Maxima limit() regression

[rwst]

var('n'); u = (1+sqrt(n))^(-n); limit(u(n=n+1)/u,n=infinity): this was reported in http://ask.sagemath.org/question/25647/cannot-calculate-limit/ and worked at least in Sage-4.7

Upstream: Reported upstream. Developers acknowledge bug.

CC: @sagetrac-tmonteil

Component: calculus

Keywords: limit

Issue created by migration from https://trac.sagemath.org/ticket/17709

[kcrisman]

comment:1

Upstream here.

[kcrisman]

Upstream: Reported upstream. No feedback yet.

[mkoeppe]

comment:2

Seems fixed in 9.2.beta10 - 0 is returned

[mkoeppe]

comment:3

(The upstream bug in maxima is still present; it seems we are using something else for computing the limit.)

[kcrisman]

comment:4

My guess is that we now, as with integration, go through several "algorithms"/programs to get limits.

I guess technically this is still a Sage bug, then, if that is true and one then specifies the algorithm? Otherwise I'd at the very least add a doctest.

[fchapoton]

Changed keywords from none to limit

[fchapoton]

comment:6

Replying to @kcrisman:

My guess is that we now, as with integration, go through several "algorithms"/programs to get limits.

Not yet, as nobody did it..

I guess technically this is still a Sage bug, then, if that is true and one then specifies the algorithm? Otherwise I'd at the very least add a doctest.

[kcrisman]

comment:7

Hmm, that is interesting. Maxima returns a nounform 'limit((sqrt(n)+1)<sup>n*(sqrt(n+1)+1)</sup>((-n)-1),n,inf) inside of Sage 9.2.beta1

Maxima 5.42.2 http://maxima.sourceforge.net
using Lisp ECL 16.1.2

But I don't have the most recent Maxima. Can you test this?

sage -maxima
<messages about Maxima 5.44, hopefully>
(%i1) limit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf);

If you get zero then they fixed it, and then a doctest suffices. Otherwise we may have something really weird going on in our own processing, though I don't see what would have changed - Frédéric is right about that, as far as I can tell.

[kcrisman]

comment:8

Can you also test this in maxima_calculus in the most recent Sage rc? Upstream says it is not fixed. I still get

sage: maxima_calculus("limit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf)")
'limit((sqrt(n)+1)^n*(sqrt(n+1)+1)^((-n)-1),n,inf)

[fchapoton]

comment:9

I get

sage: banner()                                                                  
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.2.rc2, Release Date: 2020-10-12                 │
│ Using Python 3.8.5. Type "help()" for help.                        │
└────────────────────────────────────────────────────────────────────┘
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Warning: this is a prerelease version, and it may be unstable.     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: maxima_calculus("limit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf)")     
'limit((sqrt(n)+1)^n*(sqrt(n+1)+1)^((-n)-1),n,inf)

EDIT:
with

Maxima 5.44.0 http://maxima.sourceforge.net
using Lisp ECL 20.4.24

[kcrisman]

comment:10

That is really weird. I really can't find any branch of the code that should just avoid Maxima completely without adding an algorithm. Can you confirm Matthias' contention that

var('n'); u = (1+sqrt(n))^(-n); limit(u(n=n+1)/u,n=infinity)

now returns zero in that rc version?

[fchapoton]

comment:11

no, this does not return 0. Maybe Matthias was looking at something else ?

[mkoeppe]

comment:12

I cannot confirm my claim from comment 2 above either. I don't know what I may have tested there.

[kcrisman]

comment:13

Ok, thanks - setting back settings then. At least now Maxima has acknowledged bug :-)

[kcrisman]

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

[mkoeppe]

comment:14

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[fchapoton]

comment:18

in 9.7.b1

sage: limit(u(n=n+1)/u,n=infinity,algorithm="sympy")
0
sage: limit(u(n=n+1)/u,n=infinity,algorithm="fricas")
0
sage: limit(u(n=n+1)/u,n=infinity,algorithm="giac")
// Giac share root-directory:/home/chapoton/sage/local/share/giac/
// Giac share root-directory:/home/chapoton/sage/local/share/giac/
Help file /home/chapoton/sage/local/share/giac/doc/fr/aide_cas not found
Added 0 synonyms
0
sage: limit(u(n=n+1)/u,n=infinity,algorithm="maxima")
limit((sqrt(n + 1) + 1)^(-n - 1)*(sqrt(n) + 1)^n, n, +Infinity)

[kcrisman]

For what it's worth, apparently this is fixed upstream in 5.47. Assuming this is true and that we have that version, adding some tests to confirm it against regressions would be all we need here, right?