Ralf Hemmecke <[EMAIL PROTECTED]> writes: > >> 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.
Quite true. Thus, also the CIS of partitions should be implemented using this formula. I am exaggerating, I know. It does make sense to implement certain special cases more efficiently. But, I think the *main* goal in this species project (remember: species can be seen as a *combinatorial model* for formal power series, and that was the initial motivation for Joyal et al.) should be to make "decompositions" efficient. > But I somehow don't like your SpeciesExpression implementation. Me neither, since it doesn't work. ALthough, that should be fixable. > 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. I don't see how this could be done. > From the beginning we wanted a series to be the stream of coefficients *and* > a "closed" formula. We just haven't implemented it. Yes, at least I wanted that. Currently, there is no CAS that would be able to do such a thing. By the way, this idea of "bundling" power series with "expressions" is quite connected to the idea of caching individual coefficients, as "needed" for functorial composition: as you know, there are generating series that have a "nice" closed form expression, although their coefficients are not "nice". Conversely, there are also generating series that do not have a "nice" closed form, but this time the coefficients are "nice". A very good example are the Bell numbers, I think. > 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. If you want to announce a "release", please go ahead. I will certainly do some advertising next Tuesday, although I will probably use the iso-experiment branch, since people are interested in isomorphism types mainly. (Do not worry, I will add that we meanwhile have a better design...) Martin ------------------------------------------------------------------------- Take Surveys. Earn Cash. Influence the Future of IT Join SourceForge.net's Techsay panel and you'll get the chance to share your opinions on IT & business topics through brief surveys-and earn cash http://www.techsay.com/default.php?page=join.php&p=sourceforge&CID=DEVDEV _______________________________________________ Aldor-combinat-devel mailing list Aldor-combinat-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/aldor-combinat-devel
