Jean,
Ok, I will implement the method at the level of
Coxeter groups and use reflections.
For Weyl groups I will put in a method that
converts reflections to positive (co)roots.
Concerning the numbering of reflections:
For infinite Coxeter groups (including affine Weyl groups,
which I use a lot
Just a remark.
The list of inversions, in my view, should preferably be a list of
reflections (which does not need the existence of roots and makes sense for
abstract Coxeter groups).
That is, for w=s_1...s_n, the list of right inversions is the list
s_n, s_n s_{n-1} s_n, ... , s_
Nicolas,
>> 1. I want to have a version of bruhat_lower_covers
>> and bruhat_upper_covers which returns pairs
>> (weyl_group_element, coroot) where the coroot
>> tells you which reflection you used.
>
> Ok; then the output would probably be a dictionary
>
> {root: group_element}
Why is this p
On Fri, Mar 23, 2012 at 09:09:23AM -0400, msh...@math.vt.edu wrote:
> I can do it.
Cool.
> Can I sneak in a few other things while I'm at it?
>
> 1. I want to have a version of bruhat_lower_covers
> and bruhat_upper_covers which returns pairs
> (weyl_group_element, coroot) where the coroot
> tel
I can do it.
Can I sneak in a few other things while I'm at it?
1. I want to have a version of bruhat_lower_covers
and bruhat_upper_covers which returns pairs
(weyl_group_element, coroot) where the coroot
tells you which reflection you used.
2. A method that, given a (co)root,
returns the associ
On Fri, Mar 23, 2012 at 08:24:06AM -0400, msh...@math.vt.edu wrote:
> It is easy to get the inversion set directly from any reduced word of the
> Weyl group element.
>
> If w = s_{i_l} ... s_{i_2} s_{i_1}
>
> then the set of positive roots alpha such that w alpha is negative, is
>
> \alpha_{i_1}
It is easy to get the inversion set directly from any reduced word of the
Weyl group element.
If w = s_{i_l} ... s_{i_2} s_{i_1}
then the set of positive roots alpha such that w alpha is negative, is
\alpha_{i_1}, s_{i_1} \alpha_{i_2}, s_{i_1} s_{i_2} \alpha_{i_3},...
This produces "right inver
*
* *
* Tbilisi Mathematical Journal
*
* Special Issue *
* Symbolic computation
On Fri, Mar 23, 2012 at 03:37:11AM -0700, Frédéric Chapoton wrote:
>Here is a correct version. I am not currently able to post patches (still
>working with 4.7.1 here..)
I extracted the method from Mike's patch, and put it in
weyl_group_inversions-fc.patch. I wrote it as:
return [
Here is a correct version. I am not currently able to post patches (still
working with 4.7.1 here..)
def inversions(self):
"""
EXAMPLES::
sage: W = WeylGroup(['A',3])
sage: w = W.from_reduced_word([1,2,1])
sage: w.inversions()
[(0, 1, -1, 0, 0, 0), (1
On Fri, Mar 23, 2012 at 01:14:00AM -0700, Frédéric Chapoton wrote:
>Trying to use inversions for elements of Weyl groups, I found that it
>exists, but does not work, and is badly documented and tested. In which
>patch is this located ?
sage: w.inversions??
Tells it is in sage/
Hi Vivace,
it would be great if you worked on that. some of it has already be
done in the patch trac_11571_catalan_objects-nm.patch
the files are in sage/combinat/catalan
it has been written by Nevena Milojkovic who was a student in
Marne-la-Vallee. She didn't stay and is no longer working on it
Hello,
Trying to use inversions for elements of Weyl groups, I found that it
exists, but does not work, and is badly documented and tested. In which
patch is this located ?
Frederic
sage: W=WeylGroup(['A',3])
sage: w=W.from_reduced_word([1,2,1])
sage: w.inversions()
AttributeError: 'WeylGroup
Hi,
> I am totally new to this. But would very much like to work on
> http://trac.sagemath.org/sage_trac/ticket/11571
>
> Some classes for objects that can be counted by the catalan numbers.
> What would be a good place to start to look for the format i would
> need to follow.
You should
Hi
I am totally new to this. But would very much like to work on
http://trac.sagemath.org/sage_trac/ticket/11571
Some classes for objects that can be counted by the catalan numbers.
What would be a good place to start to look for the format i would
need to follow.
cheers
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