#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-6.1
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):
This ticket currently adds a separate class Quiver, inheriting from
`UniqueRepresentation` and from `DiGraph`, and the main reason was the
fact that immutable graphs have been missing when Jim Stark provided the
original implementation.
But now we have immutable graphs. So, now I would prefer to remove the new
Quiver class, and instead add two methods to DiGraph, namely
- .semigroup(),that returns the (partial) semigroup formed by the paths-
with-composition, and
- .algebra(), that would be a short-cut for .semigroup().algebra()
I would not like to turn quivers into a `UniqueRepresentation`. I mean,
what's the point? `DiGraphs` are no parents, and hence the "unique parent"
mantra won't apply to them. Only the path semigroup and the path algebra
should be `UniqueParent`, but not the underlying quiver.
This is a question mainly to Nathann: Could you live with two additional
methods for `DiGraph`? I think the discussion on this ticket suggest the
answer "yes", but to be on the safe side I'm asking again...
I would like to see the following workflow for constructing a quiver
representation:
- Create a digraph (aka quiver) `Q`
- Create a path algebra `P = Q.algebra(k)` over a field `k`
- Create a representation of `P` via `P.representation(...)`.
This would avoid adding more stuff to the global namespace and is, I
think, the natural way to construct a quiver representation.
--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:152>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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