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‎doc/manual/index.rst‎

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* The class SetMembershipFunction
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* Extension to custom expressions
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* :ref:`sec-domains-tubes`
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* :ref:`sec-domains-tubes-tdomain`
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* :ref:`sec-domains-tubes-slicedtube`
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* The Trajectory classes
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* Increasing performances using views
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* :ref:`sec-tubes-trajectories`
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* :ref:`sec-trajectories-sampledtraj`
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* :ref:`sec-trajectories-analytictraj`
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* :ref:`sec-trajectories-operations`
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* :ref:`sec-trajectories-io`
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* :ref:`sec-tubes-tdomain`
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* :ref:`sec-tubes-slice`
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* :ref:`sec-tubes-slicedtube`
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* :ref:`sec-tubes-examples`
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* Contractors
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* What are contractors?
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* Related papers
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* Contributors
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* How to cite Codac
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:ref:`sec-ref-codac-logos`
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* :ref:`sec-ref-codac-logos`
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How-to guides

‎doc/manual/manual/cn/index.rst‎

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Contractor Networks
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===================
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.. toctree::
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What is a CN? <http://codac.io>
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The ContractorNetwork class <http://codac.io>

‎doc/manual/manual/contractors/basic/index.rst‎

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Basic contractors
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=================
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.. toctree::
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CtcIdentity <http://codac.io>
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CtcEmpty <http://codac.io>
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CtcLazy <http://codac.io>
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CtcFixpoint <http://codac.io>

‎doc/manual/manual/contractors/index.rst‎

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.. _sec-ctc:
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Contractors, separators
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=======================
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‎doc/manual/manual/contractors/linear/index.rst‎

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Linear contractors
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==================
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.. toctree::
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CtcGaussElim <http://codac.io>
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CtcGaussSeidel <http://codac.io>
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CtcLinearPrecond <http://codac.io>

