#12630: Add representations of quivers and quiver algebras to sage
-------------------------------------+-------------------------------------
Reporter: JStarx | Owner: AlexGhitza
Type: enhancement | Status: needs_review
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 | a6b04c6c57b2362cbfa2e300a5d592ef79757fc8
Report Upstream: N/A | Stopgaps:
Branch: |
public/combinat/quivers |
Dependencies: #12412, #12413, |
#14806, #15491, #15623, #15810 |
-------------------------------------+-------------------------------------
Comment (by darij):
I changed the doc again. Simon, can you keep working on the
public/combinat/quivers branch? Otherwise the branch field is getting
changed over and over here -- I certainly cannot push onto a branch in
your namespace.
Do you think the following notions are now well-documented enough:
1) what "path" means in the context of quivers;
2) what "partial semigroup" means and that the path semigroup is a such?
By "well-documented enough" I mean, in particular, that the documentation
is in those places where one would be looking for it.
I don't understand why we have two ways to compute paths in a path
semigroup:
{{{
def all_paths(self, start=None, end=None):
}}}
on the one hand, and
{{{
def iter_paths_by_length_and_startpoint(self, d, v):
def iter_paths_by_length_and_endpoint(self, d, v):
}}}
on the other. Does the former have any advantages at all, such as speed in
the acyclic case? All I can say is that it is broken even in the acyclic
case:
{{{
sage: Q = DiGraph({i: {i+1: "a"+str(i)} for i in range(2)})
sage: Q.edges()
[(0, 1, 'a0'), (1, 2, 'a1')]
sage: Q.path_semigroup().all_paths()
[e_0, a, 0, a*a, a*1, 0*a, 0*1, e_1, a, 1, e_2]
}}}
Apparently somewhere deep in the code it believes that every edge label is
one character long. And it seems to check for acyclicity twice (and, for
some reason, also checks for absence of loops?). Either way, is there a
reason for this method to exist?
--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:206>
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