Stephen¶

This module contains the single class Stephen which implements a version of Stephen’s procedure for computing the size and number of \(\mathscr{R}\)-classes of a finitely presented inverse monoid.

class step_hen.Stephen(presn: step_hen.presentation.InverseMonoidPresentation)¶

The class encodes a rudimentary version of Stephen’s procedure as described in [Cut01]

__init__(presn: step_hen.presentation.InverseMonoidPresentation) → None¶

Construct a new Stephen from an inverse monoid presentation.

Parameters: presn (InverseMonoidPresentation) – the inverse monoid presentation
Returns: None

Example

P = InverseMonoidPresentation()
P.set_alphabet("xy")
P.add_relation("xxx", "x")
P.add_relation("yyyyy", "y")
P.add_relation("xyxy", "xx")

S = Stephen(P)

number_of_r_classes() → int¶

Returns the number of \(\mathscr{R}\)-classes of the inverse monoid defined by the presentation used to define an instance of this type.

Parameters: None
Returns: An int.

Warning

The procedure implemented by method may never terminate. In particular, it terminates if and only if the inverse monoid defined by the inverse monoid presentation used to construct the class is finite. Even if the monoid defined by the presentation is finite, there is no bound on the run time of this method.

Example

P = InverseMonoidPresentation()
P.set_alphabet("xy")
P.add_relation("xxx", "x")
P.add_relation("yyyyy", "y")
P.add_relation("xyxy", "xx")

S = Stephen(P)
S.number_of_r_classes()  # returns 3

size() → int¶

Returns the size of the inverse monoid defined by the presentation used to define an instance of this type.

Parameters: None
Returns: An int.

Warning

The procedure implemented by method may never terminate. In particular, it terminates if and only if the inverse monoid defined by the inverse monoid presentation used to construct the class is finite. Even if the monoid defined by the presentation is finite, there is no bound on the run time of this method.

Example

P = InverseMonoidPresentation()
P.set_alphabet("xy")
P.add_relation("xxx", "x")
P.add_relation("yyyyy", "y")
P.add_relation("xyxy", "xx")

S = Stephen(P)
S.size()  # returns 13