On 22 August 2014 14:51, Ralf Hemmecke <[email protected]> wrote: > On 08/22/2014 08:36 PM, Bill Page wrote: >> How could this be made easier? > > Good question. > Answer: Teaching people with lots of examples to get the general idea of > how to construct the actual domain.
Your example is very good -- for a SPAD programmer. But I think it is completely unrealistic to believe that someone familiar with just the FriCAS interpreter would go to this kind of trouble. The interpreter expected to do most of that for you, and it does it in a large number of cases. But the types here are not "user-friendly". > Yes, that actually involves a bit of thinking on the side of the user, > even though (like in this) case, one only wants to have a multivariate > power series. Too much. Most people would not do this. > Nevertheless, there is no such thing as THE multivariate power series. I disagree. I think most people would have no trouble describing what they mean by a multivariate power series. > > The result that FriCAS prints for > > x:=taylor 'x > y:=taylor 'y > sinh(x)*cosh(y) > > is actually also OK. If by "OK", you mean "technically correct" then I can sort of accept that, but it does not seem "mathematically correct" to me. If you think it is the latter, then could you explain? Do you know some way to convert this result to what Maple produces? > But it is in Q[[x]][[y]], i.e. power series in y > with coefficients being power series in x. FriCAS gives you, what you > have asked for What makes you (and the interpreter) think that is what I asked for? > and it is even "smart" to construct a common domain where > x an y both live. I think the interpreter's solution is essentially a "no-brainer", i.e. trivial, and not useful. The problem perhaps, is that there is no % * % operation in the Univariate domain. If there was such an operation, i.e. (Univariate,Univariate)->Multivariate, then maybe the interpreter would have choosen that. But as far as I can see, this operation would not be trivial. > > Maple obviously chooses (more or less) by default the approach that I've > put on the axiom-wiki, only that it hides the nasty details. I don't think so. Maple has no types so it is not possible to construct the kind of trivial solution given by the interpreter. > > So I guess, one could convince the Interpreter to be a bit "smarter". > But since that is quite a fuzzy thing to achieve (everyone wants > something else), I would tend to leave it as it is until we have better > ideas to simplify how users do things in FriCAS. I was not thinking of any sort of general solution to making the interpreter smarter - just what might be done to make the construction of multivariate power series easier. For example, there is a significant difference in the "user interface" between the Polynomial domain and the GeneralDistributedMultivariatePolynomial domain. The first one is friendly to the interpreter, the second one might only be interesting or necessary for a SPAD programmer. > > But try to get Maple to give you the result in Q[[x]][[y]]. > Only after you have done this, I will provide you with a number n and > ask you for the coeffient of y^n. As far as I know this is not possible and also not interesting. > >> I am in favour also of generalizing this for other series (where possible). > > Can you clarify, what exactly you mean by that? > I mean multivariate series other than Taylor series. Bill. -- 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.
