Hmm, interesting. So the sorts of issues I imagined, don't in fact occur. Thanks for the response.
Looking forward to seeing what you get done over the summer! Bill. On Jun 7, 3:05 pm, Fredrik Johansson <fredrik.johans...@gmail.com> wrote: > On Mon, Jun 7, 2010 at 3:46 PM, Bill Hart <goodwillh...@googlemail.com>wrote: > > > > > > > Hi Fredrik, > > > Congratulations. That looks fantastic. > > > I see you now even have elliptic functions! > > > Can I ask you a question. I haven't been following your blog (but > > should have). Perhaps you can point me to a post if you already deal > > with this somewhere. However, I am interested to know how you deal > > with computation of transcendental functions in general. I presume you > > make use of power series expansions for some of them. > > > Do you ever have the situation where you have to multiply, or > > exponentiate power series, etc? If so, how do you deal with the > > accuracy issues in that case? My knowledge of such things is woefully > > inadequate. > > > Bill. > > Hi Bill, > > Indeed, most functions are computed from power series. Unfortunately, there > isn't much manipulation of power series as such going on (coefficients for > special functions are generally known explicitly, or at least have explicit > recurrence formulas). > > Accuracy is an issue for evaluation, of course. As far as I know, the only > way to insure accuracy short of using exact arithmetic is to track the > errors of operations using either interval arithmetic or significance > arithmetic (rigorous or heuristic). > > Fredrik -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
