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.wy-nav-content { | ||
max-width: 1000px; | ||
} |
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.. Copyright (c) 2019, J. D. Mitchell | ||
Distributed under the terms of the GPL license version 3. | ||
The full license is in the file LICENSE, distributed with this software. | ||
Actions | ||
======= | ||
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.. cpp:namespace:: libsemigroups | ||
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This page contains an overview summary of the functionality in | ||
``libsemigroups`` for finding actions of semigroups, or groups, on sets. The | ||
notion of an "action" in the context of ``libsemigroups`` is analogous to the | ||
notion of an orbit of a group. | ||
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You are unlikely to want to use :cpp:class:`Action` directly, but rather via | ||
the more convenient aliases :cpp:any:`RightAction` and :cpp:any:`LeftAction`. | ||
To use :cpp:any:`RightAction` and :cpp:any:`LeftAction` with custom types, | ||
actions, and so on, see :cpp:class:`ActionTraits`. | ||
See also :cpp:any:`ImageLeftAction` and :cpp:any:`ImageRightAction`. | ||
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.. code-block:: cpp | ||
using namespace libsemigroups; | ||
RightAction<PPerm<16>, PPerm<16>, ImageRightAction<PPerm<16>, PPerm<16>>> o; | ||
o.add_seed(PPerm<16>::identity(16)); | ||
o.add_generator( | ||
PPerm<16>({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, | ||
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0}, | ||
16)); | ||
o.add_generator( | ||
PPerm<16>({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, | ||
{1, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, | ||
16)); | ||
o.add_generator( | ||
PPerm<16>({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, | ||
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, | ||
16)); | ||
o.add_generator( | ||
PPerm<16>({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, | ||
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, | ||
16)); | ||
o.reserve(70000); | ||
o.size(); // returns 65536 | ||
The classes in ``libsemigroups`` for actions are: | ||
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.. toctree:: | ||
:maxdepth: 1 | ||
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_generated/libsemigroups__action.rst | ||
_generated/libsemigroups__actiontraits | ||
api/left-action | ||
api/right-action | ||
_generated/libsemigroups__side.rst |
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.. Copyright (c) 2019, J. D. Mitchell | ||
Distributed under the terms of the GPL license version 3. | ||
The full license is in the file LICENSE, distributed with this software. | ||
.. _Adapters: | ||
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Adapters | ||
======== | ||
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Declared in ``adapters.hpp``. | ||
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This file contains class templates for adapting a user-defined type for use | ||
with the algorithms in ``libsemigroups``. There are explicit implementations for | ||
relevant element types from ``libsemigroups`` and ``HPCombi``, details of which | ||
can be found elsewhere in this documentation. | ||
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No default implementation | ||
~~~~~~~~~~~~~~~~~~~~~~~~~ | ||
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The following adapters have no default implementation for arbitrary types: | ||
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.. toctree:: | ||
:maxdepth: 1 | ||
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_generated/libsemigroups__complexity.rst | ||
_generated/libsemigroups__degree.rst | ||
_generated/libsemigroups__imageleftaction.rst | ||
_generated/libsemigroups__imagerightaction.rst | ||
_generated/libsemigroups__increasedegree.rst | ||
_generated/libsemigroups__inverse.rst | ||
_generated/libsemigroups__lambda.rst | ||
_generated/libsemigroups__lambdavalue.rst | ||
_generated/libsemigroups__one.rst | ||
_generated/libsemigroups__product.rst | ||
_generated/libsemigroups__rho.rst | ||
_generated/libsemigroups__rhovalue.rst | ||
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Default implementation | ||
~~~~~~~~~~~~~~~~~~~~~~ | ||
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The following adapters do have a default implementation for arbitrary types: | ||
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.. The following are not in the yml setup because JDM couldn't figure out how | ||
to generate the rst page for EqualTo::operator(). | ||
.. toctree:: | ||
:maxdepth: 1 | ||
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api/equalto.rst | ||
api/hash.rst | ||
api/less.rst | ||
api/ontuples.rst | ||
api/onsets.rst | ||
_generated/libsemigroups__rankstate.rst | ||
api/swap.rst |
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.. Copyright (c) 2019-21, J. D. Mitchell | ||
Distributed under the terms of the GPL license version 3. | ||
The full license is in the file LICENSE, distributed with this software. | ||
Validating Bipartitions | ||
======================= | ||
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.. doxygenfunction:: libsemigroups::validate(Bipartition const&) | ||
:project: libsemigroups |
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.. Copyright (c) 2020-2022, J. D. Mitchell | ||
Distributed under the terms of the GPL license version 3. | ||
The full license is in the file LICENSE, distributed with this software. | ||
Helper functions for ActionDigraph | ||
================================== | ||
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Overview | ||
-------- | ||
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Defined in ``action-digraph-helper.hpp``. | ||
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This page contains the documentation for helper function for the class | ||
:cpp:type:`libsemigroups::ActionDigraph`. | ||
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Full API | ||
-------- | ||
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.. doxygenfunction:: libsemigroups::operator<<(std::ostream&, ActionDigraph<T> const&) | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::follow_path | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::follow_path_nc(ActionDigraph<T> const&, node_type<T> const, word_type const&) noexcept | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::follow_path_nc(ActionDigraph<T> const&, node_type<T> const, S, S) noexcept | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::last_node_on_path | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::last_node_on_path_nc | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::is_acyclic(ActionDigraph<T> const&) | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::is_acyclic(ActionDigraph<T> const&, node_type<T>) | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::is_reachable | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::topological_sort(ActionDigraph<T> const&) | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::topological_sort(ActionDigraph<T> const&, node_type<T>) | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::add_cycle(ActionDigraph<T>&, U, U) | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::add_cycle(ActionDigraph<T>&, size_t) | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::make(size_t, std::initializer_list<std::initializer_list<T>>) | ||
:project: libsemigroups | ||
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.. doxygenfunction:: libsemigroups::action_digraph_helper::is_connected(ActionDigraph<T> const&) | ||
:project: libsemigroups |
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.. Copyright (c) 2019, J. D. Mitchell | ||
Distributed under the terms of the GPL license version 3. | ||
The full license is in the file LICENSE, distributed with this software. | ||
.. This file only exists because JDM couldn't figure out how to get the | ||
operator() to appear using the yml setup. | ||
EqualTo | ||
======= | ||
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.. doxygenstruct:: libsemigroups::EqualTo | ||
:project: libsemigroups | ||
:members: |
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