Closed stumpc5 closed 8 years ago
Author: Christian Stump
Description changed:
---
+++
@@ -13,6 +13,4 @@
{(1, 2), (3, 4), (0, 4), (2, 3), (0, 1)}
-I will upload the patch as soon as the patch on Coxeter groups is ready. +Depends on Tickets #8359 and #11122.
Changed keywords from none to subword complex, simplicial complex
Description changed:
---
+++
@@ -5,12 +5,10 @@
The subword complex Delta(Q,pi) is then defined to be the simplicial complex with vertices being {0,...,n-1}, (n = len(Q), one vertex for each letter in Q) and with facets given by all (indices of) subwords Q' of Q for which Q\Q' is a reduced expression for pi.
-Depends on Tickets #8359 and #11122.
Dependencies: 11187, 11122
Changed dependencies from 11187, 11122 to #11187, #11122
Changed dependencies from #11187, #11122 to #11122
Changed dependencies from #11122 to #12774
Replying to @fchapoton:
Okay, I must confess that I tend to not finish implementations once the patch does what I want it to do...
The dependencies of this patch must (unfortunately) inherit as well the dependencies of #11122. This is to say that this patch actually relies on many things implemented in #11187.
I would be very, very glad if anyone would finally start reviewing the universal cyclotomic field, #8327 on which #11187 depends (I would first need to rebase it, and make sure that the trac version is updated to the newest version on the combinat queue).
Cheers, Christian
Changed dependencies from #12774 to #11187, #12774
Attachment: trac_11010-subword_complex-cs.patch.gz
Branch: u/chapoton/11010
The code needs to be 100% doctested. Some empty methods should be removed.
Work Issues: coverage
Changed dependencies from #11187, #12774 to #11187, #12774, #15456
Hello Christian, do you really think that this ticket depends on #11187 ?
I am tempted to ressurect this one, without waiting for the famous category-and-axiom ticket.
With not so much work, I managed to get a branch with only 19 failures.
Here is a better branch.
I am removing the dependencies to #11187, #15456 as I think they are not really needed.
There are still 16 failing doctests. Work in progress.
Changed dependencies from #11187, #12774, #15456 to #12774
Dear Frederic,
Thanks for your work on that -- I am super busy with other stuff, hopefully this will get better in about 4 weeks from now.
I am not sure if I/we should keep the construction for positive genus:
Mathematically, this has not been considered before,
it is not quite the right generalization of subword complexes as defined by Knutson-Miller. In particular, such complexes do not need to be vertex-decomposable or shellable.
we have a proper generalization which will have similar combinatorics and will capture the needed behaviour for positive genus
our paper in which I introduce these things is still on hold and we will need at least another 3-6 months before getting this into a state to make it publicly available
I should be able to quickly look at your branch during the weekend to clean things up a bit. Or do you prefer to work things out yourself?
Cheers, Christian
Branch pushed to git repo; I updated commit sha1. New commits:
8864315 | trac #11010 one more doctest passing |
Hello Christian,
I would be happy to see you come back here. The code is not very easy to understand by me alone.
The remaining issues (15 doctests) seem to be related to a strange use of roots, where Weyl group elements seem to be supposed to act on the indices of roots in the list of roots. And they do not, of course.
I will not do anything more on the ticket until next week.
Replying to @fchapoton:
Hi,
I would be happy to see you come back here. The code is not very easy to understand by me alone.
I spend some time today trying to get Sage working properly again, but I failed so far. I guess I need someone helping me to work properly with git...
error: command 'gcc' failed with exit status
, so this is my first problemI don't know how to resolve that now (and I also don't know if I tried to upgrade to the newest development version or the latest stable version).
The remaining issues (15 doctests) seem to be related to a strange use of roots, where Weyl group elements seem to be supposed to act on the indices of roots in the list of roots. And they do not, of course.
I use the CHEVIE implementation of finite reflection groups which are implemented as permutation groups on indices of roots. This speed things drastically, but it is not reall mathematically clean. Moreover, I just looked at the code, and
Hello Frederic,
I now spent some time playing with the patch.
My main concern is: I can re-implement things to work with any implementation of Coxeter groups (i.e., with the current implementations of Weyl groups and Coxeter groups). BUT: this will slow down things drastically!
