With a member of the community I had some discussion about using Maple for limits of sequences.

The specific task was about F:=4*sqrt(n)*sin(Pi*sqrt(4*n^2+sqrt(n))) and limit F for n --> infinity for integers, which is asserted to be Pi, see https://math.stackexchange.com/questions/2493385/find-the-limits-lim-n4-sqrtn-sin-pi-sqrt4n2-sqrtn.

For moderate size of integers n it can be 'confirmed' by numerical evaluations. Formally it is not 'obvious' at all.

However Maple answers by

limit(F, n = infinity) assuming n::posint;

                              undefined

This is 'explained' by the help about assuming/details:

"The assuming command does not place assumptions on integration or summation dummy variables in definite integrals and sums, nor in limit or product dummy variables, because all these variables already have their domain restricted by the integration, summation or product range or by the method used to compute a limit. ..."
The help continues with suggestions how to treat the situation.

Which means that the limit is taken in the Reals, not in the discrete Naturals.

A more simple example may be limit(sin(n*Pi), n = infinity) assuming n::posint which returns "-1 .. 1".

But here we go:

MultiSeries:-asympt(F, n):
simplify(%) assuming n::posint: collect(%, n); #lprint(%);
limit(%, n=infinity);

   O(1/2048*Pi^3/n^(5/2)) + Pi -1/96*Pi^3/n - 1/16*Pi/n^(3/2) + 1/30720*Pi^5/n^2

                                  Pi

As desired.

The board is going to work now with FF for me after latest updates.

NB: I got some mails advicing to delete (old) cookies for Mapleprimes, but
as my browser is alsways completely cleared on close (or on demand) that can
not have been the reason.

It works at least, if I give up all security settings. Which I do not want,
so I sketch a way to use them.

Be aware that not all in a page comes from Mapleprimes. Some is from another
server maplesoft.com and thus considered as 3rd party. Same for some scripts
and CSS etc, which stem from Google, jquery (or else)

If using NoScript or some blockers or similar essentially one has to allow
ajax.googleapis.com, which was needed in the previous version as well (see
below). Dito code.jquery.com is needed (both are 3rd party to Mapleprimes).

It still may hang up at loading ajax-loader.gif, which is located on the
server mapleprimes.com - I do not know why. After allowing a request policy
from mapleprimes.com to ajax.googleapis.com it loads.

That allows to still block all the social media stuff (especially FB connect
is disabled)

And currently I do not see calls to 2o7, just Omniture is trying to work.

---

For the call to Google: it seems to be needed only for their jquery library,
ajax.googleapis.com/ajax/libs/jquery/ and .../jquery/.

But the site calls the open source code.jquery.com/ui anyway. So why using
Google as well? Why not change and stay on code.jquery.com?

Calling to Google transmits my IP and browser header, it is like a fingerprint
and allows GG to identify me later on as Maple user. I dislike that very much.

Edited: edit works as well

After disabling all security addons the Ajax gif loads, then it shows an error and after that it jumps to a page displaying "2013", but that page actually does not have any content (use ctrl + u to see it).

And the I see, that the browser tries to load from maplesoft.112.2o7.net and hangs up in that transfer (have not checked the ports).

In reality I would forbid to load from 2o7, as I receject almost all trackers.

But looking at Adobe http://www.adobe.com/de/privacy/analytics.html or others http://www.makeuseof.com/tag/that-mysterious-2o7-net-tracking-cookie-all-you-need-to-know/ those are 3rd party cookies (Omniture ---> Adobe)

Every reasonable person aware of security and xss forbids dubious sources from other websites (and I am not happy that this sites call Ajax at Google)

And if that is the reason for the bad behaviour of the new sites it would be a good joke, really.

For me it only works with IE and all its security issues (and I have to use "preview" before posting is possible)

I can post answers, but those are not shown

PS: would have done at other threads - but as alreyd said ...

PPS: how about testing? grrrrrrrrrr .......

Since it is not possible for me to reply directly in that new Maple Primes:
I branched. Feel free to re-join for a reasonable structure. What a mess.

http://www.mapleprimes.com/questions/145527-Is-This-Matrix-Primitive

I am rusty on such (may be it is 'obvious' via Lie theory). Your group is just the
group of invertible matrices over the integers (this follows from algebra). And as