#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 | f7fc2eca6347a5abbebcad50bc7abe41a73a60e2
Report Upstream: N/A | Stopgaps:
Branch: |
public/combinat/quivers |
Dependencies: #12412, #12413, |
#14806, #15491, #15623, #15810 |
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Comment (by SimonKing):
Concerning the empty quiver:
{{{
sage: Q = DiGraph().path_semigroup()
sage: Q
Partial semigroup formed by the directed paths of Digraph on 0 vertices
sage: A = Q.algebra(QQ)
sage: A
Path algebra of Digraph on 0 vertices over Rational Field
sage: A.homogeneous_component(0)
Free module spanned by [] over Rational Field
sage: A.homogeneous_component(1)
Free module spanned by [] over Rational Field
}}}
However, the attempt to construct a coercion of the path semigroup of an
empty quiver into the path algebra of a non-empty quiver fails with an
"empty set error". So, in the commit to come I'll also try to fix that
corner case.
--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:198>
Sage <http://www.sagemath.org>
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