simple incorrect limit

[Pablo Angulo]

Sage incorrectly computes:

var('n')
l  = (3^n + (-2)^n) / (3^(n+1) + (-2)^(n+1))
l.limit(n=oo)

gives 0.

However,

var('n')
l  = (3^n + (-2.0)^n) / (3^(n+1) + (-2)^(n+1))
l.limit(n=oo)

gives the correct result 1/3, and

var('n')
assume(n,'integer')
l  = (3^n + (-2)^n) / (3^(n+1) + (-2)^(n+1))
l.limit(n=oo)

also does.

maxima also gives the value 0 to the corresponding limits, but changing (-2)\^{n by (-2.0)\}n only produce meaningless results.

[Karl-Dieter Crisman]

Did you report this upstream?

[Dima Pasechnik]

Replying to kcrisman:

Did you report this upstream?

I'd rather say: did you try this with maxima 5.28.0 ? (Sage still uses 5.26.0)

[Karl-Dieter Crisman]

Well, fair enough.

Maxima 5.28.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.55.0-abb03f9

(%i2) limit( (3^n+(-2.0)^n)/(3^(n+1)+(-2)^(n+1)),n,inf);

rat: replaced -2.0 by -2/1 = -2.0

rat: replaced -2.0 by -2/1 = -2.0

rat: replaced 3.141592653589793 by 80143857/25510582 = 3.141592653589793

rat: replaced 3.141592653589793 by 80143857/25510582 = 3.141592653589793

rat: replaced -.693147180559945 by -13614799/19642003 = -.693147180559946

rat: replaced -.693147180559945 by -13614799/19642003 = -.693147180559946

rat: replaced -.693147180559945 by -13614799/19642003 = -.693147180559946

rat: replaced -.693147180559945 by -13614799/19642003 = -.693147180559946

rat: replaced -.693147180559945 by -13614799/19642003 = -.693147180559946

rat: replaced .6931471805599453 by 13614799/19642003 = 0.693147180559946
(%o2)                                  0
(%i3) limit( (3^n+(-2)^n)/(3^(n+1)+(-2)^(n+1)),n,inf);
(%o3)                                  0

while

sage: [l.subs(n=k) for k in [1.,10.^1,10.^2,10.^4,10.^6,10.^8,10.^10]]
[0.0769230769230769, 0.343080200343806, 0.333333333333333, 0.333333333333333, 0.333333333333333, 0.333333333333333, 0.333333333333333]

[Pablo Angulo]

Karl, thanks for testing. By "report upstream": you mean to maxima? I didn't. I was puzzled that Sage and maxima behave so differently, so I chose to leave it for the expert. Should I?

[Dima Pasechnik]

Replying to pang:

Karl, thanks for testing. By "report upstream": you mean to maxima? I didn't. I was puzzled that Sage and maxima behave so differently, so I chose to leave it for the expert. Should I?

Well, 5.26.0 is an old version, and if the bug does not show itself in 5.28.0, such a report makes little sense. By the way, Karl's 5.28.0 is compiled with a different Lisp compiler, SBCL, not ECL, so it's not the end of the story. E.g. there could be a bug in ECL, and not in Maxima.

[Pablo Angulo]

Replying to dimpase:

Well, 5.26.0 is an old version, and if the bug does not show itself in 5.28.0, such a report makes little sense.

The bug does show in 5.28: it gives 0 instead of 1/3.

[Dima Pasechnik]

Replying to pang:

Replying to dimpase:

Well, 5.26.0 is an old version, and if the bug does not show itself in 5.28.0, such a report makes little sense.

The bug does show in 5.28: it gives 0 instead of 1/3.

oops, I wasn't paying enough attention :-) Then, sure, report it to upstream, by all means!

[Jeroen Demeyer]

Fixed in Maxima 5.30.0: #13973.

[Peter Bruin]

Added the example from the original report as a doctest.

[Travis Scrimshaw]

LGTM.

[Karl-Dieter Crisman]

Ah, and this branch is properly based on the Maxima update, phew :-)