> 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

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