Dan Drake wrote: > sage: f = sqrt(1-x^2) > sage: g = diff(f, x); g > -x/sqrt(1 - x^2) > sage: limit(g, x=1, dir='below') > +Infinity > > It's a semicircle, so the derivative should go to negative infinity on > the right side.
Hmm. Did you mean the left side? I'm probably missing something. There are 2 things going on here. (1) Maxima (current cvs version) has trouble with this problem. (2) Maxima returns the symbol infinity for this limit (and others) which represents complex infinity, as opposed to real positive or negative infinity, which are inf and minf, respectively. About (1), (1a) limit (-x/sqrt(1 - x^2), x, 1); => limit(...) (just rephrased) (1b) limit (-x/sqrt(1 - x^2), x, 1, minus); => infinity (1c) limit (-x/sqrt(1 - x^2), x, 1, plus); => limit(...) (just rephrased) (1a) seems OK although in similar situations sometimes limit returns und (undefined). I guess (1b) isn't incorrect but it could be more precise (namely minf). As for (1c) I would expect infinity. I hope someone from the Maxima project can weigh in on the correct results to be expected from 1a, 1b, and 1c. About (2), if Sage's Maxima interface doesn't distinguish infinity from inf, probably it should. Maybe it does already. If someone can post a bug report to the Maxima bug tracker for this problem, that would be great. HTH Robert Dodier --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
