implementation of the cluster complex #10819

stumpc5 · 2011-02-21T22:33:33Z

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

The text was updated successfully, but these errors were encountered:

fchapoton · 2011-06-08T15:18:52Z

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 · 2011-06-08T20:56:44Z

Dependencies: 10538,

fchapoton · 2011-06-10T09:29:16Z

comment:3

Apply trac_10819-cluster_complex-cs.patch

fchapoton · 2011-06-10T09:39:39Z

Changed dependencies from 10538, to #10538

fchapoton · 2011-06-10T17:15:40Z

comment:5

Hi,

here also, the header is not correct, you should add ticket number implementation of the cluster complex #10819.
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 · 2011-06-10T17:43:18Z

comment:6

Replying to @fchapoton:

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!

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 · 2011-10-05T18:29:51Z

comment:8

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

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

stumpc5 · 2011-10-05T20:45:02Z

comment:9

Replying to @fchapoton:

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).

type A_n is in n+3 sided polygon

formatting of doc is not correct in cartan_type

I will update the patch fixing these issues.

Best, Christian

stumpc5 · 2011-10-08T12:43:59Z

comment:10

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.

loefflerd · 2012-03-30T07:35:54Z

comment:11

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 · 2012-03-30T10:27:10Z

comment:12

Replying to @loefflerd:

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

stumpc5 · 2013-01-23T17:42:49Z

comment:13

Attachment: trac_10819-cluster_complex-cs.patch.gz

stumpc5 · 2013-01-23T17:42:49Z

Changed dependencies from #10538 to #11010

sagetrac-git · 2016-03-07T14:27:17Z

Branch pushed to git repo; I updated commit sha1. New commits:

`8878fdc`	`added a few tests and docs, commented 2 methods that depend on #11187`

tscrim · 2016-03-07T14:31:25Z

comment:40

In a perfect world, I would just put it directly in a branch which depends on the branch which implements the reflection groups. However, I know that can be a hassle. So if it is just few lines, then I would say yes it is okay, but make sure to state clearly which ticket will change those lines. If they are entire methods, I'm more reluctant, but again, I'm not strictly opposed to it...

stumpc5 · 2016-03-07T14:33:40Z

comment:41

I already pushed that change, so have a look and tell me what you think concretely there...

stumpc5 · 2016-03-07T14:35:53Z

comment:42

It is the two methods

+    # the following methods only make sense for the implementation using #11187:
+
+    #def upper_cluster(self):
+    #def product_of_upper_cluster(self):

I might actually implement them in a much slower way now, so I guess that might be the way to go... (and then commenting out the possible speed improvement with #11187)

sagetrac-git · 2016-03-07T14:43:26Z

Branch pushed to git repo; I updated commit sha1. New commits:

`9f6fe10`	`added naive implementations of upper cluster and its product`

sagetrac-git · 2016-03-07T14:43:26Z

Changed commit from 8878fdc to 9f6fe10

stumpc5 · 2016-03-07T14:46:13Z

comment:44

Okay, I now use a naive implementation. But I am missing

AttributeError: 'CoxeterMatrixGroup_with_category' object has no attribute 'root_to_reflection'

Is there chance to get this method ? Otherwise, I will just delete that method needing this for now. I can then get it back later, if desired.

New commits:

`9f6fe10`	`added naive implementations of upper cluster and its product`

tscrim · 2016-03-07T14:54:52Z

comment:45

I think this is the best way to do things (at least because their implementation was simple).

