#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 |
-------------------------------------+-------------------------------------
Comment (by ncohen):
> I believe that listing the paths (in the sense of: concatenation of
arrows, with multiple different paths between the same vertices) should be
the job of the path-semigroup: After all, these are the elements of the
path-semigroup.
Yet, you would be surprised to know the number of persons who have a clear
understanding of what the set of all paths is, and have no idea of what a
semigroup is. A set is a set, a semi-group is a set with additional
structure. I don't get why enumerating the paths should make one define a
structure on them. If an object representing a set of paths is to be
defined somewhere, it has to be defined from a digraph, not from some
specific semigroup. As I guess you can define one thousand different
semigroups on a given set.
> So, I would prefer to *not* add it as a new method of `DiGraph` (perhaps
calling it `all_quiver_paths()`) and of course I would prefer to *not*
override the `all_paths()` method of `DiGraph`, but I'd prefer to let it
be a `PathSemigroup` method.
I don't get it. You can define a set of paths from a DiGraph, THEN you add
(one) semigroup structure on top of it. Why on earth would the set of
paths be obtained from a semigroup while the semigroup is the one which
needs a set of paths, and not the other way around ?
Then again, just for user-friendliness reasons, you cannot reasonably ask
a user to know what a semigroup is in order to enumerate the paths of a
graph.
Nathann
--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:165>
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.
