Presentations
The libsemigroups C++ library, and hence the
libsemigroups_pybind11 Python package, implements several algorithms for
computing with finitely presented semigroups and monoids. The implementation of
the finite presentations on which these algorithms can be run is described
below.
In libsemigroups_pybind11, a presentation is modelled as a collection of
rules, each of which is a pair of words (although these rules are stored as
a non-nested list with the left- and right-hand sides in the even and odd indexed positions respectively). Each word is made up of letters.
Presently, for any given presentation, all letters must either be of the type
str or int. In a presentation where letters are of the type
str, words have the type str. In a presentation where letters are
of the type int, words will be lists of int types.
Once a presentation is constructed, the type of its letters and words cannot be changed.
In what follows, we will use the pseudo-types Letter and Word instead of
str | int and str | list[int] to further indicate that two types of
letters and words cannot be interchanged once a presentation is constructed.
The classes and modules in libsemigroups_pybind11 for finitely presented
semigroups and monoids are: