Maxima limit() regression

[rws]

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

[kcrisman]

Upstream ​here.

[mkoeppe]

Seems fixed in 9.2.beta10 - 0 is returned

[mkoeppe]

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

[kcrisman]

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.

[chapoton]

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]

Hmm, that is interesting. Maxima returns a nounform 'limit((sqrt(n)+1)^n*(sqrt(n+1)+1)^((-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]

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)

[chapoton]

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]

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?

[chapoton]

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

[mkoeppe]

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

[kcrisman]

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