Regarding special functions, I am obviously aware of the symbolic capabilities of Sage that are inherited from Maxima, which has a collection of stuff that can be dressed up one way or another. Maxima is hardly complete even with respect to the functions included, and the external list developed by DLMF includes more esoterica.
On Wednesday, September 11, 2013 12:27:25 AM UTC-7, Robert Bradshaw wrote: > > On Tue, Sep 10, 2013 at 5:24 PM, rjf <fat...@gmail.com <javascript:>> > wrote: > > > > On Tuesday, September 10, 2013 1:36:02 PM UTC-7, Eviatar wrote: > >> > >> Hello, > >> > >> I made a table of the status of special functions in Sage, based on the > >> one in the Digital Library of Mathematical Functions. I thought it > would be > >> of interest to some people here. It also links to pending patches > >> implementing or making improvements to functions in Sage. > >> > >> Eviatar > > > > > > It is kind of naive, in a discussion relevant to Sage, to talk about > > mathematical functions being > > "implemented" as a checklist. Compare DLMF to (say) the Wolfram > functions > > web site. > > > > When you say F is "implemented", does that mean numerical evaluation for > > double-precision float arguments? How about arbitrary precision? How > about > > integration of F(x) and expressions involving it? How about > derivatives? > > How about addition formulas and relations with other functions? > > I disagree, in the (yes, specific) context of DLMF they're clearly > looking for "numerical evaluation for double-precision float > arguments" thought it's true we can (and often do) provide much more. > This in itself could be summarized by a table. > > Here I quite disagree back, unless you mean a vastly superior kind of table than a "check list". For example just for the numerical treatment... what kind of error bounds are being offered? relative or absolute error? what ranges? what treatment for (say) overflow or evaluation at a singular point like log(0)? If you want to put in a table "much more" you are opening up a whole can of worms requiring diagrams for branch cuts, correct treatment of assumptions like simplification for "positive integer N" etc, sets of transformations like: (e.g. trig funcs) do you implement half-angle formulas, complex exponential form, ways of representing ALL the solutions of exp(x)=-1, etc. It seems to me that to address complex analysis, essential to special functions, it is inadequate to essentially start with algebra and try to make it up by patch upon patch. But go ahead. Sage would not be the first to try it. Probably not even the 4th. I mentioned the Wolfram functions web site not as a solution to the problem, but as an indication of what is included as part of the problem . RJF -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
