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https://github.com/nthiery/sage-semigroups


https://github.com/nthiery/sage-semigroups

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README 

        
sage-semigroups: A semigroup (representation) theory library for SageMath

=========================================================================



.. image:: https://mybinder.org/badge.svg

   :target: https://mybinder.org/v2/gh/nthiery/sage-semigroups/master?filepath=demo.ipynb

   :alt: Run on binder



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.



News

----



- 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!



Future plans

------------



- 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).



Installation

------------



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



Usage

-----



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.

    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.



Acknowledgements

----------------



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.