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.

[chapoton]

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.

[chapoton]

Apply trac_10819-cluster_complex-cs.patch

[chapoton]

Hi,

1) here also, the header is not correct, you should add ticket number #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]

Replying to chapoton:

1) here also, the header is not correct, you should add ticket number #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...

[chapoton]

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

[stumpc5]

Replying to chapoton:

I really appreciate that you do some progress on these patches, thanks!

I think I will reimplement this patch using subword complexes rather than the cluster implementation. This will be much faster, and I don't expect that the cluster package will become part of main sage soon (see the dependency above). On the other hand, the subword complexes depend on my new implementation of finite reflection groups (#11187) which depends on the implementation of the universal cyclotomic field (#8327), so it will also be unlikely that it will get positively reviewed soon (and I see that all of them have rejects in the newest versions, so it will be an even longer way).

1) type A_n is in n+3 sided polygon 2) formatting of doc is not correct in cartan_type

I will update the patch fixing these issues.

Best, Christian

[stumpc5]

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.

[davidloeffler]

Applying this and its dependencies to 5.0.beta11 results in a Sage install that won't start up, and hence fails every doctest in the library -- see patchbot logs.

[stumpc5]

Replying to davidloeffler:

Applying this and its dependencies to 5.0.beta11 results in a Sage install that won't start up, and hence fails every doctest in the library -- see patchbot logs.

Thanks for looking at it - for now, I would prefer if we postpone this patch, since I want to make some further improvements here.

Best, Christian