> 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/...)
We use 'style' in WeylCharacterRing elements. (Thus style="coroots".)
> Yep. I would be perfectly fine just putting a systematic cache on all
> those methods. At least for the moment. If someone comes up with a use
> case where caching actually hurts, then it will still be time to go
> the extra mile.
The harm is that it creates potentially huge RAM-eating dictionaries.
There is optional caching in WeylCharacter rings. See Michael Abshoff's
comments in this message:
http://groups.google.com/group/sage-combinat-devel/msg/f26b726871ab0796?hl=en
and the thread.
> 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.
So KazhdanLusztigPolynomials would be a new class, and R,P
would be methods of it. I think I agree.
I'll look again at unique_representation and address your
other comments later.
Dan
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