#12630: Add representations of quivers and quiver algebras to sage
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Reporter: JStarx | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.13
Component: algebra | Resolution:
Keywords: algebra, quiver, | Merged in:
module, days49 | Reviewers: Simon King
Authors: Jim Stark, Simon | Work issues:
King, Mathieu Guay-Paquet, Aladin | Commit:
Virmaux | fda4012f91c357f3db86fb07271573886ad0da74
Report Upstream: N/A | Stopgaps:
Branch: |
u/SimonKing/ticket/12630 |
Dependencies: #12412, #12413, |
#14806 |
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Comment (by SimonKing):
Hi Nicolas,
Replying to [comment:133 nthiery]:
> > > What about `path_monoid` (if it is a monoid) ? `:-P`
> >
> > This would have been my choice, too. But sadly it is a monoid if and
only if the quiver has precisely one vertex (which is certainly not always
the case).
>
> ...
>
> I am even tempted by the shorter path_monoid or path_semigroup.
> Granted, this is an abuse.
Why? AFAIK, a semigroup is the same as an associative magma (which we have
here). It is not needed to have an identity in a semigroup. Hence, it is
no
abuse at all. And I think path semigroup is both short and descriptive,
and relatively easy to guess.
I feel tempted to call it path semigroup.
> I like path_algebra too, and it's consistent with the above. I'd say
> it's fair at this point to change this name.
Nobody has complained since you posted your comment (hence, 7 weeks ago).
I'd
say that in this case we are entitled to change the terminology towards
something that we both find more common, namely "path algebra" rather than
"quiver algebra".
> > > > - `.quiver_representation(...)`: Create a module over the quiver
algebra.
> > >
> > > To me this should be `.quiver_algebra().representation()`.
> >
> > To me as well. But it seems that some people really think of it in
terms of the graph.
>
> My feeling:
>
> - Provide the feature as ....algebra.representation() now.
> - Add .quiver_representation() later, as an alias, if there really is a
> popular request for it.
In other words: Nathann, Nicolas and I all agree that that it is the path
algebra that is represented, not the quiver.
--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:142>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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