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doc: link libsemigroups
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docs/source/authors.rst

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- `Nicolas Thiery`_ helped the authors understand the ecosystem for integrating
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C++ code into python, and to some preliminary versions of the python bindings
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for ``libsemigroups`` using cython, and cppyy.
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for libsemigroups_ using cython, and cppyy.
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- Chinmaya Nagpal (chinmaya1011@gmail.com) resolved some issues with the
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packaging.
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.. _nicolas thiery: http://nicolas.thiery.name/
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/

docs/source/data-structures/adapters/index.rst

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========
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This page describes some of the adapters used in ``libsemigroups_pybind11``.
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These are classes that permit the generic classes in ``libsemigroups`` to be
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These are classes that permit the generic classes in libsemigroups_ to be
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used with arbitrary types, provided that the adapters are implemented for these
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types.
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/
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.. toctree::
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:maxdepth: 1
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docs/source/data-structures/elements/index.rst

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Elements
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========
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This page contains an overview summary of the functionality in ``libsemigroups``
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This page contains an overview summary of the functionality in libsemigroups_
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for defining elements of semigroups.
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/
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.. toctree::
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:maxdepth: 1
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docs/source/data-structures/misc/libsemigroups-error.rst

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This is the main type of exception raised by the custom data-structures and
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algorithms of ``libsemigroups_pybind11``. It is raised when the underlying
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C++ code from ``libsemigroups`` raises a ``LibsemigroupsException``.
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C++ code from libsemigroups_ raises a ``LibsemigroupsException``.
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.. doctest:: python
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`issue tracker
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<https://github.com/libsemigroups/libsemigroups_pybind11/issues>`_.
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.. autofunction:: error_message_with_prefix
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.. autofunction:: error_message_with_prefix
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/

docs/source/data-structures/presentations/index.rst

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Presentations
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=============
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The ``libsemigroups`` C\ **++** library, and hence the
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The libsemigroups_ C\ **++** library, and hence the
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``libsemigroups_pybind11`` Python package, implements several algorithms for
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computing with finitely presented semigroups and monoids. The implementation of
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the finite presentations on which these algorithms can be run is described
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The classes and modules in ``libsemigroups_pybind11`` for finitely presented
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semigroups and monoids are:
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/
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.. toctree::
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:maxdepth: 1
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docs/source/main-algorithms/kambites/index.rst

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On this page there are links to the documentation for the algorithms in
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``libsemigroups_pybind11`` for small overlap monoids by Mark Kambites and the
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authors of ``libsemigroups``; see :cite:`Kambites2009aa`,
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authors of libsemigroups_; see :cite:`Kambites2009aa`,
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:cite:`Kambites2009ab`, and :cite:`Mitchell2021aa`.
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/
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.. toctree::
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:maxdepth: 1
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docs/source/main-algorithms/todd-coxeter/index.rst

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============
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This page contains documentation related to the implementation of the
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Todd-Coxeter algorithm :cite:`Coleman2022aa` in ``libsemigroups``.
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Todd-Coxeter algorithm :cite:`Coleman2022aa` in libsemigroups_.
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The purpose of this algorithm is to find the :any:`WordGraph` of the action of a
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semigroup or monoid on the classes of a 1-sided (right), or 2-sided congruence;
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see :cite:`Coleman2022aa` for more details.
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Similar to other places in ``libsemigroups`` it is possible to create a
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Similar to other places in libsemigroups_ it is possible to create a
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:any:`ToddCoxeter` object from a presentation consisting of strings or lists of
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integers.
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/
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.. toctree::
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:maxdepth: 1
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src/cong.cpp

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:any:`KnuthBendix`, and :any:`ToddCoxeter` in parallel.
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On this page we describe the functionality relating to the class
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:any:`Congruence` in ``libsemigroups``. This class can be used for computing a
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:any:`Congruence` in libsemigroups_. This class can be used for computing a
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congruence over a semigroup or monoid by running every applicable algorithm
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from ``libsemigroups`` (and some variants of the same algorithm) in parallel.
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from libsemigroups_ (and some variants of the same algorithm) in parallel.
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This class is provided for convenience, at present it is not very customisable,
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and lacks some of the fine grained control offered by the classes implementing
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individual algorithms, such as :any:`Kambites`,
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congruence has infinitely many classes.
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)pbdoc");
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} // bind_cong
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} // namespace
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} // namespace
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void init_cong(py::module& m) {
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bind_cong<word_type>(m, "CongruenceWord");

src/errors.cpp

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Return whether :any:`LibsemigroupsError` messages have a C++ prefix.
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Since ``libsemigroups_pybind11`` is built on top of the C++ library
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``libsemigroups``, many of the errors thrown in ``libsemigroups_pybind11``
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libsemigroups_, many of the errors thrown in ``libsemigroups_pybind11``
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emanate from C++. This function returns whether :any:`LibsemigroupsError`
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messages contain a prefix that indicates which C++ function raised the
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exception.
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:return: Whether :any:`LibsemigroupsError` messages contain a prefix about the
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C++ function that raised the exception.
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:rtype: bool
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/
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)pbdoc");
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m.def("error_message_with_prefix",
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py::overload_cast<bool>(&error_message_with_prefix),
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Specify whether :any:`LibsemigroupsError` messages have a C++ prefix.
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Since ``libsemigroups_pybind11`` is built on top of the C++ library
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``libsemigroups``, many of the errors thrown in ``libsemigroups_pybind11``
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libsemigroups_, many of the errors thrown in ``libsemigroups_pybind11``
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emanate from C++. This function specifies whether :any:`LibsemigroupsError`
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messages should contain a prefix that indicates which C++ function raised the
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exception. By default, this information is not included.
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:param val: Whether :any:`LibsemigroupsError` messages should contain a prefix
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about the C++ function that raised the exception.
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:type val: bool
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/
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)pbdoc");
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}
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} // namespace libsemigroups

src/word-graph.cpp

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Returns the adjacency matrix of a word graph.
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This function returns the adjacency matrix of the word graph *wg*. The
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type of the returned matrix depends on whether or not ``libsemigroups`` is
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type of the returned matrix depends on whether or not libsemigroups_ is
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compiled with `eigen <http://eigen.tuxfamily.org/>`_ enabled. The returned
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matrix has the number of edges with source ``s`` and target ``t`` in the
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``(s, t)``-entry.
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:returns: The adjacency matrix.
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:rtype: numpy.ndarray | Matrix
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.. _libsemigroups: https://libsemigroups.github.io/libsemigroups/
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)pbdoc");
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m.def(

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