On Mon, Jun 7, 2010 at 3:46 PM, Bill Hart <[email protected]>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 [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
