#14261: Iwahori-Hecke algebra with several bases
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Reporter: brant | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: Iwahori Hecke | Merged in:
algebra | Reviewers: Andrew Mathas, Brant
Authors: Brant Jones, | Jones, Travis Scrimshaw
Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: #13735 #14014 |
#14678 #14516 |
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Comment (by andrew.mathas):
'''How should we print elements of the Hecke algebra?'''
Currently the Hecke algebra elements in different bases are printed in
different ways:
{{{
sage: R<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra(['A',2], v**2)
sage: H.T()[1,2,1]
T1*T2*T1
sage: H.C()[1,2,1]
C[s1*s2*s1]
}}}
I think that the default printing for the different bases should be
consistent. We clearly cannot print the KL-bases as `C1*C2*C1` as this is
not equal to `C[1,2,1]`.
I also think that it is good to have the (default) output being valid
input so that you can cut and paste it directly back into sage. For these
reasons I would prefer:
{{{
sage: H.T()[1,2,1]
T[1,2,1]
sage: H.C()[1,2,1]
C[1,2,1]
}}}
I also think this is more readable than the current output because it is
easier to identify the permutation, as a Coxeter word, which indexes each
basis element. Another advanatage is that it simplifies the code.
Please let me know what you think.
--
Ticket URL: <http://trac.sagemath.org/ticket/14261#comment:45>
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