Hi Anne,
I just had another idea. The k-bounded subspace is sort of an algebra if
you increase the value of k. Maybe it should automatically put it in the
larger k'-bounded space.
I completely forgot about this rule that s_\lambda^{(k)}*s_\mu^{(ell)} is
in the (k+\ell)-bounded subspace. I can even tell you what the minimal
value of r is for which it is in the r-bounded subspace. I don't think it
should automatically put it in the minimal r-bounded space, but it seems
like a good idea that the product on the k-bounded space * an element in
the ell-bounded space should have a result which is in the (k+\ell)-bounded
space (don't raise an error if you don't have to).
If for f and g in Sym, if r = max {\lambda_1 : lambda in
support(s(g[(1-t)X]*f[(1-t)X]) } then f*g will be in the r-bounded subspace.
FYI, in case you didn't notice from what I just wrote, I just learned
something... I know why Mark Haiman said that was a conjecture and I can
track down its origin.
-Mike
On Sunday, 17 June 2012 03:10:17 UTC-4, Nicolas M. Thiery wrote:
>
> On Fri, Jun 15, 2012 at 11:19:54PM -0700, Anne Schilling wrote:
> > It think Mike found a good solution to my problem. Just add an extra
> line
> >
> > sage: Sym.rename()
> >
> > which changes the name back to its original.
>
> That works indeed. The other approach I used elsewhere in this file
> was to use a different base ring, like ZZ, for my examples. See
> e.g. the doctests of inject_shorthands in sf.py.
>
> Cheers,
> Nicolas
> --
> Nicolas M. Thi�ry "Isil" <nthi...@users.sf.net>
> http://Nicolas.Thiery.name/
>
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