SimonRohou · Oct 22, 2026 · Oct 22, 2026 · Oct 22, 2026 · Oct 22, 2026 · Oct 22, 2026
diff --git a/doc/manual/index.rst b/doc/manual/index.rst
@@ -214,11 +214,15 @@ User manual
       * The class SetMembershipFunction
       * Extension to custom expressions
 
-* :ref:`sec-domains-tubes`
-   * :ref:`sec-domains-tubes-tdomain`
-   * :ref:`sec-domains-tubes-slicedtube`
-   * The Trajectory classes
-   * Increasing performances using views
+* :ref:`sec-tubes-trajectories`
+   * :ref:`sec-trajectories-sampledtraj`
+   * :ref:`sec-trajectories-analytictraj`
+   * :ref:`sec-trajectories-operations`
+   * :ref:`sec-trajectories-io`
+   * :ref:`sec-tubes-tdomain`
+   * :ref:`sec-tubes-slice`
+   * :ref:`sec-tubes-slicedtube`
+   * :ref:`sec-tubes-examples`
 
 * Contractors
    * What are contractors?
@@ -354,7 +358,7 @@ User manual
    * Related papers
    * Contributors
    * How to cite Codac
-   :ref:`sec-ref-codac-logos`
+   * :ref:`sec-ref-codac-logos`
 
 
 How-to guides

diff --git a/doc/manual/manual/cn/index.rst b/doc/manual/manual/cn/index.rst
@@ -0,0 +1,7 @@
+Contractor Networks
+===================
+
+.. toctree::
+
+   What is a CN? <http://codac.io>
+   The ContractorNetwork class <http://codac.io>
diff --git a/doc/manual/manual/contractors/basic/index.rst b/doc/manual/manual/contractors/basic/index.rst
@@ -0,0 +1,9 @@
+Basic contractors
+=================
+
+.. toctree::
+
+   CtcIdentity <http://codac.io>
+   CtcEmpty <http://codac.io>
+   CtcLazy <http://codac.io>
+   CtcFixpoint <http://codac.io>
diff --git a/doc/manual/manual/contractors/index.rst b/doc/manual/manual/contractors/index.rst
@@ -1,4 +1,5 @@
 .. _sec-ctc:
+
 Contractors, separators
 =======================
 

diff --git a/doc/manual/manual/contractors/linear/index.rst b/doc/manual/manual/contractors/linear/index.rst
@@ -0,0 +1,8 @@
+Linear contractors
+==================
+
+.. toctree::
+
+   CtcGaussElim <http://codac.io>
+   CtcGaussSeidel <http://codac.io>
+   CtcLinearPrecond <http://codac.io>
diff --git a/doc/manual/manual/contractors/set/ctcunion.rst b/doc/manual/manual/contractors/set/ctcunion.rst
@@ -0,0 +1,188 @@
+.. _sec-ctc-set-ctcunion:
+.. _sec-sep-set-sepunion:
+
+Union: CtcUnion and SepUnion
+============================
+
+  Main author: `Simon Rohou <https://www.simon-rohou.fr/research/>`_
+
+
+``CtcUnion`` and ``SepUnion`` implement the logical union/disjunction counterpart of
+``CtcInter`` and ``SepInter``:
+
+.. list-table::
+  :header-rows: 1
+  :widths: 20 35 45
+
+  * - Class
+    - Combines
+    - Meaning
+  * - ``CtcUnion``
+    - contractors
+    - disjunction of constraints, obtained by joining the contracted branches
+  * - ``SepUnion``
+    - separators
+    - separator associated with the union of the represented sets
+
+Both classes can be constructed explicitly or with the ``|`` operator.
+
+
+CtcUnion: disjunction of contractors
+------------------------------------
+
+For box contractors, ``CtcUnion`` applies every stored contractor independently to the
+same input box and returns a box enclosing the union of the resulting branches:
+
+.. math::
+
+  \mathcal{C}_{\mathrm{union}}([\mathbf{x}])
+  =
+  \operatorname{hull}\!\left(
+    \bigcup_{i=1}^{n}\mathcal{C}_i([\mathbf{x}])
+  \right),
+
+where :math:`\operatorname{hull}` denotes the smallest box containing the union.
+
+This evaluation differs from ``CtcInter``: the branches are **not** applied
+sequentially. Each contractor receives the original input domain.
+
+.. note::
+
+  The exact union of several boxes is generally not a box. ``CtcUnion`` therefore
+  returns a box enclosure of this union. This enclosure may contain points that do not
+  belong to any individual branch.
+
+The usual construction uses ``|`` or the ``CtcUnion`` constructor.
+
+.. tabs::
+
+  .. group-tab:: Python
+
+    .. literalinclude:: src.py
+      :language: py
+      :start-after: [union-ctc-1-beg]
+      :end-before: [union-ctc-1-end]
+      :dedent: 4
+
+  .. group-tab:: C++
+
+    .. literalinclude:: src.cpp
+      :language: c++
+      :start-after: [union-ctc-1-beg]
+      :end-before: [union-ctc-1-end]
+      :dedent: 2
+
+Applying it to a box gives the hull of the contracted branches:
+
+.. tabs::
+
+  .. group-tab:: Python
+
+    .. literalinclude:: src.py
+      :language: py
+      :start-after: [union-ctc-2-beg]
+      :end-before: [union-ctc-2-end]
+      :dedent: 4
+
+  .. group-tab:: C++
+
+    .. literalinclude:: src.cpp
+      :language: c++
+      :start-after: [union-ctc-2-beg]
+      :end-before: [union-ctc-2-end]
+      :dedent: 2
+
+For the two boxes used here, the exact union is not itself a box. Its interval hull is
+
+.. math::
+
+  [-12,10]\times[-2,4].
+
+
+SepUnion: union of represented sets
+-----------------------------------
+
+``SepUnion`` is the separator counterpart. If separators
+:math:`\mathcal{S}_1,\ldots,\mathcal{S}_n` are associated with sets
+:math:`\mathbb{S}_1,\ldots,\mathbb{S}_n`, then ``SepUnion`` is associated with
+
+.. math::
+
+  \mathbb{S}_{\mathrm{union}}
+  =
+  \mathbb{S}_1 \cup \cdots \cup \mathbb{S}_n.
+
+Construction follows the same syntax as for ``CtcUnion``:
+
+.. tabs::
+
+  .. group-tab:: Python
+
+    .. literalinclude:: src.py
+      :language: py
+      :start-after: [union-sep-1-beg]
+      :end-before: [union-sep-1-end]
+      :dedent: 4
+
+  .. group-tab:: C++
+
+    .. literalinclude:: src.cpp
+      :language: c++
+      :start-after: [union-sep-1-beg]
+      :end-before: [union-sep-1-end]
+      :dedent: 2
+
+
+Building a union incrementally
+------------------------------
+
+Both classes support ``|=`` and ``nb()``.
+
+For ``CtcUnion``, a union may be created from the dimension only. Before a branch is
+added, it represents the empty disjunction: contracting a box with it returns the empty
+domain. Adding contractors with ``|=`` then builds the disjunction incrementally.
+
+.. tabs::
+
+  .. group-tab:: Python
+
+    .. literalinclude:: src.py
+      :language: py
+      :start-after: [union-ctc-3-beg]
+      :end-before: [union-ctc-3-end]
+      :dedent: 4
+
+  .. group-tab:: C++
+
+    .. literalinclude:: src.cpp
+      :language: c++
+      :start-after: [union-ctc-3-beg]
+      :end-before: [union-ctc-3-end]
+      :dedent: 2
+
+``SepUnion`` currently has no constructor taking only a dimension, so incremental
+construction starts from an existing separator:
+
+.. tabs::
+
+  .. group-tab:: Python
+
+    .. literalinclude:: src.py
+      :language: py
+      :start-after: [union-sep-2-beg]
+      :end-before: [union-sep-2-end]
+      :dedent: 4
+
+  .. group-tab:: C++
+
+    .. literalinclude:: src.cpp
+      :language: c++
+      :start-after: [union-sep-2-beg]
+      :end-before: [union-sep-2-end]
+      :dedent: 2
+
+
+.. admonition:: Technical documentation
+
+  See the `C++ API documentation of CtcUnion <../../api/html/classcodac2_1_1_ctc_union.html>`_
+  and the `C++ API documentation of SepUnion <../../api/html/classcodac2_1_1_sep_union.html>`_.
diff --git a/doc/manual/manual/contractors/temporal/index.rst b/doc/manual/manual/contractors/temporal/index.rst
@@ -0,0 +1,14 @@
+Temporal contractors
+====================
+
+.. toctree::
+
+   Using static contractors on tubes <http://codac.io>
+   CtcDeriv <http://codac.io>
+   CtcEval <http://codac.io>
+   CtcDelay <http://codac.io>
+   CtcLinobs <http://codac.io>
+   CtcLohner <http://codac.io>
+   CtcPicard <http://codac.io>
+   CtcChain <http://codac.io>
+   CtcDiffInclusion <http://codac.io>
diff --git a/doc/manual/manual/extensions/ibex/index.rst b/doc/manual/manual/extensions/ibex/index.rst
@@ -0,0 +1,7 @@
+Interface with the IBEX library
+===============================
+
+.. toctree::
+
+   Installing the codac-ibex extension <http://codac.io>
+   How to use <http://codac.io>
diff --git a/doc/manual/manual/extensions/unsupported/index.rst b/doc/manual/manual/extensions/unsupported/index.rst
@@ -0,0 +1,6 @@
+Unsupported features of Codac
+=============================
+
+.. toctree::
+
+   Installing the codac-unsupported extension <http://codac.io>
diff --git a/doc/manual/manual/functions/analytic/analytic_operators.rst b/doc/manual/manual/functions/analytic/analytic_operators.rst
@@ -350,6 +350,8 @@ Temporal operations for involving trajectories or tubes in analytic expressions
     );
 
