#10527: Implementation of quiver mutation type
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Reporter: stumpc5 | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: combinatorics | Resolution:
Keywords: quiver mutation type days38 | Work issues:
Report Upstream: N/A | Reviewers: Hugh Thomas
Authors: Christian Stump | Merged in:
Dependencies: #10349 | Stopgaps:
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Comment (by stumpc5):
> I think the right thing to do is to implement a !CartanType for general
root data -- the general version would probably mainly know about its
Cartan matrix, for starters, but eventually you'd want it to know about
the associated Weyl group, for example.
Hi Hugh --
I recently implemented a !CartanMatrix (available in the patch on
reflection groups). I now added a patch
{{{
trac_10527-quiver_mutation_type-ht.patch
trac_???-cartan_matrix_for_quiver_mutation_type-cs.patch
}}}
and now, we have the following behaviour:
{{{
sage: mt = QuiverMutationType(['A',3])
sage: C = mt.cartan_matrix()
sage: G = C.reflection_group()
sage: G.cardinality()
24
sage: mt = QuiverMutationType(['GR',(10,3)])
sage: C = mt.cartan_matrix()
sage: G = C.reflection_group()
sage: G.cardinality()
+Infinity
}}}
Sweet, he? Beside that, the class !CartanMatrix is not yet very advanced,
and several important decisions are still to be made (e.g., how should
!CartanMatrix, !CartanType, !RootSystem, !RootSpace, and so on,
interact?), but that's a different topic.
How do you think to change the organization of the methods by using
!CartanMatrix (or !CartanType)?
Best, Christian
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10527#comment:51>
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