Dear Ralf, Ralf Hemmecke <[EMAIL PROTECTED]> writes:
> > I can imagine that there is only one expansion of a implicitely given > > series t with maximal order, if the equation is of the form t = f(1, t^2, > > t^3, ...), f being a polyonomial with coefficients in N[x]. At least, > > that's pretty close to what one can currently do with series.as.nw. > > Yes, I think I was stumbling about the same problem when I wrote the > ToDo. Both series have order 0, but only one of them has non-negative > coefficients. I am not yet sure how to prove that there can only be one > series solution with maximal order and non-negative coefficients. (But I > haven't yet bothered to even think about a proof, either.) > > The problem is probably more difficult for virtual species where both series > solutions are valid. But we don't yet deal with virtual species. In fact, I don't really think it is that much of a problem by now. I just wrote a replacement for seriesSolve that actually works, although it doesn't try to be as clever. And, for the moment, it is only univariate. It takes as "defining equation" a function that transforms a Taylor series into another one, and, additionally, a list of n initial values, corresponding to the y(0), y'(0), ..., where n is the 1 plus the highest derivative. For example, for any algebraic equation it needs exactly one initial value, and I believe that y(0) determines the expansion uniquely. I guess that this approach could also be used to define (virtual) species, we would have a constructor that takes the equation plus some initial values. Of course, I don't know yet whether (as initial values) the number of structures suffice, or whether one needs the structures themselves. (Representing a virtual species as a pair of usual species) 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
