Converting to a Congruence

This page contains documentation relating to converting libsemigroups_pybind11 objects into Congruence instances using the to function.

See also

The to function for an overview of possible conversions between libsemigroups_pybind11 types.

Various uses

Recall that the signature for the to function is to(*args, Return). In what follows, we explain how different values of args and Return may be used to construct Congruence objects. The following options are possible:

Converting a FroidurePin to a Congruence

To construct a Congruence from a FroidurePin, specify all of the following values for args:

Additionally, specify one of the following tuples for Return:

  • (Congruence, str) for constructing a Congruence on words of type str; or

  • (Congruence, list[int]) for constructing a Congruence on words of type list[int].

This function converts the FroidurePin object fpb into a Congruence object using the WordGraph wg (which should be either the FroidurePin.left_cayley_graph or the FroidurePin.right_cayley_graph of fpb).

This returned Congruence object represents the trivial congruence over the semigroup defined by fpb.

This will throw a LibsemigroupsError if wg is not the FroidurePin.left_cayley_graph or the FroidurePin.right_cayley_graph of fpb.

>>> from libsemigroups_pybind11 import (
...     Bipartition,
...     congruence_kind,
...     Congruence,
...     FroidurePin,
...     to,
... )

>>> b1 = Bipartition([[1, -1], [2, -2], [3, -3], [4, -4]])
>>> b2 = Bipartition([[1, -2], [2, -3], [3, -4], [4, -1]])
>>> b3 = Bipartition([[1, -2], [2, -1], [3, -3], [4, -4]])
>>> b4 = Bipartition([[1, 2], [3, -3], [4, -4], [-1, -2]])
>>> S = FroidurePin(b1, b2, b3, b4)

>>> cong = to(
...     congruence_kind.twosided,   # knd
...     S,                          # fpb
...     S.right_cayley_graph(),     # wg
...     rtype=(Congruence, str),
... )

>>> cong.run()
>>> S.size() == cong.number_of_classes()
True