Opened 9 years ago

Closed 7 years ago

#13526 closed defect (fixed)

simple incorrect limit

Reported by: pang Owned by: burcin
Priority: trivial Milestone: sage-6.3
Component: symbolics Keywords: symbolic, limit
Cc: Merged in:
Authors: Peter Bruin Reviewers: Travis Scrimshaw
Report Upstream: N/A Work issues:
Branch: 5f3154b (Commits, GitHub, GitLab) Commit: 5f3154b1ae2ce3271d614220d7320cd86adcb690
Dependencies: #13973 Stopgaps:

Status badges

Description

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.

Change History (15)

comment:1 follow-up: Changed 9 years ago by kcrisman

Did you report this upstream?

comment:2 in reply to: ↑ 1 Changed 9 years ago by dimpase

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)

comment:3 Changed 9 years ago by kcrisman

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]

comment:4 follow-up: Changed 9 years ago by 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?

comment:5 in reply to: ↑ 4 ; follow-up: Changed 9 years ago by dimpase

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.

comment:6 in reply to: ↑ 5 ; follow-up: Changed 9 years ago by 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.

comment:7 in reply to: ↑ 6 Changed 9 years ago by dimpase

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!

comment:8 Changed 8 years ago by jdemeyer

  • Milestone set to sage-5.11
  • Report Upstream changed from N/A to Fixed upstream, in a later stable release.

Fixed in Maxima 5.30.0: #13973.

comment:9 Changed 8 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:10 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:11 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:12 Changed 7 years ago by pbruin

  • Authors set to Peter Bruin
  • Branch set to u/pbruin/13526-maxima_rational_function_limit
  • Commit set to 5f3154b1ae2ce3271d614220d7320cd86adcb690
  • Dependencies set to #13973
  • Priority changed from minor to trivial
  • Report Upstream changed from Fixed upstream, in a later stable release. to N/A
  • Status changed from new to needs_review

Added the example from the original report as a doctest.

comment:13 Changed 7 years ago by tscrim

  • Reviewers set to Travis Scrimshaw
  • Status changed from needs_review to positive_review

LGTM.

comment:14 Changed 7 years ago by kcrisman

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

comment:15 Changed 7 years ago by vbraun

  • Branch changed from u/pbruin/13526-maxima_rational_function_limit to 5f3154b1ae2ce3271d614220d7320cd86adcb690
  • Resolution set to fixed
  • Status changed from positive_review to closed
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