limit bug: should be -Infinity, but gives +Infinity

[ddrake]

As discussed in  http://groups.google.com/group/sage-devel/browse_thread/thread/7afc9f414413906 , some limits are not evaluated correctly:

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

The last command should give -Infinity, of course, since f is a semicircle. At the other endpoint, the limit is correct (+Infinity).

[kcrisman]

As it happens, this is still a problem in Sage 4.1.x - but the problem is somewhat more subtle than just some Maxima bug, or Sage incorrectly parsing Maxima output:

(%i1) limit(-x/sqrt(1-x^2),x,1,minus);
(%o1)                                            infinity

BUT Maxima's infinity is not Sage's infinity; it is the complex infinity! If the answer is +infinity, Maxima would return 'inf'. I've asked the Maxima list about this, so we'll see what happens.

[kcrisman]

This is fixed in the latest Maxima CVS version, so whenever we upgrade again, this one will hopefully be closed.

Maxima 5.19post http://maxima.sourceforge.net
using Lisp SBCL 1.0.24
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) limit(-x/sqrt(1-x^2),x,1,minus);
(%o1)                                minf

[kcrisman]

This is now correct in Maxima 5.20.1, so it just needs a doctest once the new spkg is merged.

[kcrisman]

The patch here depends on the spkg at #7745 to work properly. It also depends on the patch there, and at #6423, but will probably still apply if someone forgot to apply them first.

[kcrisman]

Based on 4.3.alpha1

[ddrake]

The spkg and patch at #7745 fix this problem, and the doctest passes. Positive review; this can be merged as soon as #7745 is in.