>> http://axiom-wiki.newsynthesis.org/TaylorSeries
> I think that currently MultivariateTaylorSeriesCategory is > deliberatly incomplete. Really? But that makes it somewhat useless. > Namely in practice one needs some term ordering and for mutivariate > series there is no single distinguished order. Right. But look into the representation. In fact, SparseMultivariateTaylorSeries is as stream of things that are given as the third parameter P (SparseMultivariatePolynomial in my case). So there is a structure, that SMTS is in fact a univariate series of homogeneous multivariate polynomials. What "homogenous" means could be up to the type P itself. So, maybe in SMTS we could have a function smts(s: Stream P): % == ... where the input s is required to be a stream of homogeneous elements of P of degree 0, 1, 2, 3, etc. or (equivalently) smts(f: NonNegativeInteger -> P): % == ... That would (at least) remove the need for "pretend" and would be easy to understand. It wouldn't probably cover all possible term orders, but certainly all the ones that SMTS covers now. > We could add 'coefficients' and 'series' function to SMTS. You probably mean by 'series' what I denoted by 'smts'. Yes, I would be in favour of such 'series' construction. > Or maybe have 'addiag' defined on series level. Possible, but also that requires some concept of (total) degree, so that the result can nicely be interpreted as a multivariate series. I think direct construction via a stream of homogeneous elements of the third parameter of SMTS would be preferrable. I somehow have the feeling, that was also the intention by the original author(s), because otherwise one could have hardcoded the third parameter inside the domain and only offer two parameters to the user. Ralf -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
