Sorry for following up on my own mail...
Martin Rubey <[EMAIL PROTECTED]> writes:
> -- Idea 2
> ---------------------------------------------------------------------
>
> Similar to the current approach in AC of computing cycle index series via, it
> might be possible to compute only certain coefficients of the cycle index
> series.
So, I tried the easiest non-trivial example, namely that of Times:
We'd have
[x^\sigma] Z_{f*g} = \sum_{\tau <= \sigma} [x^\tau] Z_f [x^{\sigma-\tau}] Z_g
where
* \sigma is a cycle type
* x^\sigma = x1^{\sigma_1} x2^{\sigma_2} ...
* [x^\sigma] Z_f denotes the coefficient in Z_f
* \tau <= \sigma is to be understood componentwise.
I believe that this would imply a significant speedup in functorialCompose.
Ralf, don't you do something like this internally anyway, in order to obtain
the product of cycle index series? (Well, it doesn't seem so. Maybe that's a
point for having multivariate series...) In this case, it would only be a
matter of refactoring code.
Martin
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