codac-team · SimonRohou · Apr 19, 2026 · Apr 19, 2026 · Apr 19, 2026
diff --git a/doc/manual/manual/extensions/capd/capd.rst b/doc/manual/manual/extensions/capd/capd.rst
@@ -12,7 +12,6 @@ To use CAPD with Codac, you first need to install the CAPD library. You can find
 Note that as CAPD is a C++ only library, the content present in this page is **only available in C++**.
 
 
-.. _subsec-extensions-capd-capd-install:
 Installing the ``codac-capd`` extension
 ---------------------------------------
 
@@ -52,6 +51,18 @@ The header of the ``codac-capd`` extension is not included by default. You need
   #include <codac-capd.h>
   #include <capd/capdlib.h>
 
+Furthermore, you need to link the extension to your project, for instance by updating your ``CMakeLists.txt`` with::
+
+  add_executable(${PROJECT_NAME} main.cpp)
+  target_compile_options(${PROJECT_NAME} PUBLIC ${CODAC_CXX_FLAGS})
+  target_include_directories(${PROJECT_NAME} SYSTEM PUBLIC ${CODAC_INCLUDE_DIRS} ${CODAC_CAPD_INCLUDE_DIR})
+  target_link_libraries(${PROJECT_NAME} PRIVATE
+    ${CODAC_LIBRARIES}
+    ${CODAC_CAPD_LIBRARY} # linking to the codac-capd extension
+    capd::capd # linking to CAPD
+    Ibex::ibex
+  )
+
 You can use the functions ``to_capd`` and ``to_codac`` to convert between CAPD and Codac objects as follows:
 
 .. tabs::
@@ -200,4 +211,4 @@ The result is the following figure, with in green the initial set (:math:`t=0s`)
 .. figure:: img/pendulum_result.png
   :width: 500px
 
-  Result of the CAPD integration of the pendulum, enclosed in a Codac tube.
+  Result of the CAPD integration of the pendulum, enclosed in a Codac tube.
diff --git a/doc/manual/manual/extensions/capd/index.rst b/doc/manual/manual/extensions/capd/index.rst
@@ -5,210 +5,7 @@ CAPD (rigorous numerics in dynamical systems)
 
   Main author: `Maël Godard <https://godardma.github.io>`_
 
-This page describes how to use the CAPD library with Codac. CAPD is a C++ library for rigorous numerics in dynamical systems.
+.. toctree::
 
