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