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doc: add docs for kambites,tc,cong,stephen to pres
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‎docs/source/data-structures/presentations/to-present.rst‎

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- :ref:`presentation-to-presentation`;
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- :ref:`presentation-and-function-to-presentation`;
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- :ref:`knuth-bendix-to-presentation`; and
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- :ref:`froidure-pin-to-presentation`.
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- :ref:`knuth-bendix-to-presentation`;
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- :ref:`froidure-pin-to-presentation`;
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- :ref:`kambites-to-presentation`;
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- :ref:`todd-coxeter-to-presentation`;
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- :ref:`congruence-to-presentation`; and
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- :ref:`stephen-to-presentation`.
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.. _presentation-to-presentation:
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>>> p = to(S, rtype=(Presentation, str))
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>>> len(p.alphabet()) == 4
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True
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.. _kambites-to-presentation:
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Converting a :any:`Kambites` to a :any:`Presentation`
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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To construct a :any:`Presentation` from a :any:`Kambites`, specify the
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following values for *args*:
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- **k** (:any:`Kambites`) -- the :any:`Kambites` from which to obtain
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the presentation.
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Additionally, specify one of the following for *Return*:
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- ``(Presentation,)`` for constructing a :any:`Presentation` over words of
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the same type as that in *k*.
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- ``(Presentation, str)`` for constructing a :any:`Presentation` over words
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of type ``str``.
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- ``(Presentation, list[int])`` for constructing a :any:`Presentation` over
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words of type ``list[int]``.
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This function constructs and returns a :any:`Presentation` object that is
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equivalent to the presentation used to construct the :any:`Kambites` object.
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When the word type matches, this function returns a reference to ``k.presentation()``.
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When the word types differ, a converted copy is returned.
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No computation is performed by this function; it simply retrieves the
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presentation that was used to define the :any:`Kambites` object.
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.. seealso::
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- :any:`Kambites.presentation`.
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.. doctest:: Python
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>>> from libsemigroups_pybind11 import (
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... congruence_kind,
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... Kambites,
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... Presentation,
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... presentation,
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... to,
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... )
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>>> p = Presentation([5, 6, 7, 8, 9])
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>>> presentation.add_rule(p, [5, 6], [7])
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>>> presentation.add_rule(p, [6, 7], [8])
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>>> presentation.add_rule(p, [7, 8], [9])
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>>> presentation.add_rule(p, [8, 9], [5])
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>>> presentation.add_rule(p, [9, 5], [6])
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>>> k = Kambites(congruence_kind.twosided, p)
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>>> result = to(k, rtype=(Presentation, list[int]))
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>>> result == p
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True
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>>> result_str = to(k, rtype=(Presentation, str))
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>>> result_str.alphabet()
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'abcde'
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>>> result_str.rules
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['ab', 'c', 'bc', 'd', 'cd', 'e', 'de', 'a', 'ea', 'b']
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.. _todd-coxeter-to-presentation:
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Converting a :any:`ToddCoxeter` to a :any:`Presentation`
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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To construct a :any:`Presentation` from a :any:`ToddCoxeter`, specify the
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following values for *args*:
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- **tc** (:any:`ToddCoxeter`) -- the :any:`ToddCoxeter` from which to obtain
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the presentation.
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Additionally, specify one of the following for *Return*:
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- ``(Presentation,)`` for constructing a :any:`Presentation` over words of
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the same type as that in *tc*.
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- ``(Presentation, str)`` for constructing a :any:`Presentation` over words
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of type ``str``.
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- ``(Presentation, list[int])`` for constructing a :any:`Presentation` over
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words of type ``list[int]``.
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This function constructs and returns a :any:`Presentation` object that is
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equivalent to the presentation used to construct the :any:`ToddCoxeter` object.
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When the word type matches, this function returns a reference to ``tc.presentation()``.
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When the word types differ, a converted copy is returned.
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No computation is performed by this function; it simply retrieves the
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presentation that was used to define the :any:`ToddCoxeter` object.
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.. seealso::
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- :any:`ToddCoxeter.presentation`.
