        |
-|      Rips complex representation                               | distance function and is inserted until a user-given threshold         |
-|                                                                | value.                                                                 |
-|                                                                |                                                                        |
-|                                                                | This complex can be built from a point cloud and a distance function,  |
-|                                                                | or from a distance matrix.                                             |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| :doc:`rips_complex_user`                                       | :doc:`rips_complex_ref`                                                |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
+   +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+
+   | .. figure::                                                    | Rips complex is a simplicial complex constructed from a one skeleton   | :Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse |
+   |      ../../doc/Rips_complex/rips_complex_representation.png    | graph.                                                                 |                                                                      |
+   |      :figclass: align-center                                   |                                                                        | :Introduced in: GUDHI 2.0.0                                          |
+   |                                                                | The filtration value of each edge is computed from a user-given        |                                                                      |
+   |                                                                | distance function and is inserted until a user-given threshold         | :Copyright: GPL v3                                                   |
+   |                                                                | value.                                                                 |                                                                      |
+   |                                                                |                                                                        |                                                                      |
+   |                                                                | This complex can be built from a point cloud and a distance function,  |                                                                      |
+   |                                                                | or from a distance matrix.                                             |                                                                      |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+
+   | * :doc:`rips_complex_user`                                     | * :doc:`rips_complex_ref`                                                                                                                     |
+   +----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/simplex_tree_sum.inc b/src/cython/doc/simplex_tree_sum.inc
index fb0e54c1..086c69d5 100644
--- a/src/cython/doc/simplex_tree_sum.inc
+++ b/src/cython/doc/simplex_tree_sum.inc
@@ -1,14 +1,13 @@
-=================================================================  ===================================  ===================================
-:Author: Clément Maria                                             :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-=================================================================  ===================================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| .. figure::                                                    | The simplex tree is an efficient and flexible data structure for       |
-|      ../../doc/Simplex_tree/Simplex_tree_representation.png    | representing general (filtered) simplicial complexes.                  |
-|      :alt: Simplex tree representation                         |                                                                        |
-|      :figclass: align-center                                   | The data structure is described in                                     |
-|                                                                | :cite:`boissonnatmariasimplextreealgorithmica`                         |
-|      Simplex tree representation                               |                                                                        |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| :doc:`simplex_tree_user`                                       | :doc:`simplex_tree_ref`                                                |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
+   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------+
+   | .. figure::                                                    | The simplex tree is an efficient and flexible data structure for       | :Author: Clément Maria      |
+   |      ../../doc/Simplex_tree/Simplex_tree_representation.png    | representing general (filtered) simplicial complexes.                  |                             |
+   |      :alt: Simplex tree representation                         |                                                                        | :Introduced in: GUDHI 2.0.0 |
+   |      :figclass: align-center                                   | The data structure is described in                                     |                             |
+   |                                                                | :cite:`boissonnatmariasimplextreealgorithmica`                         | :Copyright: GPL v3          |
+   |                                                                |                                                                        |                             |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------+
+   | * :doc:`simplex_tree_user`                                     | * :doc:`simplex_tree_ref`                                                                            |
+   +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/tangential_complex_sum.inc b/src/cython/doc/tangential_complex_sum.inc
index 72b4d7ba..0f03ffb3 100644
--- a/src/cython/doc/tangential_complex_sum.inc
+++ b/src/cython/doc/tangential_complex_sum.inc
@@ -1,15 +1,14 @@
-=================================================================  ===================================  ===================================
-:Author: Clément Jamin                                             :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-:Requires: CGAL :math:`\geq` 4.8.0                                 Eigen3
-=================================================================  ===================================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| .. figure::                                                    | A Tangential Delaunay complex is a simplicial complex designed to      |
-|      ../../doc/Tangential_complex/tc_examples.png              | reconstruct a :math:`k`-dimensional manifold embedded in :math:`d`-    |
-|      :figclass: align-center                                   | dimensional Euclidean space. The input is a point sample coming from   |
-|                                                                | an unknown manifold. The running time depends only linearly on the     |
-|      Tangential complex representation                         | extrinsic dimension :math:`d` and exponentially on the intrinsic       |
-|                                                                | dimension :math:`k`.                                                   |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
-| :doc:`tangential_complex_user`                                 | :doc:`tangential_complex_ref`                                          |
-+----------------------------------------------------------------+------------------------------------------------------------------------+
+   +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------+
+   | .. figure::                                                    | A Tangential Delaunay complex is a simplicial complex designed to      | :Author:    Clément Jamin          |
+   |      ../../doc/Tangential_complex/tc_examples.png              | reconstruct a :math:`k`-dimensional manifold embedded in :math:`d`-    |                                    |
+   |      :figclass: align-center                                   | dimensional Euclidean space. The input is a point sample coming from   | :Introduced in:    GUDHI 2.0.0     |
+   |                                                                | an unknown manifold. The running time depends only linearly on the     |                                    |
+   |                                                                | extrinsic dimension :math:`d` and exponentially on the intrinsic       | :Copyright: GPL v3                 |
+   |                                                                | dimension :math:`k`.                                                   |                                    |
+   |                                                                |                                                                        | :Requires: CGAL :math:`\geq` 4.8.0 |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------+
+   | * :doc:`tangential_complex_user`                               | * :doc:`tangential_complex_ref`                                                                             |
+   +----------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/doc/witness_complex_sum.inc b/src/cython/doc/witness_complex_sum.inc
index a8a126a0..49577745 100644
--- a/src/cython/doc/witness_complex_sum.inc
+++ b/src/cython/doc/witness_complex_sum.inc
@@ -1,19 +1,17 @@
-=================================================================  ===================================  ===================================
-:Author: Siargey Kachanovich                                       :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
-:Euclidean version requires: CGAL :math:`\geq` 4.6.0               Eigen3
-=================================================================  ===================================  ===================================
+.. table::
+   :widths: 30 50 20
 