Coxeter groups don't necessarily have all of the methods that Weyl groups have (since they are not tied to a particular root lattice). You should be able to use W.reflections()[beta] from #20027, and it should work as well for Weyl groups now that the behavior is consistent.

tscrim · 2016-03-07T14:55:37Z

comment:46

However, that's not to say we should not implement a method root_to_reflection for (finite) Coxeter groups.

sagetrac-git · 2016-03-07T15:10:09Z

Changed commit from 9f6fe10 to e1f49c3

sagetrac-git · 2016-03-07T15:10:09Z

Branch pushed to git repo; I updated commit sha1. New commits:

`e1f49c3`	`added product of upper cluster`

stumpc5 · 2016-03-07T15:13:03Z

Changed dependencies from #20111 to #20111, #20027

stumpc5 · 2016-03-07T15:13:03Z

New commits:

`e1f49c3`	`added product of upper cluster`

sagetrac-git · 2016-03-07T15:25:40Z

Changed commit from e1f49c3 to f1d1dff

sagetrac-git · 2016-03-07T15:25:40Z

Branch pushed to git repo; I updated commit sha1. New commits:

`90b278a`	`Reversing the family for reflections.`
`8c9b809`	`Making CoxeterGroup.reflections return a Family and some touchups.`
`2595826`	`Removing caching of CoxeterGroup.positive_roots().`
`7ed4c2a`	`Merge 7.1.beta6.`
`3c32075`	`Fixing doctest failures in the thematic tutorials.`
`35eb71c`	`Fixing some documentation and adding note to WeylGroup.reflections.`
`46565ec`	`Missed (hopefully the last) one instance of the flipped keys/values.`
`a93c402`	`Merge branch 'u/stumpc5/20027' into u/stumpc5/10819`
`e72d0a3`	`removed product of upper cluster for now`
`f1d1dff`	`product is back again, though not clear why`

stumpc5 · 2016-03-07T15:26:47Z

comment:50

(hey travis, are you in korea at the moment?)

sagetrac-git · 2016-03-07T22:24:33Z

Branch pushed to git repo; I updated commit sha1. New commits:

`28ebb5b`	`Some reviewer changes.`

sagetrac-git · 2016-03-07T22:24:33Z

Changed commit from f1d1dff to 28ebb5b

sagetrac-git · 2016-03-07T22:28:44Z

Changed commit from 28ebb5b to 3c7d5ae

sagetrac-git · 2016-03-07T22:28:44Z

Branch pushed to git repo; I updated commit sha1. New commits:

`3c7d5ae`	`Missed a trailing whitespace.`

tscrim · 2016-03-07T22:30:28Z

Reviewer: Travis Scrimshaw

tscrim · 2016-03-07T22:30:28Z

Changed author from Christian Stump to Christian Stump, Frédéric Chapoton

tscrim · 2016-03-07T22:30:28Z

comment:54

Indeed, greetings from Korea.

I pushed some changes:

I moved the description of the cluster complex to the class-level doc (instead of the module-level doc) so it can be visible from ClusterComplex?.
I updated the reference bibliographic info.
I added more tests to __classcall__ to make sure it covers all of the code paths/input formats.
I removed the verbose output from TestSuite as these can change as tests get added and it's annoying to make these trivial changes all over Sage (not that it happens that often).
Other misc tweaks.

If you agree with my changes, then you can set a positive review.

vbraun · 2016-03-09T08:29:04Z

Changed branch from public/ticket/10819 to 3c7d5ae

stumpc5 added c: combinatorics labels Feb 21, 2011

stumpc5 assigned sagetrac-sage-combinat Feb 21, 2011

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stumpc5 added the s: needs review label Jun 8, 2011

fchapoton unassigned sagetrac-sage-combinat Jun 10, 2011

stumpc5 added this to the sage-4.7.2 milestone Jun 11, 2011

fchapoton added s: needs work and removed s: needs review labels Oct 5, 2011

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stumpc5 added s: needs review and removed s: needs work labels Oct 8, 2011

loefflerd mannequin added s: needs work and removed s: needs review labels Mar 30, 2012

jdemeyer modified the milestones: sage-5.11, sage-5.12 Aug 13, 2013

stumpc5 added s: needs review and removed s: needs info labels Mar 7, 2016

stumpc5 added s: positive review and removed s: needs review labels Mar 8, 2016

vbraun removed the s: positive review label Mar 9, 2016

vbraun closed this as completed in 1802e7f Mar 9, 2016

implementation of the cluster complex #10819

implementation of the cluster complex #10819

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