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

@Britzel 
The answer is in the previous reply. Take a look at the guide for tensor computations mentioned. Scrolling one page of that post you will see a section "Tetrads and the local system of references." There is a Tetrads package, not new; it is there in your copy of Maple 2018. The relation between the components of a tensor in a coordinate and non-coordinate bases is as you know, A[mu] = e_[~a, mu] A[a], and A[a] = e_[a,~mu] A[mu]. You can compute with both bases at the same time using different kinds of indices, Simplify tensorial expressions having both types of indices, etc. To compute components in either basis (is that what you want?) you can use TensorArray, say as in TensorArray(A[mu]) and TensorArray(A[a]).

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

@nm 
It works fine here. You have had problems installing this updated, manually moving files around as you told me in private email. I suggests you to entirely delete the toolbox/2019 directory, and reinstall the Updates.

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

@vv 

Nice workaround. When looking at this problem I thought that wouldn't work in this case because bc[2] would depend on t on the lhs and on x, t, on the rhs, but no, that is not a problem, only the dependence of the PDE and the evaluation points in the BC count; and in the PDE, x only appears within u(x, y, t), and there are no derivatives with respect to x, and in the BC x is not evaluated at a point. Indeed replace u(y, t) in your solution (2) by u(x, y, t) and pdetest against the original problem in three variables and you see the solution is correct.

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

@tomleslie 

The first Physics Updates for Maple 2019 is already available for download through the MapleCloud.

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

@acer 

This is just a bug in the extended typesetting of eval. The expected display for convert( u, Diff ) is indeed the one you see in this moment with typesetting = standard. I'll take a look at this during the week and write again here.

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