As I noted in my previous message, #13461 implements Demazure characters
in WeylCharacterRings as a replacement for the Freudenthal multiplicity
formula.
This was intended as a speedup, and it is quite effective in reducing the
time
for {{{sage -t --long weyl_characters.py}}} by a surprising factor of 2.5.
In a second patch, I implemented Demazure-Lusztig operators also as
methods of WeightRing elements. These were introduced by Lusztig in his
paper
on Equivariant K-theory and Hecke Algebras, and used by Kazhdan and Lusztig
to prove a major theorem in representation theory of p-adic groups. Later
they were
popularized by Cherednik.
I kept the two patches separate to make things easier for someone to
review. Both are posted at:
http://trac.sagemath.org/sage_trac/ticket/13461
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