sage-semigroups is a library for computational semigroup (representation) theory, for the open source mathematical system SageMath. Its intention is to serve as a repository where experimental features can be shared among researchers and mature until they get integrated into the main SageMath library or discarded.

• June 2017: up to now, that repository had been a mostly empty shell. At the occasion of a sprint with Franco Saliola, most of the semigroup code from the Sage-Combinat queue was imported in sage-semigroups, together with private code from Franco. As a result, a dozen semigroups are available in the semigroups.* catalog. In principle, the code to compute the representation theory of j-trivial / aperiodic monoids is there too. However the latter code has been imported as is, and still remains to be updated w.r.t. the new environment.

  Most tests don't pass at this stage

  Use at your own risk, and expect many failures!

• Clean up to get all tests to pass;
• As much as possible, use libsemigroups and GAP's Semigroups package for the semigroups;
• Focus on the representation theory aspects (e.g. representation theory of general semigroups) and on providing special families of monoids whose definition use other features of Sage (e.g. root systems).

Stable version (not much there yet):

sage -pip install sage-semigroups

For the bleeding edge version:

git clone https://github.com/nthiery/sage-semigroups.git
cd sage-semigroups
sage -pip install .

In both cases, this installs the library in the Sage tree. You may instead want to install sage-semigroup in your user directory:

sage -pip install --user ...

Or to install it in editable mode for development:

sage -pip install --user -e ...

See the help of the corresponding pip options for details

See the brief demo notebook, or try it live on Binder.

In short:

sage: import sage_semigroups

The features are then available as if they were native Sage features:

sage: semigroups.<tab>
sage: H = semigroups.HeckeMonoid(["A",3])
sage: H.is_l_trivial()
True
sage: H.quiver()
Digraph on 8 vertices
sage: H.cartan_matrix()
[1 0 0 0 0 0 0 0]
[0 1 1 1 0 0 0 0]
[0 1 2 1 1 0 0 0]
[0 1 1 1 0 0 0 0]
[0 0 1 0 2 1 1 0]
[0 0 0 0 1 1 1 0]
[0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 1]

The intention is to make the later integration of those features into Sage as transparent as possible. To enable this, the code is structured as in the SageMath library; for example the features implemented in:

sage_semigroups.categories.j_trivial_monoids.JTrivialMonoids

get merged into the corresponding native Sage category:

sage.categories.j_trivial_monoids.JTrivialMonoids

This is achieved using the Recursive Monkey Patching package, which see for details.

A lot of the code was authored by Florent Hivert, Franco Saliola, Nicolas M. Thiéry, ... and resurrected from the former Sage-Combinat patch queue.

You can use this bib file to cite this work.