@ecterrab Fantastic! Thanks once more, and sorry that I missed that out in your previous reply!

@ecterrab Thanks for the reply and all the usefull info! I will check that out.

However, if you could just answer me this short question it would be great: can the package handle non-coordinate bases, and calculate the components of geometric object with respect to such a basis?

@Carl Love Cheers!

@Carl Love This makes a lot of sense, thanks a lot!

Followup question: Say, if

limit(f(x,y),{x=a,y=b})

returns a value, does that then mean that the limit for all possible paths gives the same value, i.e. that the limit is independent of the chosen path?

@Carl Love I guess an example would be the shortest path between two points: https://en.wikipedia.org/wiki/Calculus_of_variations#Example

The constraints would be that the boundary points y(x₁) and y(x₂) have a certain value.

I suppose a way to do it is to write out the function and integral in finite difference form, and treat it as a function of the values of y at the grid points.

@Carl Love Thanks for your answer! You must have looked into that while I edited my start post. I found out about that already! But your answer was still usefull to me, since I didn't know the thing with the infolevel.

I didn't look deep anough into the package and problem I need to solve yet, but in the end I need to minimize a functional F[f, g, h, ...]. The solvers which the package provides, as far as I have seen are only suited to minimize functions f(x, y, z, ...) however. How would I tackle such a problem with a functional?

I suppose the answer is something along the lines of, evaluate the functions in the argument of the functional on a grid, and then treat the functional as function again. But if you would have any suggestions, I would be glad to hear your opinion, as I have never solved a minimization problem so far. (Appart from simple ones of course.)

@Carl Love Hi there! I did not find the time to test this, but I will and really do appreciate the help and effort!

Just in case I find this proc really usefull, is there a nice way to put it in a file where I can load it from for each new document, or would I have to coppy-paste the code into every new document and then execute it every time?

@Joe Riel Thanks for the answer! Yes, I do mean a piecewise expression. I tried out the op. I guess it does the job, but I didn't quite figure out in what order I have to call the expressions. Perhaps there is no optimal solution here. Anyway, cheers for help!

@ThU That was it, thank you! True, it may depend on the case if it is more readable or not. ; ) Thanks again!

@acer 

Hi, and thanks for the answer. Hm, I do know ArrayInterpolation. Didn't think of that. That should do it, thanks!

But in addition I would still be interested if there are interpolation techniques, which give the whole function, which are superior to others in the sense that the resulting expression is not so huge as with a Spline?

Thank you all very much for you answers. I understand now! : )

@Carl Love Hi Thank you ver ymuch for all the detailed ansers. This helps a lot! : )

@Carl Love Yeah, I already thought on that I should make my procedures better in this respect. Thanks for your solutions, this is of great use to me! : )

How do I mark this question as answered? -.^

@Sujaan Kunalan Does the job, thanks a lot! : )