 
+For a detailed example using ``SampledTraj.as_function()`` and information on pointwise ``AnalyticFunction.traj_eval(...)``, see :ref:`sec-trajectories-operations`.
+
 Direct use of operators
 ^^^^^^^^^^^^^^^^^^^^^^^
 

diff --git a/doc/manual/manual/functions/analytic/index.rst b/doc/manual/manual/functions/analytic/index.rst
@@ -5,7 +5,5 @@ Analytic inclusion functions
 
 .. toctree::
 
-   analytic_functions.rst
-   analytic_operators.rst
-   Extension to custom expressions
-   Temporal functions
+  analytic_functions.rst
+  analytic_operators.rst
diff --git a/doc/manual/manual/functions/index.rst b/doc/manual/manual/functions/index.rst
@@ -4,9 +4,9 @@ Inclusion functions
 ===================
 
 .. toctree::
+  :maxdepth: 1
 
-   analytic/analytic_functions.rst
-   analytic/analytic_operators.rst
-   parallelepiped/parallelepiped_eval.rst
-   peibos/peibos.rst
-   .. Set-membership functions
+  analytic/analytic_functions.rst
+  analytic/analytic_operators.rst
+  parallelepiped/parallelepiped_eval.rst
+  peibos/peibos.rst
diff --git a/doc/manual/manual/functions/setmembership/index.rst b/doc/manual/manual/functions/setmembership/index.rst
@@ -0,0 +1,7 @@
+Set-membership functions
+========================
+
+.. toctree::
+
+   The class SetMembershipFunction <http://codac.io>
+   Extension to custom expressions <http://codac.io>
diff --git a/doc/manual/manual/intervals/Interval_class.rst b/doc/manual/manual/intervals/Interval_class.rst
@@ -257,6 +257,8 @@ For instance, ``x < y`` returns:
 - ``BoolInterval.UNKNOWN`` otherwise.
 
 
+.. _sec-intervals-class-un-bin-ary:
+
 Unary and binary functions
 --------------------------
-Original file line number
+Diff line change
@@ Expand Up @@
         );
+    For a detailed example using ``SampledTraj.as_function()`` and information on pointwise ``AnalyticFunction.traj_eval(...)``, see :ref:`sec-trajectories-operations`.
     Direct use of operators
     ^^^^^^^^^^^^^^^^^^^^^^^
@@ Expand Down @@