On 03/15/2007 11:41 AM, Martin Rubey wrote: > 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.
What? If you look at cis$Partition then you see that I *don't* implement it as compose(cisSet, cisNonemptySet), but rather use the direct formula from BLL. > 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. We will certainly do in the future, but I think a more interesting project is the "symbolic" approach even if that doesn't help much for the general CIS since there are not so many closed forms. >> 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. How do you think I compute an approximate order for a recursively defined power series? Right, the data structure contains information about the way the series is defined. For species it is approximately the same. Building a species like A above, it knows that it is a Plus of E and C=X*B*B*B. E should know that it is a leaf, same for X. C knows that it is a product etc. etc. One just has to walk down the structure until one arrives at a leaf or at A again (then it's recursive). So to exaggerate a bit: a species *is* an expression. But perhaps we must be able to convert it to ExpressionTree. Maybe we should first think about what we want to do with that information. 1) It could be used to implement special series/symbolic expressions for series if we know the symbolic expressions of the input series. 2) It could and should be used for printing. 3) It should be used for something like the attributed grammar (see Maple combstruct). >> 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. It is amazing... one starts a little project and after a while there are too many branches one could work one. > 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. More thinking needed (at least on my side) ... >> 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. OK. Ralf ------------------------------------------------------------------------- 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
