#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-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:165 ncohen]:
> 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.
... but not "the" path-semigroup.
> 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 ?
HEY, I thought ''you'' are the guy who doesn't like to have the graph
namespace polluted `;-P`
> 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.
That's the point. It seems that there are two different notions of "paths
of a graph". One notion is "sequence of vertices that are met along the
path", another notion is "sequence of directed edges that are travelled
along the path".
If I see that correctly, the current implementation of `all_paths()` for
digraphs does the former, but the path-semigroup relies on the latter.
So, let me re-formulate my question to you.
1. Do you want a new method called, say, `DiGraph.all_quiver_paths()` or
`DiGraph.all_arrow_sequences()` that returns what the path semigroup
needs?
2. Do you want me to replace the current `DiGraph.all_paths()` so that it
returns what the path semigroup needs?
3. Do you want that the path semigroup computes its underlying data on its
own, without introducing a new method of `DiGraph`?
I'd be surprised if you answer "yes" to 1., and shocked if you replied
"yes" to 2. Thus, I suppose you prefer 3., but perhaps I am mistaken.
--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:166>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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