#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: Split into
different modules. Use parents and elements.
Report Upstream: N/A | Reviewers:
Authors: Jim Stark, Simon King | Merged in:
Dependencies: #12412, #12413 | Stopgaps:
---------------------------------------------------+------------------------
Changes (by {'newvalue': u'Jim Stark, Simon King', 'oldvalue': u'Jim Stark'}):
* keywords: algebra, quiver, module => algebra, quiver, module, days49
* author: Jim Stark => Jim Stark, Simon King
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.
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:quiver_distributed_code.patch]
--
Comment:
Even though my patch isn't finished, I'll post it, so that we can discuss
about it at SD49. Many doctests currently fail.
Apply trac_12630_quivers_v2.patch quiver_distributed_code.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:49>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