So we either leave this ticket open and wait for my CHEVIE version of Coxeter groups,
Cheers, Christian
Changed branch from u/chapoton/11010 to u/stumpc5/ticket/11010
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
014fec2 | got the doctests of complex reflection group category pass |
d3198f9 | fixing a few bugs on coxeter number and fundamental invariants |
e2736f6 | added another doctest |
8db1dee | first version of adding functionality to coxeter group categories |
425ca38 | first version of coxeter groups from chevie with all tests passing! |
c0a036b | Avoid creation of _reduced_word during iteration |
405b26c | turned well-generated into an axiom |
0639665 | fixed a but with Word(reduced_word) we worked on yesterday |
28f8abd | added a test for well generated |
ab914f5 | first version of the subword complexes as of 2015 |
Changed branch from u/stumpc5/ticket/11010 to u/vpilaud/ticket/11010
Branch pushed to git repo; I updated commit sha1. New commits:
bd4f2ad | improve the subword complex, first version of plot in type B |
Vincent, please remove the c
and the html
file again from the branch since they are not supposed to be going into sage.
Branch pushed to git repo; I updated commit sha1. New commits:
f165d54 | pseudoline representation of facets of type B subword complexes, more documentation |
does not apply, needs to be rebased
Changed dependencies from #12774 to #12774, #11187
I have made a new branch, by disentangling u/vpilaud/ticket/11010 from #11187 (but sadly still depending on #11187).
It seems that all my previous work on this ticket was lost. I do not appreciate.
New commits:
bbff606 | first version of the subword complexes as of 2015 |
0aa6989 | trac #11010 full pep8 and pyflakes |
Changed branch from u/vpilaud/ticket/11010 to u/chapoton/11010
It seems that all my previous work on this ticket was lost. I do not appreciate.
I don't understand. How can work be lost on a ticket?
Sorry for having been a little rude. I was tired and angry yesterday evening.
It remains that I have done twice the same clean-up work. I think it was because the branch by Vincent was not based on my previous branch.
I would really like if this ticket would no longer depend on #11187, which has no hope to enter sage as long as it depends on gap3.
You said once that it could be possible, but with a high speed penalty. Maybe this is nevertheless the way to go.
Branch pushed to git repo; I updated commit sha1. New commits:
0468798 | trac #11010 make sure that doc builds |
As far as I can see, just one thing is needed:
reflections()
(technically nr_reflections()
, but we can just do len(self.reflections())
)We can construct this easily enough by conjugation of simple reflections:
sage: W = CoxeterGroup(['A',2])
sage: S = W.simple_reflections()
sage: I = W.index_set()
sage: R = RecursivelyEnumeratedSet(S, lambda x: [S[i]*x*S[i] for i in I if not x.has_descent(i)], structure="graded")
sage: list(R)
[
[-1 1] [ 1 0] [ 0 -1]
[ 0 1], [ 1 -1], [-1 0]
]
sage: all(x.absolute_length() for x in R)
True
The apply_simple_reflection
is already a part of Sage for Coxeter groups.
Aside - This probably deserves to be in the category of finite Coxeter groups, but there is some slight conflict with this
sage: W = WeylGroup(['A',2], prefix='s')
sage: W.reflections()
Finite family {s1*s2*s1: (1, 0, -1), s1: (1, -1, 0), s2: (0, 1, -1)}
(Trying to do this on the Weyl group on the root system seems to run forever and ctrl-C
out results in a nasty error message.)
Branch pushed to git repo; I updated commit sha1. New commits:
2d84a4b | trac #11010 little more doc |
This patch provides an implementation of the subword complex:
Fix a Coxeter system (W,S). Let Q = be a finite word in S and pi in W.
The subword complex Delta(Q,pi) is then defined to be the simplicial complex with vertices being {0,...,n-1}, (n = len(Q), one vertex for each letter in Q) and with facets given by all (indices of) subwords Q' of Q for which Q\Q' is a reduced expression for pi.
Component: combinatorics
Keywords: subword complex, simplicial complex
Author: Christian Stump
Branch/Commit:
17518c1
Reviewer: Frédéric Chapoton
Issue created by migration from https://trac.sagemath.org/ticket/11010