#14844: Implement cluster algebras with universal coefficients
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Reporter: etn40ff | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.2
Component: combinatorics | Resolution:
Keywords: cluster algebras | Merged in:
Authors: Salvatore Stella | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/ticket/14844 | 5d7bc4df616bc055a9c58906c6030975feea68de
Dependencies: | Stopgaps:
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Changes (by etn40ff):
* status: needs_info => needs_review
* changetime: 03/05/14 04:32:32 => 03/05/14 04:32:32
* time: 07/01/13 05:23:10 => 07/01/13 05:23:10
Old description:
> This is a first implementation of cluster algebras with universal
> coefficients.
>
> It is far from being optimal for several reasons. The biggest issues
> comes from an incompatibility between QuiverMutationType and CartanType:
> there is no clean way to translate one into the other. A more subtle
> issue is that CartanType does not allow to choose the ordering on simple
> roots while in a cluster algebra everything is defined up to relabeling.
> To solve these issues, in this patch, the set of positive roots is
> computed by hand. As a consequence the order in which they appear is not
> the standard one.
>
> For the overall development of sage we might consider a cleanup and
> extension of CartanType, RootSystem etc to allow Cartan matrices as
> input.
New description:
This is a first implementation of cluster algebras with universal
coefficients.
It is far from being optimal for several reasons. The biggest issues comes
from an incompatibility between QuiverMutationType and CartanType: there
is no clean way to translate one into the other. A more subtle issue is
that CartanType does not allow to choose the ordering on simple roots
while in a cluster algebra everything is defined up to relabeling.
To solve these issues, in this patch, the set of positive roots is
computed by hand. As a consequence the order in which they appear is not
the standard one.
For the overall development of sage we might consider a cleanup and
extension of CartanType, RootSystem etc to allow Cartan matrices as input.
--
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Ticket URL: <http://trac.sagemath.org/ticket/14844#comment:7>
Sage <http://www.sagemath.org>
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