#10527: Implementation of quiver mutation type
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Reporter: stumpc5 | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.3
Component: combinatorics | Resolution:
Keywords: quiver mutation type days38 | Work issues:
Report Upstream: N/A | Reviewers: Hugh Thomas
Authors: Christian Stump | Merged in:
Dependencies: | Stopgaps:
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Comment (by hthomas):
Sorry for the delay. I still had a bit of mathematical review to do. I
corrected one significant error, in the calculation of duals for non-
simply-laced elliptics (though I can't claim a lot of credit for having
done so, since it was an error I had introduced myself at an
earlierstage).
Types B,2,1 and B,2,-1 are now aliases for CC,2,1 (=C,2,1) and BB,2,1
(=C,2,-1). (I.e., the affine types associated to B,2). Formerly this
produced an error.
I fiddled a little bit with phrasing in the documentation.
I made the titles referred to in the class_size method agree with the
articles being referred to.
**
There is a mention in the documentation of "class_size" that the formulas
for affine B and affine C
have been proved, but the proof is unpublished. In the code, though, it
says that the formulas are not proved. This should be corrected to be
consistent. I didn't do it myself because I wasn't completely clear which
formulas it was being claimed had been proved: affine C and its dual
(which is not affine B) or affine C and affine B (and their duals) or just
affine C and affine B.
I think I see that the elements of a class and its dual class are
naturally in bijective correspondence in acyclic types, but it's not
obvious
to me outside that setting (though that's all that matters here).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10527#comment:84>
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