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)