#12630: Add representations of quivers and quiver algebras to sage
-------------------------------------------+--------------------------------
Reporter: JStarx | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.10
Component: algebra | Resolution:
Keywords: algebra, quiver, module | Work issues: Split into
different modules. Use parents and elements.
Report Upstream: N/A | Reviewers:
Authors: Jim Stark | Merged in:
Dependencies: #12412, #12413 | Stopgaps:
-------------------------------------------+--------------------------------
Changes (by SimonKing):
* dependencies: #12412, #12413, #14535 => #12412, #12413
Comment:
It seems that inheriting from both Parent and Category would mean to ask
for trouble (e.g., if F is the free small category of a quiver, then
F.element_class of F-the-parent would be used for the paths in F, while
F.element_class of F-the-category would be used for the elements of F's
objects, i.e., of its vertices). Moreover, providing a general framework
for immutable graphs means "opening a can of worms".
By the latter, I start to understand the motivation for introducing a
separate class for "quiver-the-graph": It is mainly a digraph, but it is
made immutable by overriding certain mutating methods. At the end of the
day, it would be better to keep the class `Quiver`, but perhaps using
`UniqueRepresentation` (because this yields a fast hash) rather than a
`UniqueFactory`.
Still, I think the code should be split up into smaller pieces, and there
should be a proper parent for "quiver-the-associative-magma", called
`FreeSmallCategory` (which for now should just be a Parent, but not
inherit from Category) and turning `QuiverPath` into a proper element (and
I still don't see why it should be a `UniqueRepresentation`).
I removed the dependency on "immutable graphs" that I had introduced.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:42>
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?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
