I've uploaded a new version of the patch for Trac 10744:
http://trac.sagemath.org/sage_trac/ticket/10744

See the comments there for changes. I've also uploaded images produced
using the `plot` method if you are curious what the plots look like.
These are at the following URLs:

https://bluedrive.uwstout.edu/users/facultystaff/jonesbe/research/sage/ex_1.png
https://bluedrive.uwstout.edu/users/facultystaff/jonesbe/research/sage/ex_2.png
https://bluedrive.uwstout.edu/users/facultystaff/jonesbe/research/sage/ex_3.png
https://bluedrive.uwstout.edu/users/facultystaff/jonesbe/research/sage/ex_4.png

---

Anne-

Thanks. That's a good question. In principle I think it should be easy
-- we would just need a special case in the _demazure helper method to
deal with the simple root indexed by zero. The weight lattice and Weyl
group are implemented for affine Cartan types, but the
WeylCharacterRing, and hence WeightRing, are not. I don't see why we
couldn't decouple WeightRing from WeylCharacterRing a little by
providing an alternate constructor.

Dan can probably say more since he wrote that code.

--
Benjamin Jones


On Feb 5, 1:41 am, Anne Schilling <[email protected]> wrote:
> Hi Benjamin,
>
> This is very nice! Thanks for implementing it. One question I have is
> how easy it would be to upgrade this to also compute affine Demazure
> characters. I suppose WeylCharacterRing does not yet exist in this
> setting, right?
>
> Best wishes,
>
> Anne
>
> On 2/4/11 1:30 PM, BFJ wrote:
>
>
>
>
>
>
>
> > Hi all,
>
> > This is now Trac #10744 (http://trac.sagemath.org/sage_trac/ticket/
> > 10744). I've uploaded a patch to provide demazure_character (based on
> > Daniel Bump's patch above), plot, and degree for the WeightRingElement
> > class.
>
> > Comments, suggestions, and kibitzing are appreciated!
>
> > --
> > Benjamin Jones
> > University of Wisconsin-Stout
> > [email protected]
> > [email protected]
>
> > On Feb 1, 1:54 pm, BFJ<[email protected]>  wrote:
> >> Ok, great. I'll start working on a patch and reply here again when
> >> it's on the trac server.
>
> >> --
> >> Benjamin Jones
> >> University of Wisconsin-Stout
> >> [email protected]
> >> [email protected]
>
> >> On Jan 31, 2:17 pm, Daniel Bump<[email protected]>  wrote:
>
> >>>> I don't know if it's helpful to post so much code, but here is my code
> >>>> for the Demazure character and rank 2 plotting. The Demazure character
> >>>> code contains the same idea as bump's code.
>
> >>> There were a couple of mistakes in the code snippet that I posted.
>
> >>> Here is another attempt, probably correct:
>
> >>>http://match.stanford.edu/bump/patches/demazure.patch
>
> >>> After this patch you can do this:
>
> >>> sage: B2 = WeylCharacterRing("B2")
> >>> sage: b2 = WeightRing(B2)
> >>> sage: W = B2.space().weyl_group(prefix="s")
> >>> sage: [s1,s2] = W. simple_reflections()
> >>> sage: w0 = W.long_element()
> >>> sage: [b2(h).demazure(w0) for h in B2.space().fundamental_weights()]
> >>> [b2(-1,0) + b2(0,-1) + b2(0,0) + b2(0,1) + b2(1,0), b2(-1/2,-1/2) + 
> >>> b2(-1/2,1/2) + b2(1/2,-1/2) + b2(1/2,1/2)]
> >>> sage: [b2(B2(h)) == b2(h).demazure(w0) for h in 
> >>> B2.space().fundamental_weights()]
> >>> [True, True]
>
> >>>> I should add more examples and flesh out the docstrings, of course. I
> >>>> need to clean up my plotting code a bit as well.
>
> >>>> I'd be happy to start a ticket to add the following methods to
> >>>> WeightRingElement:
>
> >>> Sure, go ahead and make a ticket. If you want to work on a patch, I can 
> >>> kibbitz.
> >>> I won't work on this any more if you want to do it. (I need Demazure
> >>> characters for my own work.)
>
> >>> As for waiting for #7922, my belief is that the amount of code that we are
> >>> talking about is not so great that we cannot reimplement quickly. So we
> >>> should not wait.
>
> >>> Dan

-- 
You received this message because you are subscribed to the Google Groups 
"sage-combinat-devel" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to 
[email protected].
For more options, visit this group at 
http://groups.google.com/group/sage-combinat-devel?hl=en.

Reply via email to