#12630: Add representations of quivers and quiver algebras to sage
-------------------------------------+-------------------------------------
Reporter: JStarx | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.2
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 | 72fb2eb71459f4ac76b0d922a7ad788c660a8017
Report Upstream: N/A | Stopgaps:
Branch: |
u/SimonKing/ticket/12630 |
Dependencies: #12412, #12413, |
#14806, #15491, #15623 |
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Comment (by SimonKing):
Replying to [comment:158 ncohen]:
> > Just random suggestions. Adding those methods to digraphs sounds
> > reasonable, with slightly more explict names like
> > {{{Q.path_semigroup()}}} and {{{Q.path_algebra()}}}. The latter could
> > possibly be {{{Q.path_semigroup().algebra(QQ)}}}.
>
> No problem with that.
OK, the names make sense, and `Q.path_algebra(QQ)` wouldn't be more than a
short-cut for `Q.path_semigroup().algebra(QQ)` anyway.
> > For {{{Q.all_paths()}}}, it depends on the meaning.
>
> What do you mean ? `DiGraph.all_paths` already exists.
Yes, but IIRC the `all_paths` method implemented here has a different
meaning. The difference is: In one case, the resulting paths are lists of
visited vertices, in the other case, the resulting paths are lists of
adjacent arrows. In particular, if you have multiple arrows between two
vertices, the first meaning of `all_paths` would count it as ''one'' path,
but the second meaning would distinguish the different arrows.
--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:161>
Sage <http://www.sagemath.org>
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