Hi Nicolas,
This does not seem to work (implementing _mul_ in
KBoundedSubspaceBasis in ElementMethods. Is that the right
spot for it?
sage: Sym = SymmetricFunctions(QQ['t'])
sage: ks = Sym.kschur(3)
sage: ks[2]*ks[1]
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (980, 0))
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (980, 0))
....
Best,
Anne
On 6/19/12 1:12 PM, Nicolas M. Thiery wrote:
> 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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