‎doc/manual/manual/contractors/set/ctcunion.rst‎

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.. _sec-ctc-set-ctcunion:
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.. _sec-sep-set-sepunion:
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Union: CtcUnion and SepUnion
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============================
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Main author: `Simon Rohou <https://www.simon-rohou.fr/research/>`_
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``CtcUnion`` and ``SepUnion`` implement the logical union/disjunction counterpart of
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``CtcInter`` and ``SepInter``:
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.. list-table::
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:header-rows: 1
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:widths: 20 35 45
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* - Class
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- Combines
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- Meaning
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* - ``CtcUnion``
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- contractors
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- disjunction of constraints, obtained by joining the contracted branches
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* - ``SepUnion``
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- separators
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- separator associated with the union of the represented sets
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Both classes can be constructed explicitly or with the ``|`` operator.
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CtcUnion: disjunction of contractors
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------------------------------------
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For box contractors, ``CtcUnion`` applies every stored contractor independently to the
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same input box and returns a box enclosing the union of the resulting branches:
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.. math::
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\mathcal{C}_{\mathrm{union}}([\mathbf{x}])
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=
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\operatorname{hull}\!\left(
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\bigcup_{i=1}^{n}\mathcal{C}_i([\mathbf{x}])
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\right),
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where :math:`\operatorname{hull}` denotes the smallest box containing the union.
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This evaluation differs from ``CtcInter``: the branches are **not** applied
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sequentially. Each contractor receives the original input domain.
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.. note::
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The exact union of several boxes is generally not a box. ``CtcUnion`` therefore
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returns a box enclosure of this union. This enclosure may contain points that do not
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belong to any individual branch.
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The usual construction uses ``|`` or the ``CtcUnion`` constructor.
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.. tabs::
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.. group-tab:: Python
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.. literalinclude:: src.py
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:language: py
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:start-after: [union-ctc-1-beg]
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:end-before: [union-ctc-1-end]
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:dedent: 4
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.. group-tab:: C++
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.. literalinclude:: src.cpp
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:language: c++
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:start-after: [union-ctc-1-beg]
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:end-before: [union-ctc-1-end]
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:dedent: 2
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Applying it to a box gives the hull of the contracted branches:
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.. tabs::
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.. group-tab:: Python
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.. literalinclude:: src.py
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:language: py
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:start-after: [union-ctc-2-beg]
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:end-before: [union-ctc-2-end]
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:dedent: 4
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.. group-tab:: C++
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.. literalinclude:: src.cpp
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:language: c++
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:start-after: [union-ctc-2-beg]
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:end-before: [union-ctc-2-end]
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:dedent: 2
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For the two boxes used here, the exact union is not itself a box. Its interval hull is
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.. math::
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[-12,10]\times[-2,4].
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SepUnion: union of represented sets
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-----------------------------------
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``SepUnion`` is the separator counterpart. If separators
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:math:`\mathcal{S}_1,\ldots,\mathcal{S}_n` are associated with sets
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:math:`\mathbb{S}_1,\ldots,\mathbb{S}_n`, then ``SepUnion`` is associated with
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.. math::
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\mathbb{S}_{\mathrm{union}}
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=
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\mathbb{S}_1 \cup \cdots \cup \mathbb{S}_n.
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Construction follows the same syntax as for ``CtcUnion``:
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.. tabs::
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.. group-tab:: Python
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.. literalinclude:: src.py
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:language: py
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:start-after: [union-sep-1-beg]
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:end-before: [union-sep-1-end]
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:dedent: 4
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.. group-tab:: C++
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.. literalinclude:: src.cpp
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:language: c++
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:start-after: [union-sep-1-beg]
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:end-before: [union-sep-1-end]
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:dedent: 2
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Building a union incrementally
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------------------------------
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Both classes support ``|=`` and ``nb()``.
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For ``CtcUnion``, a union may be created from the dimension only. Before a branch is
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added, it represents the empty disjunction: contracting a box with it returns the empty
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domain. Adding contractors with ``|=`` then builds the disjunction incrementally.
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.. tabs::
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.. group-tab:: Python
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.. literalinclude:: src.py
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:language: py
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:start-after: [union-ctc-3-beg]
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:end-before: [union-ctc-3-end]
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:dedent: 4
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.. group-tab:: C++
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.. literalinclude:: src.cpp
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:language: c++
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:start-after: [union-ctc-3-beg]
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:end-before: [union-ctc-3-end]
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:dedent: 2
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``SepUnion`` currently has no constructor taking only a dimension, so incremental
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construction starts from an existing separator:
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.. tabs::
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.. group-tab:: Python
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.. literalinclude:: src.py
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:language: py
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:start-after: [union-sep-2-beg]
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:end-before: [union-sep-2-end]
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:dedent: 4
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.. group-tab:: C++
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.. literalinclude:: src.cpp
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:language: c++
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:start-after: [union-sep-2-beg]
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:end-before: [union-sep-2-end]
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:dedent: 2
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.. admonition:: Technical documentation
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See the `C++ API documentation of CtcUnion <../../api/html/classcodac2_1_1_ctc_union.html>`_
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and the `C++ API documentation of SepUnion <../../api/html/classcodac2_1_1_sep_union.html>`_.

‎doc/manual/manual/contractors/temporal/index.rst‎

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Temporal contractors
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====================
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.. toctree::
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Using static contractors on tubes <http://codac.io>
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CtcDeriv <http://codac.io>
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CtcEval <http://codac.io>
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CtcDelay <http://codac.io>
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CtcLinobs <http://codac.io>
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CtcLohner <http://codac.io>
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CtcPicard <http://codac.io>
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CtcChain <http://codac.io>
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CtcDiffInclusion <http://codac.io>

‎doc/manual/manual/extensions/ibex/index.rst‎

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Interface with the IBEX library
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===============================
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.. toctree::
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Installing the codac-ibex extension <http://codac.io>
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How to use <http://codac.io>

‎doc/manual/manual/extensions/unsupported/index.rst‎

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Unsupported features of Codac
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=============================
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.. toctree::
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Installing the codac-unsupported extension <http://codac.io>

‎doc/manual/manual/functions/analytic/analytic_operators.rst‎

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);
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For a detailed example using ``SampledTraj.as_function()`` and information on pointwise ``AnalyticFunction.traj_eval(...)``, see :ref:`sec-trajectories-operations`.
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Direct use of operators
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^^^^^^^^^^^^^^^^^^^^^^^
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