@umbli 

Regarding 2.: only the tensors that are "single letter" have an underscore at the end so that these single letters can be used for other purposes. These include g_, d_, D_, l_, n_, m_, gamma_, and then for consistency also D3_ gamma3_ from the ThreePlusOne package.

Regarding 1., the D_ operator is displayed with Nabla. Try D_[mu](A[nu](X)) to see that in the output. And how do you make it look that way in the input? Type it literally, as D_[mu](A[nu](X)), then right-click that input, and choose 2D - Math -> Convert To -> 2D Math input, and there you are. In the case of a procedure like the one you see after (23), I do it in two steps: first as said, and after I have the right math look of the formula I placed the cursor at the beginning and typed T ->.

I'm glad to hear you are having a pleasant experience with the Physics package. This project aimed at partly transforming the arduous sensation of some physics algebraic computations into smooth gliding. It takes some time for your brain to get convinced, but as soon as that happens, it is fantastic how the imagination unleashes (computations become a pleasure). We are not all there yet, but each year getting closer, and for me listening to questions and providing feedback is key in the development process.

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

@umbli 

Your question is not clear to me. There are four coordinates, could be any symbols, say X = (x1, x2, x3, x4).

IMPORTANT: note that, in Maple, `[]` is the selection operator. Given a list X := [a, b, c, d], there is no meaning for X[0]. So to make the notation X[0] work in the computer as we do with paper and pencil we need to map X[0] into X[n] for some n that is a positive integer. This is relevant for tensors, say the metric g_[mu,nu], because the order of lines and columns in the matrix representation is according to the ordering of the coordinates, and here again, in the context of a computer, there is no meaning to "the 0th column" of a matrix. Lines and columns are associated to positive integer numbers.

So suppose that the signature is `+ + + -`. The different sign is the last one, in position 4, and that is the timelike position . Thus the mapping we use (as in textbooks or paper and pencil) is that the value 0 for the index always points to the  timelike position, and so for this signature X[0] = X[4], and X[1..3] are the spacelike coordinates, and in the case of the metric g_[0, 0] = g_[4, 4], meaning you get the component in line 4 and column 4 of the matrix representation for g_.

If the signature is  `- + + +` then X[0] = X[1] (the timelike coordinate for this signature) and X[2..4] are the three spacelike coordinates and g_[0, 0] = g_[1, 1], you see this in the matrix representation of the metric (enter g_[]).

To see this mapping at work for the coordinates, use SpacetimeVector[0](X) with the two different settings of the signature.

If you prefer to avoid having to select the coordinate with a number and forget about this subtlety of what is the timelike position in the signature, you can always Setup(usecoordinatesastensorindices = true). Suppose your coordinates are [t, x, y, z], or [x, y, z, t] it doesn't matter: you can now index directly with the coordinates themselves, as in Christoffel[t,t,t] to get its value.

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

Hi, when posting a question, always try to see your question through the eyes of the people you are directing the question, for instance, whether you are providing enough information for someone to reproduce your problem in order to give you some useful feedback. Reading your question, for me, there is not enough information. I don't know what you are doing, but if you repost with details then try to give all that is necessary to reproduce your problem entirely and without ambiguity.

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

Hi,

Could you please post a worksheet with the formulation of the problem up to what you can do it? (You can create the worksheet, then upload it using the green arrow).

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

@Mariusz Iwaniuk 

The error you show in Run_code_2 is fixed by installing the Physics Updates v.353. The PDE problem itself is not solved in this moment, but it is solvable - we will work on this one and a couple of other ones as soon as there is a window of time.

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

Do you mean a non-symmetric metric?

@tomleslie 

I believe I identified the issue (an advanced library from the development repository interferring in my computer). So my understanding is that by installing v.350 of the Physics Updates this problem (unexpected error interruption) stops happening. As usual please post again if this change doesn't correct the problem.
 

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

What version of Maple are you using? Could you please input > version(); and show the output? Thanks

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

@Rouben Rostamian  

The pdsolve command is programmed to solve systems of PDEs, so this problem posted is the kind of problem it handles. When the system is inconsistent, it will tell you. By the way, I cannot reproduce the problem mentioned by Mac Dude: the system is solved right away (see the answer by tomleslie).

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

@prldb 
The PDE system to be solved, whose solution are the Killing vectors, is of course the same - no matter what package you use. The PDE solver is also the same, Maple's pdsolve. Some relevant options to tackle the problem, however, are not available in both packages. The Physics:-KillingVectors command has more options, regarding how to tackle the system, providing only the PDE system without tackling, and also regardng the format of the output, that it is wysiwyg. Those differences may be relevant if your problem is tough (as I understood from your original post that it is your case). The rest is a matter of preference.

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

@alaloush 

The problem admits roots that have a complicated structure - there is nothing one can do about that, but for using simplify([%], size), reducing solve's output (with option explicit) from a length of 18717 to a length of 14005.

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

Hi

For this kind of problem I'd recommend you to use the KillingVectors command of the Physics package, but besides that: could you please post a worksheet with the problem you are tackling? For that purpose you can use the green arrow. That will save time from everyone trying to help you. (If you use the Physics package command, please post the worksheet with the corresponding input lines.)

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

@deniscr 
Kind comments, thanks. If you have Maple 2019, you can install the Maplesoft Physics Updates; its latest version, 343, turns unnecessary to sum over the repeated indices of the line element, so you can skip that step and enter, directly, Setup(metric = (2)).

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

@guru kido 
ArrayElems@TensorArray returns different than an empty set when the tensorial expression you passed is not equal to zero. If you were expecting zero and are not receiving that, you'd need to revise your formulation. For example, if the Weyl tensor is (equal to its) anti-self dual, then the Bach and Eastwood–Dighton tensors vanish (see for instance Self–Dual Conformal Gravity). You can check whether these tensors vanish or not, and if they don't you have no reason to expect C + W = 0.

Your "computation of more derivatives" (equations (12) to (18)) has nothing to do with the result being or not being zero. I see, however, that your equation (11) says that some combination of third order derivatives of u(X) is equal to zero. If that is your case and you want to simplify your nonzero result taking into account identities like (11), then the way to do that is to use simplify - see the help page ?simplify,siderels

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

PS: when you want to show that something is not zero you do not need to present pages and pages of output; in case like that one just say "the following does not return zero". Otherwise, it is difficult to read your posts. Likewise, you were aware of the "misordering" but nevertheless posted that way. That does not help. You need to be more precise with your posts or otherwise it becomes too time consuming to give you some feedback.

To get feedback, it is recommended that you post your problem in a Maple worksheet, that you can upload clicking the green arrow you see when posting your question. Otherwise, by copy and paste + edition, people need to spend the time they don't have, and the result is prone to typographical mistakes. By the way, your second equation, as you posted, has typographical errors: the opening parenthesis before the number 3 does not close anywhere. Try writing your problem in a worksheet and post again (and I wouldn't assume that Maple's dsolve cannot work on it directly).

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