diff options
Diffstat (limited to 'src/python/doc')
| -rw-r--r-- | src/python/doc/_templates/layout.html | 113 | ||||
| -rw-r--r-- | src/python/doc/alpha_complex_sum.inc | 34 | ||||
| -rw-r--r-- | src/python/doc/alpha_complex_user.rst | 7 | ||||
| -rw-r--r-- | src/python/doc/installation.rst | 76 | ||||
| -rw-r--r-- | src/python/doc/rips_complex_user.rst | 4 | ||||
| -rw-r--r-- | src/python/doc/tangential_complex_sum.inc | 22 | ||||
| -rw-r--r-- | src/python/doc/witness_complex_sum.inc | 28 |
7 files changed, 137 insertions, 147 deletions
diff --git a/src/python/doc/_templates/layout.html b/src/python/doc/_templates/layout.html index bc0e9658..fe64fb3d 100644 --- a/src/python/doc/_templates/layout.html +++ b/src/python/doc/_templates/layout.html @@ -165,62 +165,63 @@ <body role="document"> <!-- GUDHI website header BEGIN --> <div id="navigation" class="sticky"> - <nav class="top-bar" role="navigation" data-topbar> - <ul class="title-area"> - <li class="name"> - <h1 class="show-for-small-only"><a href="" class="icon-tree"> GUDHI C++ library</a></h1> - </li> - <!-- Remove the class "menu-icon" to get rid of menu icon. Take out "Menu" to just have icon alone --> - <li class="toggle-topbar menu-icon"><a href="#"><span>Navigation</span></a></li> - </ul> - <section class="top-bar-section"> - <ul class="right"> - <li class="divider"></li> - <li><a href="/contact/">Contact</a></li> - </ul> - <ul class="left"> - <li><a href="/"> <img src="/assets/img/home.png" alt=" GUDHI"> GUDHI </a></li> - <li class="divider"></li> - <li class="has-dropdown"> - <a href="#">Project</a> - <ul class="dropdown"> - <li><a href="/people/">People</a></li> - <li><a href="/keepintouch/">Keep in touch</a></li> - <li><a href="/partners/">Partners and Funding</a></li> - <li><a href="/relatedprojects/">Related projects</a></li> - <li><a href="/theyaretalkingaboutus/">They are talking about us</a></li> - </ul> - </li> - <li class="divider"></li> - <li class="has-dropdown"> - <a href="#">Download</a> - <ul class="dropdown"> - <li><a href="/licensing/">Licensing</a></li> - <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5253/library-latest.zip" target="_blank">Get the latest sources</a></li> - <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5280/utils_osx-latest.zip" target="_blank">Utils for Mac OSx</a></li> - <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5279/utils_win64-latest.zip" target="_blank">Utils for Win x64</a></li> - </ul> - </li> - <li class="divider"></li> - <li class="has-dropdown"> - <a href="#">Documentation</a> - <ul class="dropdown"> - <li><a href="/doc/latest/">C++ documentation</a></li> - <li><a href="/doc/latest/installation.html">C++ installation manual</a></li> - <li><a href="/python/latest/">Python documentation</a></li> - <li><a href="/python/latest/installation.html">Python installation manual</a></li> - <li><a href="/utils/">Utilities</a></li> - <li><a href="/tutorials/">Tutorials</a></li> - <li><a href="/dockerfile/">Dockerfile</a></li> - </ul> - </li> - <li class="divider"></li> - <li><a href="/interfaces/">Interfaces</a></li> - <li class="divider"></li> - </ul> - </section> - </nav> - </div><!-- /#navigation --> + <nav class="top-bar" role="navigation" data-topbar> + <ul class="title-area"> + <li class="name"> + <h1 class="show-for-small-only"><a href="" class="icon-tree"> GUDHI library</a></h1> + </li> + <!-- Remove the class "menu-icon" to get rid of menu icon. Take out "Menu" to just have icon alone --> + <li class="toggle-topbar menu-icon"><a href="#"><span>Navigation</span></a></li> + </ul> + <section class="top-bar-section"> + <ul class="right"> + <li class="divider"></li> + <li><a href="/contact/">Contact</a></li> + </ul> + <ul class="left"> + <li><a href="/"> <img src="/assets/img/home.png" alt=" GUDHI"> GUDHI </a></li> + <li class="divider"></li> + <li class="has-dropdown"> + <a href="#">Project</a> + <ul class="dropdown"> + <li><a href="/people/">People</a></li> + <li><a href="/keepintouch/">Keep in touch</a></li> + <li><a href="/partners/">Partners and Funding</a></li> + <li><a href="/relatedprojects/">Related projects</a></li> + <li><a href="/theyaretalkingaboutus/">They are talking about us</a></li> + <li><a href="/inaction/">GUDHI in action</a></li> + </ul> + </li> + <li class="divider"></li> + <li class="has-dropdown"> + <a href="#">Download</a> + <ul class="dropdown"> + <li><a