A wrong (easy) limit

[sagetrac-jvarona]

If we define f(n)=2+1/factorial(n) the answer of sage for limit(1/f(n),n=oo) is 1, that is clearly wrong. However, limit(f(n),n=oo) gives the answer 2, that is correct.

I have seen this problem in (at least) sage 4.6 and sage 4.6.2, in several kind of computers.

Depends on #12094

Upstream: Fixed upstream, in a later stable release.

CC: @orlitzky

Component: calculus

Author: Michael Orlitzky

Reviewer: Aly Deines

Merged: sage-5.0.beta3

Issue created by migration from https://trac.sagemath.org/ticket/10868

[kcrisman]

Changed author from jvarona to none

[kcrisman]

Upstream: Reported upstream. Little or no feedback.

[kcrisman]

comment:1

This is in Maxima.

sage: maxima_console()
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/SB-BSD-SOCKETS.fas"
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/SOCKETS.fas"
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/DEFSYSTEM.fas"
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/cmp.fas"
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/sysfun.lsp"
Maxima 5.22.1 http://maxima.sourceforge.net
using Lisp ECL 10.4.1
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.
(%i3) limit(2+1/factorial(n),n,inf);
(%o3)                                  2
(%i4) limit(1/(2+1/factorial(n)),n,inf);
(%o4)                                  1

This is still present in the latest Maxima. See this report.

[kcrisman]

comment:2

This report suggests it is fixed in the latest upstream. This would need a patch to verify, once we would update Maxima to that release.

[kcrisman]

Changed upstream from Reported upstream. Little or no feedback. to Fixed upstream, but not in a stable release.

[orlitzky]

Dependencies: #12094

[orlitzky]

Changed upstream from Fixed upstream, but not in a stable release. to Fixed upstream, in a later stable release.

[orlitzky]

comment:3

This is fixed in stable maxima 5.24.0:

sage: f(n)=2+1/factorial(n)
sage: limit(1/f(n),n=oo)
1/2
sage: limit(f(n),n=oo)
2
sage: maxima.version()
'5.24.0'

[orlitzky]

Attachment: sage-trac_10868.patch.gz

Add a doctest for this result. Apply on top of #11483 and #11591 to avoid fuzz.

[orlitzky]

Author: Michael Orlitzky

[orlitzky]

comment:4

Maxima 5.24 has a positive review now, so here's a doctest. The file maxima_lib.py gets some new doctests in #11483 and #11591 so to avoid fuzz, apply on top of those (we don't require either of them for the result, though).

[adeines]

Reviewer: Aly Deines

[jdemeyer]

Merged: sage-5.0.beta3