Somehow I overlooked that email. Sorry about the delay.
Ralf Hemmecke <[EMAIL PROTECTED]> writes:
> That is a *major* rewrite. Since if you compute a series coefficient of
> degree n all coefficients for smaller degree are currently computed. If you
> don't like this then internally I would have to store whether a coefficient
> has already been computed.
I'm afraid, it's exactly what should be done. Namely, in another mail you wrote
that you currently store the CIS as
> Stream(List(Integer,PowerProduct))
>
> (because this is basically what I have now, only that I call
>
> List(Integer,PowerProduct) = Polynomial(x1,...xn,...)
At first I thought one could simply "interpret" this datastructure differently:
if a coefficient is absent in the list, it has not yet been computed. If it has
been computed, it gets added to the list, possibly with zero
coefficient. However, doing so one never knows when all coefficients of a
certain degree have been computed, so a flag would be necessary here anyway, I
guess. Unless one checks that all possible monomials are there, but that
doesn't feel like the right thing to do...
> > -- Idea 1
> > ---------------------------------------------------------------------
> > A possible approach to do that *might* also yield a brute force approach of
> > generating isotypes. I'll give an example:
> > To compute the coefficient of x3^2/aut(0,0,2) in Z_f, we generate a
> > permutation
> > of cycle type (0,0,2). Any permutation will do, so we take (1 2 3) (4 5 6).
> > Now
> > we have to find all f-structures on {1,2,3,4,5,6} that are fixed points
> > under
> > this permutation. In the present case (f = Subset), we obtain
> > {}, {1 2 3}, {4 5 6}, {1 2 3 4 5 6}
> > (More thinking is needed to see *how* to obtain these fixed points...)
> > So the coefficient we were looking for equals 4.
>
> You think the computation of number of fixed points is easier? I don't see
> that.
Me neither. It was just an idea.
Martin
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