This is an old question but a very valid question.

In my experience, do not ever mix "maple input" and "2D input"

The strangest things happens, such as array assignments suddenly not working, and after you just backspace to delete a bracket say "[" and then re-enter the bracket "[" then suddenly it assigms. 

Absolutely crazy.

Just dont mix them, especially not by loading e.g. an old maple  Version 9 (in maple input) into 22 where 2D math is default. Huge errors.

I had to completely type over a document verbatim avoiding import, and then it worked.

@Hullzie16 

It is not about ideas or such concerns, it is about copyright issues and disclosure of novel work. So I will have to rework it to something mundane which replicates the same problem.

I will rerwrite it to the simplest working form and post it. 

Might take a bit of time though, but I will do it.

@Hullzie16 

Thank you for the time you took to  answer. 
It is clear that you understand my problem.

Regarding the reason as per your response..

That would have been nice if Maple would allow me to do that, but for a specific metric it fails with a float error.
The reason is that Maple refuses to accept coordinate dependencies of a specific metric I am working on, but works without the dependencies.

It is truly weird that it gives me "float errors) when I add coordinate dependencies of metric coefficient functions,
It should not give float errors as seting up a metric has zero depndency on metric coefficient dependencies,

The only way around this is to add the dependencies after the metric is entered with Setup so I can use the built in computation of curvature tensors etc.

@alephys 
Darn that is obvious and seem to work. Why did I not think about that !

@mmcdara 
Works absolutely fantastic thank you.

Actually creates a huge lot of simplification too.

Solves the original problem.

Great !

@Hullzie16 
Gee, I did not see your response for some reason. I apologize for the oversight.
This seems to solve my problem.

I never came accross using %d instead of diff.

Can you direct me to where you got that from as I never ran accross it and is really a crucial operator.
I really want to read that up.
I was under the impression that diff was the only partial differential operator !

Thanks a lot. !! This really helps me.

@janhardo 

Thank you for helping. It is appreciated.

I tried your suggestion.
It threw the following errors.

See image attached.

Update: Unfortunately uploading images does not work as usual. The image was uploaded, but does not appear here. So I will paste the error text  below the post.

Tried to figure out online what the problem is, and it seems to be a wrong assignment of a variable.

Error1:
---------------------------------------------------------------------------------------------------

restart;
with(Physics);
Physics:-Setup(inertdiffs = true);
g_[[5, 29, 1]];
eq1 := Physics:-`*`(g_[~mu, ~nu], Diff(w(r, theta), mu), Diff(w(r, theta), nu));
Physics:-Contract(eq1);
Physics:-Check(eq1, all);
Error, (in Physics:-Setup) wrong left-hand-side in inertdiffs = true
     _______________________________________________________

Error2

----------------------------------------------------------------------------------------------------

Error, Contract is not a command in the Physics package
      The repeated indices per term are: ((...),(...),...)

        , the free indices are: (...)

                 [{}], {~mu, ~nu}

@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.