#12630: Add representations of quivers and quiver algebras to sage
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Reporter: JStarx | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.10
Component: algebra | Resolution:
Keywords: algebra, quiver, module | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Jim Stark | Merged in:
Dependencies: #12412, #12413 | Stopgaps:
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Comment (by SimonKing):
From the documentation of the patch:
{{{
9 A Quiver is a directed graph used for representation
theory. In Sage a Quiver
10 is different from a directed graph in the following ways:
11
12 - The vertices of a DiGraph are arbitrary sage objects,
but the vertices of a
13 Quiver must be labeled by integers.
14
15 - DiGraphs can have cycles (paths that start and end at
the same vertex) and
16 even loops (edges whose initial and terminal vertices
are equal). In this
17 implementation a Quiver must be acyclic (and can not
have loops).
18
19 - The edges of a DiGraph are labeled with arbitrary sage
objects or None if no
20 label is specified. Each edge of a Quiver must be
labeled with a nonempty
21 string. The label cannot begin with 'e_' or contain '*'
and distinct edges
22 must have distinct labels.
23
24 - DiGraphs do not have a unique representation in Sage;
Quivers do.
}}}
All these properties could easily be enforced by using a `UniqueFactory`
that returns plain immutable digraphs. Given the above specification, I
really don't see the need to create `Quiver_generic` as a sub-class of
`DiGraph`.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:32>
Sage <http://www.sagemath.org>
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