Staff seems to be too busy for an answer, yes? Thx anyway.

One needs to allow ajax.googleapis.com (good that GG knows the footprints then) and bootstrapcdn.com

As others already said: much of space on screen is wasted/unsused. A simple button for the 'righthanded side' would correct that. A usual screen 9*16 should lower pleasure, I suppose.

For me the loading hangs up after the initial post ... what is the system trying to load while showing "Ajax-loader.gif" ?

I had to use a completely unprotected browser to see something and to post.

Then probably I do not understand your question. Since cos is periodic
it is enough to have a solutions for cos(z) = a in the period, located
wherever you want it.

And within the period you have a symmetry (this is the 'boolean' variable
in Thomas' answer). So actually one solution is enough (which is what you
observe in your initial formulation).

For z real you need abs(a) <= 1. If you want -oo < a < + oo you can do
as well, but may want -Pi  <= Re(z) <= +Pi (or shifted). And similar for
an arbitrary complex value of a.

Your equation is linear, the result is psi[4](t) = someThing + arccos( ...), depening on various constants and functions, which depend on a variable t.

So what would you expect any system or person to suggest as solution regarding your constraints?

It 'smells' a bit like a bivariate normal with correlation and moments, so I doubt you can do it symbolically (you may wish to write 1/1000 instead of 1e-3, may be you want 0 anyway?).

The best you can do is to explain the task, its origin

@TomM I think your reasoning is not correct:

Matrix(2,2, [f(a)+c1,b,g(c)+c2,d]):
LinearAlgebra:-Determinant(%);

                    d f(a) - b g(c) - b c2 + d c1

So you would need a cancellation condition.

IIRC det and evaluation function commutes, so det( eval(Matrix, sigma=0) ) gives the constant term (*). As Carl pointed out the 'best' way is to use map(convert, Matrix, rational, exact).

(*) For that case you do not need det, you can use "Rank(sigma=0)". And for that I get rank = 6, so det(sigma=0) can not be zero, hence const term is not zero

PS: I used your latest matrix example.

I guess you talk about a Mac (mine is Windows) and perhaps a nordic (?) language. If it is so: a friend once gave me a Word document, the name had an "Umlaut", it was ä. Though it was properly displayed in the GUI I was not able to handle it the usual way. At the command line I saw that this letter was coded by 2 letters, an a and then the two signs above it. After changing the name it worked. So a first step might be to rename using ASCII code only only (and no blanks etc)

switch to 'exact' numerics to avoid round off:

data_deg_ex:=map(convert, data_deg_ex, rational);
Det_data_deg_ex := Determinant(data_deg_ex);

gives degree = 8, lowest degree = 4 (using Digits=15)
and use evalf again on that. Is that ok?

Canceling the obvious common factor it is just 

  #t^(1/n-1)*(1-t)^(n-1/n-1) = t^(1/n-1); 
  #% / t^(1/n-1); 

  (1-t)^(n-1/n-1) = 1;               # after canceling, integrands
  map(ln, %)  assuming 1<n, 0<t,t<1; # 'quadratic' equation
  solve({%, 1<n}, n);                # or pick manually from the two

                                 1/2
                                5
                           {n = ---- + 1/2}
                                 2

or let 'solve' do the work (without manually mapping log), using assumptions

Or more simply try the following, confirming vv's answer

product(mu^x[i],i = 1 .. n+1); 
simplify(%) assuming n::posint; 
combine(%) assuming n::posint;

@acer It seems that IntegrationTools:-Split(%, 0) for the integral already numerically does it quickly without choosing a method.

Then one can plot the curve directly (without restricting to some points) in a quick way:

f := x -> exp(-x^2):
g := (x,a) -> 1/(1+abs(x-a)):
Int(f(x)*g(x,a),x=-infinity..a-1);
IntegrationTools:-Split(%, 0);
plot(%, a=-1 .. 50);

I guess you mean it is slow with very lenthy output. But what do you expect?

Doing it for smaller order one can guess that an "alias" (---> help) for the constant term can shorten the display.

As a quick solution for me (?) it would be enough to have a filter giving only posts with reputation greater 0.

For example adding that to the menu bar as "Recent +" or similar.

@Markiyan Hirnyk The last sentence is insulting. No need at all for such.

http://www.maplesoft.com/support/help/Maple/view.aspx?path=operators/elementwise&term=Element-wise%20Operators

In the Help system you just type in ~ into the search field and get according topics.

PS: personally I prefer "map", for me usually it is more easy to understand (but your cited example is much more compact code)