>> On the other hand, you can do this:
>>
>> sage: W = WeylGroup("B3",prefix="s")
>> sage: [s1,s2,s3]=W.simple_reflections()
>>
>> Then you do things like this:
>>
>> sage: (s1*s2*s3)^4
>> s3*s2*s3*s1*s2*s1
>> sage: (s1*s2*s3).order()
>> 6
>
> Nice. We will want other representations as well (permutation
> representation, compact reduced word, ...). So this calls for some
> option like:
>
> sage: W = WeylGroup("B3", element_print_style = "reduced_word")
>
> Customizing the way the elements of a given parent are printed is a
> feature that we need in many other situations. So we want a standard
> user interface. I remember David Roe mentioning a couple months ago he
> had done something like this for some parent of his but I did not find
> back his e-mail. Pointers anyone?
>
> Call for votes / suggestions: what option name should we use?
>
> - element_print?
> - element_print_style? (this is long)?
> - element_repr? (this is not only about repr, but also latex/...)
>
> In practice, it will also be useful to have a method allowing for
> customizing this after the parent's creation, with a consistent name:
>
> sage: P = MyParent(...)
> sage: P.set_element_print_style()
For crystals, we used this convention:
C = CrystalOfLetters(['E',6], element_print_style = 'compact')
> It would feel more natural to me to set this as an option of the KL
> methods. Or would this be too heavy notation wise? An alternative
> approach would be to add a separate parent modeling the set of all KL
> polynomials:
>
> sage: W = WeylGroup("A3")
> sage: KL = KazhdanLusztigPolynomials(W, q = ...) (or
> W.kazhdan_luztig_polynomials(q))
> sage: KL.P(u,v)
> ...
>
> That definitely would make sense if this set has some useful algebraic
> structure; but I am too much of an ignorant in the subject to have any
> point of view.
How about something similar to k-Schur functions?
sage: ks3 = kSchurFunctions(QQ, 3)
sage: ks3.base_ring()
Univariate Polynomial Ring in t over Rational Field
sage: ks3.t
t
sage: ks3 = kSchurFunctions(QQ, 3, 1)
sage: ks3.base_ring()
Rational Field
Best wishes,
Anne
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