Why not uploading a sheet containing a small example (say 3 - 4 Arrays)
accompaning your questions? It would help to understand the problems.

Edited: and the Array not of 11 K, but also small, say 3*3 or 4*4 or so ...

f^(-1) works not in a real sheet, only in 'standard' ...

@hirnyk 

Ah - ok, I see ... sorry for ignoring that.

@hirnyk 

Ah - ok, I see ... sorry for ignoring that.

It would be a 'mechnical' answer anyway :-( ... but at least using Maple ...
so for me it is only partially satisfactory.

Just in case: do you have the expected answer to have a cross check finally?

It would be a 'mechnical' answer anyway :-( ... but at least using Maple ...
so for me it is only partially satisfactory.

Just in case: do you have the expected answer to have a cross check finally?

I could not resist: use functions, not tricks (no insulting intended),
since it is more easy for beginners

F and G are not functions ...

f:=sin;
g:=cos:

h:= x -> f(g(x)); # or 
h:= f@g

Just in case you stumble into s.th. similar again: Be careful in using fnormal,
it can be a trap, if you are working with small values

1e-13; fnormal(%);
                                  0.

If you are sure, that only Reals occure you also may want to consider 'evalc'
and 'simplify( someExpression , zero )'.

Just in case you stumble into s.th. similar again: Be careful in using fnormal,
it can be a trap, if you are working with small values

1e-13; fnormal(%);
                                  0.

If you are sure, that only Reals occure you also may want to consider 'evalc'
and 'simplify( someExpression , zero )'.

I am a bit rusty for details, but you have to be very careful: here you define a certain, new ordering
(not clear which one), but passing to absolute values shows, that the the series diverges.

Now your initial series is a re-ordering and it is known, that by such a step any value can be achieved,
http://en.wikipedia.org/wiki/Riemann_series_theorem

That Maple produces some numerical result says not much here, I would say.

I am a bit rusty for details, but you have to be very careful: here you define a certain, new ordering
(not clear which one), but passing to absolute values shows, that the the series diverges.

Now your initial series is a re-ordering and it is known, that by such a step any value can be achieved,
http://en.wikipedia.org/wiki/Riemann_series_theorem

That Maple produces some numerical result says not much here, I would say.

Or otherwise said: after 'expanding' the integrand and splitting in x=0
this is to compute fouriercos(cos(x^4),x,s) and fouriersin(sin(x^4),x,s)
and Maple seems to find/know those.

Or otherwise said: after 'expanding' the integrand and splitting in x=0
this is to compute fouriercos(cos(x^4),x,s) and fouriersin(sin(x^4),x,s)
and Maple seems to find/know those.

Maple already has problems, if only continuous function are used (for example: polynomials or roots), but in the dis-continuous case I would not expect to get an answer.

I would do it manually: looking for equality and checking for increase / decrease and finally for floor:

Differentiating 5*2^m-160/m w.r.t. m shows, that the function increases.

0=5*2^m - 160/m; isolate(%,m);evalf(%); gives a zero at m ~ 3.28,
so m around that should do it, m=4 is ok, hence m <= 4 is the solution.

f:= proc (x) local m; m := round(x); 5*2^m-floor(160/m) end proc
plot(f(x),x=1 .. 6);

shows it.

Not that nice, but it works.

Just adding:

In those case one can write myResult:= ... : # colon !!! to have it at hand for later use.

Then length(myResult) gives me an impression, for example length(myResult)/80/60
would give me the number of pages (80 characters per line, 60 lines per page).

But its only a trivial side remark on possible usage.