Wrong limit(x / (x + 2^x + cos(x)), x=-oo)

[pelegm]

Up to Sage 8.7 this limit returns "und" for "undefined":

sage: limit(x / (x + 2^x + cos(x)), x=-infinity)
und

while it should clearly be 1.

SymPy returns the correct result:

sage: limit(x / (x+2^x + cos(x)), x=-infinity, algorithm='sympy')
1

Reported to Maxima on 2018-08-15
as Maxima bug 3459,
fixed there
by Maxima commit 0c5c018
on 2018-08-30, fix included
in Maxima 5.42.2
to which we upgrade in #26625, merged in Sage 8.8.beta7.

In Sage >= 8.8 we get the correct value for this limit:

sage: limit(x / (x + 2^x + cos(x)), x=-infinity)
1

This ticket adds a doctest for that limit computation.

Depends on #26625

Upstream: Fixed upstream, in a later stable release.

CC: @slel

Component: calculus

Keywords: limit, maxima

Author: Samuel Lelièvre

Branch/Commit: 7f96496

Reviewer: Karl-Dieter Crisman

Issue created by migration from https://trac.sagemath.org/ticket/26060

[kcrisman]

Upstream: Reported upstream. No feedback yet.

[kcrisman]

comment:1

Apparently yes.

$ sage --maxima
<snip>
Maxima 5.41.0 http://maxima.sourceforge.net
using Lisp ECL 16.1.2
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 / (x+2^x+cos(x)),x,-inf)       ;
(%o1)                                 und

I've reported this at Maxima bug 3459.

[kcrisman]

Changed upstream from Reported upstream. No feedback yet. to Reported upstream. Developers acknowledge bug.

[kcrisman]

Changed upstream from Reported upstream. Developers acknowledge bug. to Fixed upstream, but not in a stable release.

[kcrisman]

comment:4

(That was pretty fast work!)

[slel]

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

[slel]

Description changed:

--- 
+++ 
@@ -12,4 +12,10 @@
 1
 ```
 
-So is it a bug in Maxima?
+This was reported to Maxima on 2018-08-15 as
+[Maxima bug 3459](https://sourceforge.net/p/maxima/bugs/3459/),
+which was fixed by
+[Maxima commit 0c5c018](https://sourceforge.net/p/maxima/code/ci/0c5c0187338060761746fbd0821ce5f28b3245cd/)
+on 2018-08-30, and the fix is included in
+[Maxima 5.42.2](https://sourceforge.net/p/maxima/code/ci/master/tree/ChangeLog-5.42.md)
+to which we will upgrade in #26625.

[slel]

Dependencies: #26625

[slel]

comment:5

After the upgrade to Maxima 5.42.2 in #26625, we should add a doctest here.