href="/licensing/">Licensing</a></li> + <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5253/library-latest.zip" target="_blank">Get the latest sources</a></li> + <li><a href="/conda/">Conda package</a></li> + <li><a href="/dockerfile/">Dockerfile</a></li> + </ul> + </li> + <li class="divider"></li> + <li class="has-dropdown"> + <a href="#">Documentation</a> + <ul class="dropdown"> + <li><a href="/introduction/">Introduction</a></li> + <li><a href="https://gudhi.inria.fr/doc/latest/installation.html">C++ installation manual</a></li> + <li><a href="https://gudhi.inria.fr/doc/latest/">C++ documentation</a></li> + <li><a href="https://gudhi.inria.fr/python/latest/installation.html">Python installation manual</a></li> + <li><a href="https://gudhi.inria.fr/python/latest/">Python documentation</a></li> + <li><a href="/utils/">Utilities</a></li> + <li><a href="/tutorials/">Tutorials</a></li> + </ul> + </li> + <li class="divider"></li> + <li><a href="/interfaces/">Interfaces</a></li> + <li class="divider"></li> + </ul> + </section> + </nav> + </div><!-- /#navigation --> <!-- GUDHI website header BEGIN --> diff --git a/src/python/doc/alpha_complex_sum.inc b/src/python/doc/alpha_complex_sum.inc index 9049e654..c5ba9dc7 100644 --- a/src/python/doc/alpha_complex_sum.inc +++ b/src/python/doc/alpha_complex_sum.inc @@ -1,20 +1,20 @@ .. table:: :widths: 30 50 20 - +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+ - | .. 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: MIT (`GPL v3 </licensing/>`_) | - | | 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 <installation.html#eigen3>`__ and `CGAL <installation.html#cgal>`__ :math:`\geq` 4.11.0 | - | | 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` | - +----------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ + +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ + | .. 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: MIT (`GPL v3 </licensing/>`_) | + | | 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: `Eigen <installation.html#eigen>`__ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`__ :math:`\geq` 4.11.0 | + | | 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/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst index d1e9c7cd..f9662a6d 100644 --- a/src/python/doc/alpha_complex_user.rst +++ b/src/python/doc/alpha_complex_user.rst @@ -28,7 +28,7 @@ This example builds the Delaunay triangulation from the given points, and initia import gudhi alpha_complex = gudhi.AlphaComplex(points=[[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]]) - simplex_tree = alpha_complex.create_simplex_tree(max_alpha_square=60.0) + simplex_tree = alpha_complex.create_simplex_tree() result_str = 'Alpha complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \ repr(simplex_tree.num_simplices()) + ' simplices - ' + \ repr(simplex_tree.num_vertices()) + ' vertices.' @@ -146,8 +146,9 @@ Prune above given filtration value ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The simplex tree is pruned from the given maximum alpha squared value (cf. `Simplex_tree::prune_above_filtration()` -in the `C++ version <http://gudhi.gforge.inria.fr/doc/latest/index.html>`_). -In the following example, the value is given by the user as argument of the program. +in the `C++ version <http://gudhi.gforge.inria.fr/doc/latest/index.html>`_). Note that this does not provide any kind +of speed-up, since we always first build the full filtered complex, so it is recommended not to use `max_alpha_square`. +In the following example, a threshold of 59 is used. Example from OFF file diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst index 1c672ce3..3a853cd9 100644 --- a/src/python/doc/installation.rst +++ b/src/python/doc/installation.rst @@ -5,16 +5,22 @@ Installation ############ +Conda +***** +The easiest way to install the Python version of GUDHI is using +`conda <https://gudhi.inria.fr/licensing/>`_. + Compiling ********* The library uses c++11 and requires `Boost <https://www.boost.org/>`_ ≥ 1.56.0, -`CMake <https://www.cmake.org/>`_ ≥ 3.1 to generate makefiles, and -`python <https://www.python.org/>`_ to compile the GUDHI Python module. +`CMake <https://www.cmake.org/>`_ ≥ 3.1 to generate makefiles, +`NumPy <http://numpy.org>`_ and `Cython <https://www.cython.org/>`_ to compile +the GUDHI Python module. It is a multi-platform library and compiles on Linux, Mac OSX and Visual Studio 2015. On `Windows <https://wiki.python.org/moin/WindowsCompilers>`_ , only Python -3.5 and 3.6 are available because of the required Visual Studio version. +≥ 3.5 are available because of the required Visual Studio version. On other systems, if you have several Python/python installed, the version 2.X will be used by default, but you can force it by adding @@ -86,12 +92,15 @@ You shall have something like: .. code-block:: none Python version 2.7.15 - python version 0.26.1 + Cython version 0.26.1 + Numpy version 1.14.1 Eigen3 version 3.1.1 - Installed modules are: off_reader;simplex_tree;rips_complex;cubical_complex;periodic_cubical_complex; - persistence_graphical_tools;reader_utils;witness_complex;strong_witness_complex;alpha_complex; + Installed modules are: off_reader;simplex_tree;rips_complex; + cubical_complex;periodic_cubical_complex;reader_utils;witness_complex; + strong_witness_complex;alpha_complex; + Missing modules are: bottleneck_distance;nerve_gic;subsampling; + tangential_complex;persistence_graphical_tools; euclidean_witness_complex;euclidean_strong_witness_complex; - Missing modules are: bottleneck_distance;nerve_gic;subsampling;tangential_complex;persistence_graphical_tools; CGAL version 4.7.1000 GMP_LIBRARIES = /usr/lib/x86_64-linux-gnu/libgmp.so GMPXX_LIBRARIES = /usr/lib/x86_64-linux-gnu/libgmpxx.so @@ -99,7 +108,7 @@ You shall have something like: Here, you can see that bottleneck_distance, nerve_gic, subsampling and tangential_complex are missing because of the CGAL version. -persistence_graphical_tools is not available as numpy and matplotlib are not +persistence_graphical_tools is not available as matplotlib is not available. Unitary tests cannot be run as pytest is missing. @@ -113,9 +122,11 @@ A complete configuration would be : Matplotlib version 2.2.2 Numpy version 1.14.5 Eigen3 version 3.3.4 - Installed modules are: off_reader;simplex_tree;rips_complex;cubical_complex;periodic_cubical_complex; - persistence_graphical_tools;reader_utils;witness_complex;strong_witness_complex;persistence_graphical_tools; - bottleneck_distance;nerve_gic;subsampling;tangential_complex;alpha_complex;euclidean_witness_complex; + Installed modules are: off_reader;simplex_tree;rips_complex; + cubical_complex;periodic_cubical_complex;persistence_graphical_tools; + reader_utils;witness_complex;strong_witness_complex; + persistence_graphical_tools;bottleneck_distance;nerve_gic;subsampling; + tangential_complex;alpha_complex;euclidean_witness_complex; euclidean_strong_witness_complex; CGAL header only version 4.11.0 GMP_LIBRARIES = /usr/lib/x86_64-linux-gnu/libgmp.so @@ -144,12 +155,10 @@ Optional third-party library CGAL ==== -The :doc:`Alpha complex </alpha_complex_user>`, -:doc:`Tangential complex </tangential_complex_user>` and -:doc:`Witness complex </witness_complex_user>` data structures, and -:doc:`Bottleneck distance </bottleneck_distance_user>` requires CGAL, which is a -C++ library which provides easy access to efficient and reliable geometric -algorithms. +Some GUDHI modules (cf. :doc:`modules list </index>`), and few examples +require CGAL, a C++ library that provides easy access to efficient and +reliable geometric algorithms. + The procedure to install this library according to your operating system is detailed @@ -166,17 +175,15 @@ The following examples requires CGAL version ≥ 4.11.0: * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` -Eigen3 -====== +Eigen +===== -The :doc:`Alpha complex </alpha_complex_user>`, -:doc:`Tangential complex </tangential_complex_user>` and -:doc:`Witness complex </witness_complex_user>` data structures and few -examples requires `Eigen3 <http://eigen.tuxfamily.org/>`_, a C++ template +Some GUDHI modules (cf. :doc:`modules list </index>`), and few examples +require `Eigen <http://eigen.tuxfamily.org/>`_, a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. -The following examples require the `Eigen3 <http://eigen.tuxfamily.org/>`_: +The following examples require `Eigen <http://eigen.tuxfamily.org/>`_ version ≥ 3.1.0: .. only:: builder_html @@ -208,27 +215,6 @@ The following examples require the `Matplotlib <http://matplotlib.org>`_: * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` -NumPy -===== - -The :doc:`persistence graphical tools </persistence_graphical_tools_user>` -module requires `NumPy <http://numpy.org>`_, a fundamental package for -scientific computing with Python. - -The following examples require the `NumPy <http://numpy.org>`_: - -.. only:: builder_html - - * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>` - * :download:`gudhi_graphical_tools_example.py <../example/gudhi_graphical_tools_example.py>` - * :download:`periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py <../example/periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py>` - * :download:`rips_complex_diagram_persistence_from_off_file_example.py <../example/rips_complex_diagram_persistence_from_off_file_example.py>` - * :download:`rips_persistence_diagram.py <../example/rips_persistence_diagram.py>` - * :download:`rips_complex_diagram_persistence_from_distance_matrix_file_example.py <../example/rips_complex_diagram_persistence_from_distance_matrix_file_example.py>` - * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>` - * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` - * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` - SciPy ===== diff --git a/src/python/doc/rips_complex_user.rst b/src/python/doc/rips_complex_user.rst index 1d340dbe..3f6b960d 100644 --- a/src/python/doc/rips_complex_user.rst +++ b/src/python/doc/rips_complex_user.rst @@ -19,7 +19,9 @@ The `Rips complex <https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex>` generalizes proximity (:math:`\varepsilon`-ball) graphs to higher dimensions. The vertices correspond to the input points, and a simplex is present if and only if its diameter is smaller than some parameter α. Considering all parameters α defines a filtered simplicial complex, where the filtration value of a simplex is its diameter. -The filtration can be restricted to values α smaller than some threshold, to reduce its size. +The filtration can be restricted to values α smaller than some threshold, to reduce its size. Beware that some +people define the Rips complex using a bound of 2α instead of α, particularly when comparing it to an ambient +Čech complex. They end up with the same combinatorial object, but filtration values which are half of ours. The input discrete metric space can be provided as a point cloud plus a distance function, or as a distance matrix. diff --git a/src/python/doc/tangential_complex_sum.inc b/src/python/doc/tangential_complex_sum.inc index c8bc1177..d84aa433 100644 --- a/src/python/doc/tangential_complex_sum.inc +++ b/src/python/doc/tangential_complex_sum.inc @@ -1,14 +1,14 @@ .. table:: :widths: 30 50 20 - +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------------------------------------+ - | .. 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: MIT (`GPL v3 </licensing/>`_) | - | | dimension :math:`k`. | | - | | | :Requires: `CGAL <installation.html#cgal>`__ :math:`\geq` 4.11.0 | - +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------------------------------------+ - | * :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: MIT (`GPL v3 </licensing/>`_) | + | | dimension :math:`k`. | | + | | | :Requires: `Eigen <installation.html#eigen>`__ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`__ :math:`\geq` 4.11.0 | + +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ + | * :doc:`tangential_complex_user` | * :doc:`tangential_complex_ref` | + +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ diff --git a/src/python/doc/witness_complex_sum.inc b/src/python/doc/witness_complex_sum.inc index 2be8b220..71b65a71 100644 --- a/src/python/doc/witness_complex_sum.inc +++ b/src/python/doc/witness_complex_sum.inc @@ -1,18 +1,18 @@ .. table:: :widths: 30 50 20 - +-------------------------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------+ - | .. 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: MIT (`GPL v3 </licensing/>`_ for Euclidean versions only) | - | | | | - | | | :Requires: `Eigen3 <installation.html#eigen3>`__ and `CGAL <installation.html#cgal>`__ :math:`\geq` 4.11.0 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` | - +-------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ + +-------------------------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------+ + | .. 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: MIT (`GPL v3 </licensing/>`_ for Euclidean versions only) | + | | | | + | | | :Requires: `Eigen <installation.html#eigen>`__ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`__ :math:`\geq` 4.11.0 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` | + +-------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |