#12630: Add representations of quivers and quiver algebras to sage
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Reporter: JStarx | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: algebra | Keywords: algebra, quiver, module
Work_issues: | Upstream: N/A
Reviewer: | Author: JStarx
Merged: | Dependencies: 12412, 12413
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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.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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