>> with the right implementation of cis in Subset, the test now runs in
>> reasonable time.
> Yes, that's not so surprising. However, as I said before, I do not think that
> this is the right cure.
Oh, but Subset is somehow as reasonable as Partition (which is
E\circ(E_+)) because Subset (which is E*E) is actually needed in the
definition of Times.
> In fact, it also implies that I should pursue my idea of "bundling" power
> series with "expressions".
Wasn't that our plan from the beginning? Of course, we should analyse
the grammar that builds the species in order to determine a better
formula for the series than the generic one. Another big and interesting
project, because that involves writing symbolic solvers, ie, turning the
grammar into good recursion formulas for the series.
But I somehow don't like your SpeciesExpression implementation. The
reason is simple. If a couple of species is defined by a set of
definitions like in
A(L: LabelType): CombinatorialSpecies L == (E + X*B*B*B)(L) add;
B(L: LabelType): CombinatorialSpecies L == (E + X*A*A)(L) add;
then the data structures of A and B already contain the knowledge about
the equation. One "simply" has to extract it. What I want to say is that
the domain "SpeciesExpression" is completely superfluous.
> The reason that your implementation of the CIS of
> Subset is fast is, that you do the multiplication "symbolic", albeit not using
> the capabilities of a CAS...
Hmm, unfortunately, we cannot do better at the moment, since SetSpecies
doesn't actually "know" that its series is exp(something). That's a pity
and should and must be changed in the future. I'm sure you remember that
there was a reason to make the series stuff external. From the beginning
we wanted a series to be the stream of coefficients *and* a "closed"
formula. We just haven't implemented it. But using the power of Aldor we
would just have to write a new coupled series domain that knows about
its closed form (if that is know or can be computed).
>> You see, the problem is the multiplication of species.
> I think that this is only one part of the problem. It would be really nice
> (and probably something one could "sell") to have a power series package where
> the timings of the two variants would be nearly the same...
As you said above that involves some "symbolic" stuff. So let the fun
begin. What we have done up to now was more or less setting the ground
for the hard stuff. So there is a good reason to make a first release
before we go on.
Ralf
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