@ecterrab 
Definately not what I am after.
As I said, I am not looking for the definition, which is all what the example shows.

I want e.g. the RHS of eq(3) expressed in the contractions and derivates of the metric coefficients before it is evaluated. Meaning the Christoffel symbols all worked out, but the entire RHS NOT evaluated blindly.

Problem is I cannot get a way to tell Maple not to evaluate it, but just to show what will be evaluated without any simplification.

I can easily do this by hand, but somehow Maple do not allow me to see that. It is however tediuous by hand, but seems like it is the only option for me.

This problem is in particular instrumental when dealing with wave equations and metric synthesis.

@ecterrab 
I did not expect ambiguity and therefore did not even try it. I will see if it works.

Ambiguity would however be correct to implement as it is how time-signatures were defined in GR.

However, after playing around with it, it seems that Only the following coordinate definition Coordinates(X = (r, theta, phi, t)) is allowed in Maple as the first column of the metric you enter seemingly may never be the time column. You alwys have to enter it in the fourth column.

Only then does the ambiguity work. In other words, the first column always have index 1

Is this correct?

@ecterrab 
That was not what I was asking. I did not ask for the definition of the tensor. I am well aware how to obtain the Definitions

If a tensor is calculated from a metric g say R[1,1], then it will be
R[1,1]=Some.Function.Expression.ito.Coordinates,

which Maple immediate evaluates, and if it is a vacuum solution it will immediately return zero and not the Functional Expression.

What I need to see is the Functional Expression before it is evaluated to zero in this case.
Therefore I need to be able to suppress the evaluation so that only the Functional Expression is shown.

e.g
F(x)=x-x=0.  

I want to see that F(x)=x-x, and not that it is 0.

This is in particular very important calculating and reconstructing wave equations, where you can alter the equation and obtain a different vcuum metric. If it is evaluated by Maple, you have no chance, and have to do it by hand rather than to use Maple.  

Exactly what I was looking for.

thanks

Deleted, was a stupid question

@acer Well, that is an utter defficiency of Maple and obviously will have to be corrected as it is a nonsensical decission to treat boundary values like that.

So, ok, according to the responses there is no workable solution other than edits, so let's leave it there.

Thanks.

@Hullzie16 
Thanks, but sorry, you are addressing a totally different problem. I know how to take the limit of f[4], the problem is taking the limit of the boundary value f[4](0) WITHOUT taking the limit of f4 also.
The solution makes no sense w.r.t the problem I posted as you altered my question fundamentally.

@acer 
Thank you for the answer.

That is utterly weird, you dont want to take the limit of the function f[4] itself and just the boundary value f[4](0).

This is akward as I now have to do hand-edits for boundary values which are asymptotic to infinity.

Maple needs to fix this.

Boundary values are staple, and need to be able to be manipulated like any variableby e.g. the limit function.

Apparently not so.

@Carl Love 
Thank you very much, this solves it for me and I awarded you the solution.

No way I could have figured that out from the manual.

How did you find out about the existence of this ?

@Mariusz Iwaniuk 
Agreed it works, but the user should not really have to manipulate the remainder in order to use the expansion. Makes no sense. Maple should do it internally and calculations on remainders should be handled internally.

@nm 
Thank you again for solving my query.
Thank you for clarifying.

This is not a bug, but great oversight from Maple. 
The calculation of the coefficients should be independent of the presence of the remainder.
It is superfluous  to convert to polynomial first, and this should be done by Maple internally.
If coeff is called on an expansion it should ignore the remainder or just state the remainder order if the user wants the coefficient of the remainder or more, or covert to polynomial automatically.
This makes no sense, but this is how it is apparently.

I marked your answer as the solution.

@nm 
Thank you very much for the great help.

Nowhere in the Clunky Maple Help could I find such a clear explanation.

These are super cryptic commands that I will never remember, so I will have to add it to my own help pages.

Thank you very much for taking the time to respond. It is much appreciated, and so much better than the argumentative support from Maple directly.

Your replies solved all my problems, and I marked your answers as solution and gave you all the positive feedback possible.

@nm 
Your solution  works, but in my case, I had to do

evalindets(rhs(sep_theta), 'specfunc'(anything, DESol), F -> op(1, F))

Thanks a lot !!  I will mark your answer as the solution,

Last question, Do you know how to get rid of the superfluos brackets { }  as in one of your solutions ?


This proxy approach by maple creates so much trouble for my workflow, and you always have to peel onions to get your docuemnt fully automated.
 

@nm 
I am using Maple 22, so I dont know if that is very old to your standards.

@nm 
Thank you very much !
The following should solve my problem.