-+-------------------------------------------------------------------+----------------------------------------------------------------------+
-| .. figure::                                                       | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on  |
-|      ../../doc/Witness_complex/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`.                          |
-|      :alt: Witness complex representation                         |                                                                      |
-|      :figclass: align-center                                      | The data structure is described in                                   |
-|                                                                   | :cite:`boissonnatmariasimplextreealgorithmica`.                      |
-|                                                                   |                                                                      |
-|      Witness complex representation                               |                                                                      |
-+-------------------------------------------------------------------+----------------------------------------------------------------------+
-| :doc:`witness_complex_user`                                       | * :doc:`witness_complex_ref`                                         |
-|                                                                   | * :doc:`strong_witness_complex_ref`                                  |
-|                                                                   | * :doc:`euclidean_witness_complex_ref`                               |
-|                                                                   | * :doc:`euclidean_strong_witness_complex_ref`                        |
-+-------------------------------------------------------------------+----------------------------------------------------------------------+
+   +-------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------------------------------------------------------+
+   | .. figure::                                                       | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on  | :Author: Siargey Kachanovich                                                |
+   |      ../../doc/Witness_complex/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`.                          |                                                                             |
+   |      :alt: Witness complex representation                         |                                                                      | :Introduced in: GUDHI 2.0.0                                                 |
+   |      :figclass: align-center                                      | The data structure is described in                                   |                                                                             |
+   |                                                                   | :cite:`boissonnatmariasimplextreealgorithmica`.                      | :Copyright: GPL v3                                                          |
+   |                                                                   |                                                                      |                                                                             |
+   |                                                                   |                                                                      | :Requires: Eigen3 and CGAL :math:`\geq` 4.6.0 for Euclidean versions only   |
+   +-------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------------------------------------------------------+
+   | * :doc:`witness_complex_user`                                     | * :doc:`witness_complex_ref`                                                                                                                       |
+   |                                                                   | * :doc:`strong_witness_complex_ref`                                                                                                                |
+   |                                                                   | * :doc:`euclidean_witness_complex_ref`                                                                                                             |
+   |                                                                   | * :doc:`euclidean_strong_witness_complex_ref`                                                                                                      |
+   +-------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------+
diff --git a/src/cython/include/Simplex_tree_interface.h b/src/cython/include/Simplex_tree_interface.h
index 3481eeff..ca98517d 100644
--- a/src/cython/include/Simplex_tree_interface.h
+++ b/src/cython/include/Simplex_tree_interface.h
@@ -45,7 +45,7 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> {
   using Simplex_handle = typename Base::Simplex_handle;
   using Insertion_result = typename std::pair<Simplex_handle, bool>;
   using Simplex = std::vector<Vertex_handle>;
-  using Complex = std::vector<std::pair<Simplex, Filtration_value>>;
+  using Filtered_simplices = std::vector<std::pair<Simplex, Filtration_value>>;
 
  public:
   bool find_simplex(const Simplex& vh) {
@@ -94,9 +94,9 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> {
     Base::initialize_filtration();
   }
 
-  Complex get_filtration() {
+  Filtered_simplices get_filtration() {
     Base::initialize_filtration();
-    Complex filtrations;
+    Filtered_simplices filtrations;
     for (auto f_simplex : Base::filtration_simplex_range()) {
       Simplex simplex;
       for (auto vertex : Base::simplex_vertex_range(f_simplex)) {
@@ -107,8 +107,8 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> {
     return filtrations;
   }
 
-  Complex get_skeleton(int dimension) {
-    Complex skeletons;
+  Filtered_simplices get_skeleton(int dimension) {
+    Filtered_simplices skeletons;
     for (auto f_simplex : Base::skeleton_simplex_range(dimension)) {
       Simplex simplex;
       for (auto vertex : Base::simplex_vertex_range(f_simplex)) {
@@ -119,29 +119,25 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> {
     return skeletons;
   }
 
-  Complex get_star(const Simplex& simplex) {
-    Complex star;
+  Filtered_simplices get_star(const Simplex& simplex) {
+    Filtered_simplices star;
     for (auto f_simplex : Base::star_simplex_range(Base::find(simplex))) {
       Simplex simplex_star;
       for (auto vertex : Base::simplex_vertex_range(f_simplex)) {
-        std::cout << vertex << " ";
         simplex_star.insert(simplex_star.begin(), vertex);
       }
-      std::cout << std::endl;
       star.push_back(std::make_pair(simplex_star, Base::filtration(f_simplex)));
     }
     return star;
   }
 
-  Complex get_cofaces(const Simplex& simplex, int dimension) {
-    Complex cofaces;
+  Filtered_simplices get_cofaces(const Simplex& simplex, int dimension) {
+    Filtered_simplices cofaces;
     for (auto f_simplex : Base::cofaces_simplex_range(Base::find(simplex), dimension)) {
       Simplex simplex_coface;
       for (auto vertex : Base::simplex_vertex_range(f_simplex)) {
-        std::cout << vertex << " ";
         simplex_coface.insert(simplex_coface.begin(), vertex);
       }
-      std::cout << std::endl;
       cofaces.push_back(std::make_pair(simplex_coface, Base::filtration(f_simplex)));
     }
     return cofaces;