@ecterrab 

I agree and disagree with some of your comments. 

1) My derivation was extremely ad hoc, I will give it that much. I knew you would eventually see my question, which is why I did my derivation the way I did, I was exploiting theorist-to-theorist correspondance. Nevertheless, I do agree that Maple does view both g and eta to be the same, so it would require h to be zero for a "correct statement" for the computer, but not for physicists to follow. I have revised this below, where we know that the background/Minkowski metric is what raises and lowers indices in the linear case.

So, I only concede that my notation was sloppy before in the original derivation. I respectfully don't agree with your result that everthing is fine because h=0 -- that is a computational assertion based on the fact Maple says g=eta. 

Download Response._.mw

2) This is not true for the metric, which is exactly my concern. You do not retain a plus on the inverse metric when you raise the indices assuming that h is a small perturbation and you require that g g^-1 = delta. 

3) I want to go beyond linear order, so I need to have correct signs. I think the only workaround at the moment is doing how I did in the new worksheet and define new tensors. 

If you find some otherway to do it, or have any other thoughts I would appreciate them. 

@C_R I assumed there was some sort of sorting going on, and I took a rather brief look at the help pages. I assume my question was somewhat trivial and not that important, I was guess I should have asked if there was a way to stop the sorting, but in the end it actually all works out fine and I was being unnecessarily dense. 

Thanks for the guidance!

@acer 

Thank you for these alternative methods for plotting, and the procedures. I always seem to forget about the remember option. 

I knew about the possible two roots, but I never thought about trying to find a way to plot both of them together. This is a nice procedure and it certainly does help me out. The implicitplott method certainly speeds things up to just look at plots. 

Thanks again.

@acer

Thank you for the comments.

I had a feeling my attempt was to simplistic, and I can see now that it was. 

Just out of curiosity, what is the purpose of the __R=R usage? 

If you post your worksheet, I could spot the error; or state what exactly you are interested in calculating I could do that explicitly. 

Either way, here is how it works for me. The key part, in how I do it, is to put the components explicitly into the definition of your tensor. 

Download Scalar.mw

@ecterrab 

Great, will update now. 

@ecterrab 

Here is the worksheet:

Minkowski.mw

@acer 

I apologize for my slight stupidity, I found the proper file, and changed the output to false and everything works great. I was not searching in the right Library.. so no wonder I was not finding what I was trying to look for. 

Thank you for guiding me to the promise land.

@acer 

There was no file there, and I have searched almost everywhere and I cannot find a GUI file anywhere...

Additionally, there wasnt any Maple folders in my Prefernces, so I created it, but of course that didn't work as I am not in the right location.

@ecterrab 

Substitue is what I was looking for, but there are still some issues...

1. In my manual method, I still have a exp term floating around. This is because I did not explicitly make a substitution for the metric term will all upper indices. If I do that it works perfectly, and I get the correct expression but you need to make sure that you have a negative exponent for the upper index metric. 

2. If I use Substitue as you propose, albeit with a rather cheeky modification, I was expecting it to take care of it and understand that for the upstairs index metric you need the negative exponential, but it sadly did not.

3. Taking your file explicitly and ammending to look at the Christoffel of the second kind, you can also see that it fails to understand that the upstairs metric needs to have the exponential being negative; yielding the exp(4phi) term. 

I can, in theory, do everything with the Christoffel symbolds of first kind and then "manually" raise one index, I was just curious if Maple could do it easily. I am starting to believe that it can't do it nicely with the one upstairs index on the Christoffel symbol. 

Could I be correct? 

Thanks! 

@ecterrab 

Thank you for this, but I wanted something a little bit different, if Maple can do that. I should also note, I should have written Phi(X), not just Phi -- it needs to be coordinate dependant. Yours will work great for known metric, but I am trying to do it with arbitray metrics, and thus want the index expressions explicitly, and how the original vs. conformal expressions are related. Example: 

I will attach a screenshot of my worksheet and re-upload and hopefully you will be able to access it. 

MyConformal.mw

So I guess my question is -- based on my worksheet/screenshot if you can see it this time -- can I take my equation (3) and apply the transformation g_[] = exp(2 Phi(X)) g_[] easily, without needing to input each index pair, and arrive at my equation (5)? 

Thank you! 

Yes you can solve it. 

Do you have a file with an attempt at it? I can help you with it. 

@segfault 

Can you post the metric you are trying to work with? I promise I wont scoop any ideas, I have far to many projects of my own to worry about. 

I am sorry if I am thinking about it too simply. 

If you have a metric that you want to use, why not just manually enter it at the start and use the Setup command? Instead of initializing a metric then trying to change it? 

It would be easiest if we could see what you have attempted. Can you upload your worksheet?