#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 |
-------------------------------------+-------------------------------------
Comment (by SimonKing):
If I understood correctly, the develop branch should only be explicitly
merged if there is a merge conflict (which is not the case here).
Could you elaborate on
{{{
#!diff
@@ -488,9 +490,16 @@ class PathAlgebra(CombinatorialFreeModule):
sage: A = P.algebra(GF(7))
sage: A.homogeneous_component(2)
Free module spanned by [a*c, b*d] over Finite Field of size 7
- """
- basis = [p for p in self._basis_keys if len(p) == n]
+ sage: D = DiGraph({1: {2: 'a'}, 2: {3: 'b'}, 3: {1: 'c'}})
+ sage: P = D.path_semigroup()
+ sage: A = P.algebra(ZZ)
+ sage: A.homogeneous_component(3)
+ Free module spanned by [a*b*c, b*c*a, c*a*b] over Integer
Ring
+ """
+ basis = []
+ for v in self._semigroup._quiver:
+
basis.extend(self._semigroup.iter_paths_by_length_and_startpoint(n, v))
M = CombinatorialFreeModule(self._base, basis, prefix='',
bracket=False)
M._name = "Free module spanned by {0}".format(basis)
return M
}}}
, please?
The text "In addition, the free algebra of a subquiver coerces into the
algebra" was a mistake. It was supposed to be "the free small category",
but since it was wrongly written "free algebra", I did not search-replace
it into "In addition, the path semigroup of a subquiver coerces into the
algebra.
I am now preparing a new commit changing this paragraph. In the meantime,
please tell what was wrong with the homogeneous components.
--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:197>
Sage <http://www.sagemath.org>
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