#10819: implementation of the cluster complex
-----------------------------+----------------------------------------------
Reporter: stumpc5 | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: combinatorics | Keywords: cluster complex
Work_issues: | Upstream: N/A
Reviewer: | Author: Christian Stump
Merged: | Dependencies: #10538
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Changes (by stumpc5):
* status: needs_work => needs_review
Old description:
> The patch contains an implementation of the cluster complex for finite
> types.
>
> {{{
> sage: ClusterComplex(['A',3])
> Cluster complex of type ['A', 3] with 9 vertices and 14 facets
> }}}
>
> The vertices of the cluster complex are almost positive roots, and the
> facets maximal subsets of compatible almost positive roots. The
> implementation uses cluster variables and clusters to construct the
> cluster complex.
New description:
The patch contains an implementation of the cluster complex for finite
types.
{{{
sage: ClusterComplex(['A',3])
Cluster complex of type ['A', 3] with 9 vertices and 14 facets
}}}
The implementation depends on its realization as a subword complex.
--
Comment:
I fixed the two issues suggested by Frederic - what I do not like now is
that the vertices are not positive roots anymore, but on the other hand
the implementation is now valid for all finite Coxeter groups and also the
multi-cluster complex can be constructed.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10819#comment:10>
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