#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 gmoose05):
Also, in my most recent patch, I also did the following:
* I separated out the cases ['F', 4, [1,2]] and ['F', 4, [2,1]], as well
as
['G', 4, [1,3]] and ['G', 4, [3,1]] in the class
!QuiverMutationType_Irreducible.
This is in preparation for changes I will be making to the !ClusterQuiver
class. These specific changes used to be in the ticket #10538, see item
(8a) of http://trac.sagemath.org/sage_trac/ticket/10538#comment:18, but
since I was changing this patch anyway, this ticket was a more natural
place to have these changes.
Once we have finalized this ticket, I will update #10538 accordingly to
fix the impending patch conflict.
* I also added the coercions ['F',4,[2,1]] -> ['F',4,[1,2]] and
['G',2,[3,1]] -> ['G',2,[1,3]] up front in the Mutation Type Casting list
to make this separation clearer. The point is that we can think of these
four cases each as different quivers, even though the two quivers of type
F listed here are mutation-equivalent, and same for the elliptic G quivers
listed here.
Similarly, the values ['GR', [2,n]] and ['TR',1], ['TR',2] are now allowed
as inputs to !QuiverMutationType_Irreducible
* See also the discussion in comments 23-25 of #10538. I also now allow
the user to type in
{{{
sage: QuiverMutationType(['A',[0,7],1])
['D',7]
}}}
This will later allow the user to construct the cyclic quiver on
n-vertices by specifying 0 clockwise arrows in a quiver of "type affine
A". Note that such a quiver is actually of finite D type, not affine A.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10527#comment:115>
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