-To use CAPD with Codac, you first need to install the CAPD library. You can find the installation instructions on the `CAPD website <http://capd.ii.uj.edu.pl/html/capd_compilation.html>`_.
-
-Note that as CAPD is a C++ only library, the content present in this page is **only available in C++**.
-
-
-Installing the ``codac-capd`` extension
----------------------------------------
-
-To install the ``codac-capd`` extension, you need to install the Codac library from its sources. This can be done :ref:`by using CMake <sec-install-cpp>` with the option ``WITH_CAPD=ON``. For example:
-
-.. code-block:: bash
-
-      cmake -DCMAKE_INSTALL_PREFIX=$HOME/ibex-lib/build_install -DCMAKE_BUILD_TYPE=Release -DWITH_CAPD=ON ..
-
-We highly recommend to test the installation of the library with the provided tests. To do so, you can use the following command:
-
-.. code-block:: bash
-
-      make test
-
-
-Content
--------
-
-The ``codac-capd`` extension provides functions to convert CAPD objects to Codac objects and vice versa.
-
-The functions are ``to_capd`` and ``to_codac``. They can be used to convert the following objects:
-
-- ``capd::Interval`` :math:`\leftrightarrow` ``codac2::Interval``
-- ``capd::IVector`` :math:`\leftrightarrow` ``codac2::IntervalVector``
-- ``capd::IMatrix`` :math:`\leftrightarrow` ``codac2::IntervalMatrix``
-- ``capd::ITimeMap::SolutionCurve`` :math:`\rightarrow` ``codac2::SlicedTube<codac2::IntervalVector>``
-
-
-How to use
-----------
-
-The header of the ``codac-capd`` extension is not included by default. You need to include it manually in your code, together with the CAPD library:
-
-.. code-block:: c++
-
-  #include <codac-capd.h>
-  #include <capd/capdlib.h>
-
-Furthermore, you need to link the extension to your project, for instance by updating your ``CMakeLists.txt`` with::
-
-  add_executable(${PROJECT_NAME} main.cpp)
-  target_compile_options(${PROJECT_NAME} PUBLIC ${CODAC_CXX_FLAGS})
-  target_include_directories(${PROJECT_NAME} SYSTEM PUBLIC ${CODAC_INCLUDE_DIRS} ${CODAC_CAPD_INCLUDE_DIR})
-  target_link_libraries(${PROJECT_NAME} PRIVATE
-    ${CODAC_LIBRARIES}
-    ${CODAC_CAPD_LIBRARY} # linking to the codac-capd extension
-    capd::capd # linking to CAPD
-    Ibex::ibex
-  )
-
-You can use the functions ``to_capd`` and ``to_codac`` to convert between CAPD and Codac objects as follows:
-
-.. tabs::
-
-  .. code-tab:: c++
-
-    codac2::Interval codac_interval(0,2);  // Codac interval [0, 2]
-    capd::Interval capd_interval = to_capd(codac_interval); // convert to CAPD interval
-    codac2::Interval codac_interval2 = to_codac(capd_interval); // convert back to Codac interval
-
-
-Example
--------
-
-.. image:: img/pendulum.png
-   :alt: State variables of the pendulum
-   :align: right
-   :width: 130px
-
-For this example we will consider the pendulum with friction.
-
-The state variables of the pendulum are its angle :math:`\theta` and its angular velocity :math:`\omega`. The pendulum follows the following dynamic:
-
-.. math::
-
-  \left(\begin{array}{c}
-  \dot{\theta}\\
-  \dot{\omega}
-  \end{array}\right)=\left(\begin{array}{c}
-  \omega\\
-  -\sin(\theta)\cdot\frac{g}{l}-0.5\omega
-  \end{array}\right),
-
-
-where :math:`g` is the gravity constant and :math:`l` is the length of the pendulum.
-
-This equation can be passed to the CAPD library as follows:
-
-.. tabs::
-
-  .. group-tab:: C++
-
-    .. literalinclude:: src.cpp
-      :language: c++
-      :start-after: [codac-capd-2-beg]
-      :end-before: [codac-capd-2-end]
-      :dedent: 2
-
-To solve this ODE, an ``IOdeSolver`` object is necessary.
-
-.. tabs::
-
-  .. group-tab:: C++
-
-    .. literalinclude:: src.cpp
-      :language: c++
-      :start-after: [codac-capd-3-beg]
-      :end-before: [codac-capd-3-end]
-      :dedent: 2
-
-CAPD then uses an ``ITimeMap`` to make the link between a time step and the solution of the ODE at this time. The ``I`` here stands for ``Interval`` as the solution is an interval guaranteed to enclose the solution. Here we will integrate the ODE between :math:`t_0=0s` and :math:`t_f=20s`.
-
-.. tabs::
-
-  .. group-tab:: C++
-
-    .. literalinclude:: src.cpp
-      :language: c++
-      :start-after: [codac-capd-4-beg]
-      :end-before: [codac-capd-4-end]
-      :dedent: 2
-
-To completly define the ODE, we need to define the initial conditions. Here we will set the initial angle to :math:`\theta_0=-\frac{\pi}{2}` and the 
-initial angular velocity to :math:`\omega_0=0`. For the purpose of this example, we will add a small uncertainty to the initial conditions. The initial conditions are then defined as follows:
-
-.. tabs::
-
-  .. group-tab:: C++
-
-    .. literalinclude:: src.cpp
-      :language: c++
-      :start-after: [codac-capd-5-beg]
-      :end-before: [codac-capd-5-end]
-      :dedent: 2
-
-There are then two ways to get the result of the integration depending on the use case.
-
-If the desired result is the solution of the ODE at a given time (here say :math:`T=1s`), we can do as follows:
-
-.. tabs::
-
-  .. group-tab:: C++
-
-    .. literalinclude:: src.cpp
-      :language: c++
-      :start-after: [codac-capd-6-beg]
-      :end-before: [codac-capd-6-end]
-      :dedent: 2
-
-**Be careful, this method modifies the initial set** ``s`` **in place**.
-
-If the desired result is the solution curve (or tube) of the ODE on the time domain :math:`[t_0,t_f]`, we can do as follows:
-
-.. tabs::
-
-  .. group-tab:: C++
-
-    .. literalinclude:: src.cpp
-      :language: c++
-      :start-after: [codac-capd-7-beg]
-      :end-before: [codac-capd-7-end]
-      :dedent: 2
-
-The variable ``solution`` is the desired solution curve (or tube). The operator ``solution(t)`` gives the solution at time :math:`t`. 
-It can be converted into a Codac ``SlicedTube<IntervalVector>`` with the function ``to_codac``. This functions takes two arguments:
-
-- the ``capd::ITimeMap::SolutionCurve`` to convert.
-- a ``codac2::TDomain`` object defining the temporal domain of the tube.
-
-The resulting ``SlicedTube`` will have the same time domain as the one given in argument, completed with the CAPD gates. An example of conversion is : 
-
-.. tabs::
-
-  .. group-tab:: C++
-
-    .. literalinclude:: src.cpp
-      :language: c++
-      :start-after: [codac-capd-8-beg]
-      :end-before: [codac-capd-8-end]
-      :dedent: 2
-
-A full display can be done with the following code:
-
-.. tabs::
-
-  .. group-tab:: C++
-
-    .. literalinclude:: src.cpp
-      :language: c++
-      :start-after: [codac-capd-9-beg]
-      :end-before: [codac-capd-9-end]
-      :dedent: 4
-
-The result is the following figure, with in green the initial set (:math:`t=0s`) and in red the final set (:math:`t=20s`). The ``SlicedTube`` is displayed in blue with a black edge for better visibility. The orange rectangles correspond to the gates (degenerate slices).
-
-.. figure:: img/pendulum_result.png
-  :width: 500px
-
-  Result of the CAPD integration of the pendulum, enclosed in a Codac tube.
+   capd.rst
+   peibos_capd.rst