#12630: Add representations of quivers and quiver algebras to sage
------------------------------------------------------------------------------+
Reporter: JStarx |
Owner: AlexGhitza
Type: enhancement |
Status: needs_work
Priority: major |
Milestone: sage-5.11
Component: algebra |
Resolution:
Keywords: algebra, quiver, module, days49 |
Work issues: Use existing infrastructure for Representation, Homspace and
Morphism.
Report Upstream: N/A |
Reviewers:
Authors: Jim Stark, Simon King, Mathieu Guay-Paquet, Aladin Virmaux |
Merged in:
Dependencies: #12412, #12413 |
Stopgaps:
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Old description:
> This will add classes dealing with quivers, quiver algebras,
> representations of quivers, elements of these representations,
> homomorphisms between these representations, and spaces of homomorphisms
> between these representations.
>
> There's a lot here that is really easily computable. We can compute
> socles, quotients, radicals, duals, and more for any finite dimensional
> representation. We can compute projective covers of modules so
> Auslander-Rieten translations have been implemented and there's certainly
> potential for future enhancements dealing with homology and cohomology.
> There's only so much I can say here but everything is fully documented
> and should be self explanatory.
>
> Two shortcomings are that quivers need to be acyclic (to keep things
> finite dimensional) and this code does not handle quivers with relations.
> As far as quivers with relations go there are comments in the code
> detailing what should be done to implement that. It's well within the
> reach of Sage, I just don't have the time to do it at the moment.
>
> __Apply__
>
> The second patch is supposed to split the code into chewable bits (so
> that maintenance and cythonization will become easier), introduces a
> parent structure for the paths of a quiver (namely: a free small
> category), makes paths inherit from Element (but ''not'' from
> `UniqueRepresentation`!) and fixes some tests. But there is more to do.
>
> * [attachment:trac_12630_quivers_v2.patch]
> * [attachment:trac12630_refactor_code.2.patch]
New description:
This will add classes dealing with quivers, quiver algebras,
representations of quivers, elements of these representations,
homomorphisms between these representations, and spaces of homomorphisms
between these representations.
There's a lot here that is really easily computable. We can compute
socles, quotients, radicals, duals, and more for any finite dimensional
representation. We can compute projective covers of modules so Auslander-
Rieten translations have been implemented and there's certainly potential
for future enhancements dealing with homology and cohomology. There's
only so much I can say here but everything is fully documented and should
be self explanatory.
Two shortcomings are that quivers need to be acyclic (to keep things
finite dimensional) and this code does not handle quivers with relations.
As far as quivers with relations go there are comments in the code
detailing what should be done to implement that. It's well within the
reach of Sage, I just don't have the time to do it at the moment.
__Apply__
The second patch is supposed to split the code into chewable bits (so that
maintenance and cythonization will become easier), introduces a parent
structure for the paths of a quiver (namely: a free small category), makes
paths inherit from Element (but ''not'' from `UniqueRepresentation`!) and
fixes some tests. But there is more to do.
* [attachment:trac_12630_quivers_v2.patch]
* [attachment:trac12630_refactor_code.patch]
--
Comment (by SimonKing):
I fixed the remaining doctest error, which is just due to a bad way of
creating the name of digraphs. I added a "todo" for this issue, which
clearly does not belong to this ticket.
It is not "needs review" yet, because I want to make homset stuff use
existing infrastructure. However, all tests pass now. Hence, if my
attempts concerning homsets won't work, we have at least something that
works.
I started with Aladin's patch, but of course I can not replace it on Trac,
and hence I went back to the name of my patch, which was the starting
point of Aladin's patch. In other words:
Apply trac_12630_quivers_v2.patch trac12630_refactor_code.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:91>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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