implementation of the cluster complex

[stumpc5]

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.

Depends on #20111
Depends on #20027

CC: @tscrim @stumpc5

Component: combinatorics

Keywords: cluster complex

Author: Christian Stump, Frédéric Chapoton

Branch/Commit: 3c7d5ae

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/10819

[fchapoton]

comment:1

some comments :

there is a typo in "facet" at the beginning.

The examples are wrong, because they call "associahedron" which has nothing to do with the simplicial complex.

There is a "tba" in the examples section, that should be removed or replaced by a true example

You should include serious tests, like the computation of the homology of an example.

[stumpc5]

Description changed:

--- 
+++ 
@@ -1,6 +1,4 @@
 The patch contains an implementation of the cluster complex for finite types.
-
-Can only applied after the cluster algebra and quiver package is installed. This contains tickets #10347, #10349, #10538, #10527.
 
 ```
 sage: ClusterComplex(['A',3])

[stumpc5]

Dependencies: 10538,

[fchapoton]

comment:3

Apply trac_10819-cluster_complex-cs.patch

[fchapoton]

Changed dependencies from 10538, to #10538

[fchapoton]

comment:5

Hi,

1. here also, the header is not correct, you should add ticket number implementation of the cluster complex #10819.

2. this seems to be a real error, which appears several times :

AttributeError: 'sage.matrix.matrix_integer_sparse.Matrix_integer_sparse' object has no attribute 'is_skew_symmetrizable'

[stumpc5]

comment:6

Replying to @fchapoton:

1. here also, the header is not correct, you should add ticket number implementation of the cluster complex #10819.

I fixed it -- now I think I know what (not why) to do in order to pass the buildbot. Thanks!

2. this seems to be a real error, which appears several times :

There was one dependency missing, see #10298. This is like only knowing one linear extension of the ordering given by the dependencies -- so getting the dependencies is really try and error...

[fchapoton]

comment:8

Hello Christian. Here are two things that need to be corrected : 

1. type A_n is in n+3 sided polygon

2. formatting of doc is not correct in cartan_type