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.. doctest:: Python
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>>> from libsemigroups_pybind11 import (
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... congruence_kind,
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... ToddCoxeter,
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... Presentation,
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... presentation,
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... to,
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... )
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>>> p = Presentation([5, 6, 7, 8, 9])
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>>> presentation.add_rule(p, [5, 6], [7])
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>>> presentation.add_rule(p, [6, 7], [8])
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>>> presentation.add_rule(p, [7, 8], [9])
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>>> presentation.add_rule(p, [8, 9], [5])
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>>> presentation.add_rule(p, [9, 5], [6])
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>>> tc = ToddCoxeter(congruence_kind.twosided, p)
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>>> result = to(tc, rtype=(Presentation, list[int]))
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>>> result == p
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True
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>>> result_str = to(tc, rtype=(Presentation, str))
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>>> result_str.alphabet()
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'abcde'
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>>> result_str.rules
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['ab', 'c', 'bc', 'd', 'cd', 'e', 'de', 'a', 'ea', 'b']
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.. _congruence-to-presentation:
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Converting a :any:`Congruence` to a :any:`Presentation`
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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To construct a :any:`Presentation` from a :any:`Congruence`, specify the
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following values for *args*:
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- **c** (:any:`Congruence`) -- the :any:`Congruence` from which to obtain
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the presentation.
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Additionally, specify one of the following for *Return*:
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- ``(Presentation,)`` for constructing a :any:`Presentation` over words of
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the same type as that in *c*.
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- ``(Presentation, str)`` for constructing a :any:`Presentation` over words
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of type ``str``.
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- ``(Presentation, list[int])`` for constructing a :any:`Presentation` over
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words of type ``list[int]``.
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This function constructs and returns a :any:`Presentation` object that is
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equivalent to the presentation used to construct the :any:`Congruence` object.
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When the word type matches, this function returns a reference to ``c.presentation()``.
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When the word types differ, a converted copy is returned.
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No computation is performed by this function; it simply retrieves the
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presentation that was used to define the :any:`Congruence` object. Note that
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any generating pairs added via :any:`Congruence.add_generating_pair`
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are not included in the returned presentation.
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.. seealso::
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- :any:`Congruence.presentation`; and
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- :any:`Congruence.add_generating_pair`.
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.. doctest:: Python
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>>> from libsemigroups_pybind11 import (
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... congruence_kind,
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... Congruence,
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... Presentation,
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... presentation,
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... to,
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... )
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>>> p = Presentation("abc")
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>>> presentation.add_rule(p, "aa", "b")
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>>> presentation.add_rule(p, "bb", "c")
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>>> presentation.add_rule(p, "cc", "a")
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>>> c = Congruence(congruence_kind.twosided, p)
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>>> result = to(c, rtype=(Presentation, str))
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>>> result == p
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True
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>>> result_word = to(c, rtype=(Presentation, list[int]))
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>>> result_word.alphabet()
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[0, 1, 2]
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>>> result_word.rules
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[[0, 0], [1], [1, 1], [2], [2, 2], [0]]
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.. _stephen-to-presentation:
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Converting a :any:`Stephen` to a :any:`Presentation`
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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To construct a :any:`Presentation` from a :any:`Stephen`, specify the
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following values for *args*:
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- **s** (:any:`Stephen`) -- the :any:`Stephen` from which to obtain
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the presentation.
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Additionally, specify one of the following for *Return*:
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- ``(Presentation,)`` for constructing a :any:`Presentation` over words of
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the same type as that in *s*.
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- ``(Presentation, str)`` for constructing a :any:`Presentation` over words
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of type ``str``.
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- ``(Presentation, list[int])`` for constructing a :any:`Presentation` over
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words of type ``list[int]``.
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This function constructs and returns a :any:`Presentation` object that is
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equivalent to the presentation used to construct the :any:`Stephen` object.
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A converted copy is always returned (even when word types match).
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No computation is performed by this function; it simply retrieves the
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presentation that was used to define the :any:`Stephen` object. Note that
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:any:`Stephen` can be constructed from either a :any:`Presentation` or an
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:any:`InversePresentation`; in both cases, this function returns a
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:any:`Presentation`.
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.. seealso::
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- :any:`Stephen.presentation`.
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.. doctest:: Python
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>>> from libsemigroups_pybind11 import (
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... Stephen,
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... Presentation,
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... presentation,
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... to,
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... )
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>>> p = Presentation([5, 6, 7, 8, 9])
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>>> presentation.add_rule(p, [5, 6], [7])
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>>> presentation.add_rule(p, [6, 7], [8])
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>>> presentation.add_rule(p, [7, 8], [9])
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>>> presentation.add_rule(p, [8, 9], [5])
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>>> presentation.add_rule(p, [9, 5], [6])
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>>> s = Stephen(p)
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>>> result = to(s, rtype=(Presentation, list[int]))
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>>> result == p
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True
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>>> result_str = to(s, rtype=(Presentation, str))
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>>> result_str.alphabet()
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'abcde'
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>>> result_str.rules
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['ab', 'c', 'bc', 'd', 'cd', 'e', 'de', 'a', 'ea', 'b']

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