#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-5.11
Component: algebra |
Resolution:
Keywords: algebra, quiver, module, days49 |
Work issues: Add a TestSuite test
Report Upstream: N/A |
Reviewers: Simon King
Authors: Jim Stark, Simon King, Mathieu Guay-Paquet, Aladin Virmaux |
Merged in:
Dependencies: #12412, #12413 |
Stopgaps:
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Comment (by SimonKing):
The next problem uncovered by test suites is this:
{{{
sage: Q = Quiver({1:{2:['a']}, 2:{3:['b']}})
sage: A = Q.algebra(GF(7))
age: A.one()
e_1 + e_2 + e_3
sage: A.an_element()
invalid path + e_1 + 2*e_2 + 3*e_3
sage: A.an_element()*A.one()
e_1 + 2*e_2 + 3*e_3
sage: A.an_element()*A.one() == A.an_element()
False
}}}
So, that's very bad. Apparently, an invalid path summand vanishes when
multiplying, but the equality test does take them into account.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:107>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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