On Tue, Jun 19, 2012 at 10:14:07AM -0700, Anne Schilling wrote:
> As I said before, I can fix the error/warning message, but I think first the
> following
> issue needs to be resolved (from a post from June 16):
>
> "For t=1 this is no problem, but for general t
> if we use as category
>
> category = GradedHopfAlgebras(R) if t == 1 else GradedCoalgebras(R)
>
> then products do not work. If in both cases we use
>
> category = GradedHopfAlgebras(R)
>
> then we get the desired behaviour:
>
> sage: Sym = SymmetricFunctions(QQ['t'])
> sage: ks = Sym.kschur(3)
> sage: ks[2]*ks[1]
> ks3[2, 1] + ks3[3]
> sage: ks[2]*ks[2]
> ---------------------------------------------------------------------------
> ValueError: s[2, 2] + s[3, 1] + s[4] is not in the image of Generic morphism:
> From: 3-Schur functions with t=t
> To: Symmetric Function Algebra over Univariate Polynomial Ring in t over
> Rational Field, Schur symmetric functions as basis
> ---------------------------------------------------------------------------
>
> But of course mathematically this is not correct, since for generic t the
> k-bounded
> subspace is not an algebra.
>
> So what should I do implementation-wise?"
>From the top of my head, it should be possible, for t!=1 to define ks
as just a coalgebra, and to define _mul_ in the element class to
return an element in Sym.
When coercion will work properly, defining that _mul_ won't be needed
anymore.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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