@umar khan 

I only executed your worksheet: it works perfectly when indexing wiht 0 or ~0. I now intercalated some comments and attached it to this reply.

right_file_(reviewed).mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@trace 

If what you want to do is to see the result of applying some transformation, then just pass that transformation to TransformCoordinates. Or, If what you want is to derive the transformation, see the help page of what's new in Physics in Maple 2017: I put an explicit example of that, ie resolving the equivalence bewteen two metrics.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@umar khan 

Maple results are correct. Your worksheet does not show a flow from top to bottom (if you execute it, you do not obtain what you show) so I do not know what you are doing, nor what of the many lines is supposed to be wrong.

So I produced a clean worksheet, attached to this reply (below) with only the computation you show in right_christoffel_symbol.pdf, showing that it suffices to enter the metric and the coordinates and you automatically get the right christoffel symbols and Ricci tensor.

Download Maple_results_are_correct.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@umar khan 
To insert an equation label, you need to use the shortcut Ctrl + L (or Command + L on a Mac), followed by the equation number. For more details see the help page ?worksheet,expressions,equationlabels

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 

What you see in Maple 2017 is the correct result, in connection with an issue fixed after the help page was ready (unfortunately we forgot to update the help page - I will make sure the page gets updated regarding this fix for 2017.1).

About your other question, progress is made at every release, and with priority for what pops up in discussions or people use more. By the way: regarding this or other suggestions for improvements, easy or difficult, it is always useful to give a reference to any method you suggest to be implemented. Work will mostly always start there.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi
Thanks for pointing this out, this is indeed a bug, and it is now fixed. The fix is available for download for everyone at the Maplesoft R&D Differential Equations and Special Functions webpage (the special functions updates are bundled with the Physics updates).

By the way, I didn't try the Mathematica app you mention but if it evaluates this to 311/312, that result is wrong. The correct result is the one mentioned by Preben Alsholm: 71/72.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions

@John Fredsted 
Where is Physics:-`^` used in your question? What copy and paste are you referring to? Generally speaking: a) yes, Physics:-`^` is used when you enter powers, because there may be noncommutative operands at play, but as soon as the command detects they are not present, it returns the power expressed using :-`^`, that is the standard power operator that only handles commutative operands, so it is not expected to appear in the output of a GR computation (unless you use noncommutative operands ...) nor in the output of copy and paste, unless you are delaying the power surrounding  with quotes, as in 'A^B' or the like.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@deniscr 
I thought your question was about how to enter the parameter E: it is TransformTetrads who enters the parameter, it uses the letter E, and if E is already in use it uses E__1, if it is in use it uses E__2, and so on.
If your question is about "how to give E a value after it was entered in the worksheet by TransformTetrads", the answer is to use the subs or the eval commands, as in subs(E = 5, <here you refer to the output_of_TransformTetrads for instance using `%` or the equation number>), or eval with the same arguments swapped, or just assign E := 5 and use the output of TransformTetrads that automatically will take E = 5.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@illuminates 

Psigma[mu] is a tensor (4-vector), you can work with it as with any other tensor, and if uppercaselatin represents spacetime indices and you defined p as a tensor (Define(p)), then Psigma[A] p[A] is a valid tensorial expression with contracted indices. Try for instance SumOverRepeatedIndices(Psigma[A] p[A]) and you see the four Pauli matrices around

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@illuminates 
In the help, search for 'labels' and you will see the third entry is about equation labels; scan the page with your eyes looking for enumerated items, the one with number 3 is the answer to your question: use Ctrl + L (or Command+L in the mac) to open a window where you write the number (not the opening and closing parenthesis - just the number), then press enter and in that way you insert an equation label. I find these equation labels one of the best features of the Maple GUI.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

If I remember correctly, you posted this somewhere else ... Anyway, the reply I gave: this is a weakness in asympt, not in FunctionAdvisor. So try asympt(EllipticE(z, k), k) and you see where the time is taken.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi

It helps if you could please post the worksheet (note also that the images with formulas are not visible).

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@vv 

What you got from Maple is what you asked to it. Look closer: when g is a rigid instruction mapping as the one you posted 

g := a -> int(f(x+a),x=a..2*a) 

by entering g(x) you can only expect the letter a replaced by the letter x, regardless of mathematics. You entered a programming instruction (the arrow operator). Anything else in the output different from replacing a by x would be just wrong, a corruption of the programming language.

Now, if what you wanted is what you refer to as 'mathematically correct substitution', then the g procedure you use should have been written differently, for instance as in

g := a -> eval(int(f(x+_a), x = a .. 2*a), _a = a)

so that eval could take care of the 'mathematically correct substitution' you expect, precisely because eval is the command that takes into account mathematical meaning at the time of making substitutions, instead of performing rigid blind substitutions (as subs or the mapping g that you posted do). 

Hope this clarifies your question?

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft
Editor, Computer Physics Communications

Hi, I'm not an expert in this but, in view that to post you need to open an account first, wouldn't a Captcha (http://www.captcha.net) at the time of opening an account resolve most if not all of this issue? 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft
Editor, Computer Physics Communications

@mskalsi 

Use instead casesplit(DetSys, [{xi, tau, phi}, f]). Again, give a look at the help page for casesplit; there you will find useful details on how to rank the functions (e.g. so that you also obtain a splitting into cases w.r.t f(u) including the related constraint equations for it), work with parameters, etc.

Edgardo S. Cheb-Terrab 
Physics, Differential Equations and Mathematical Functions, Maplesoft