Hi! I'm new using your package and have only read part of the code. I just wonder is it okay to support Symbol keys like replacing

TNewCoordinates[coordinatesID_String, coordinates_List?VectorQ] := 

by

keytype=(_String|_Symbol)
TNewCoordinates[coordinatesID:keytype, coordinates_List?VectorQ] := 

Will this replacement of patterns break codes in other place?

Or if supporting Symbol keys is hard, can String keys be auto-completed by

FE`Evaluate@FEPrivate`AddSpecialArgCompletion[_];

in this answer. Where are the right places to add this function?

Problem

I want to use the definition of Weyl Tensor:
$C_{abcd}=R_{abcd}-\frac{1}{n-2}(g_{ac}R_{db}-g_{ad}R_{cb}-g_{bc}R_{da}+g_{bd}R_{ca})+\frac{1}{(n-1)(n-2)}R(g_{ac}g_{db}-g_{ad}g_{db})$
to calculate the Weyl Tensor. But the result includes something like “( )”, which is a couple of parentheses within nothing.

And I used TGetComponents to get the component of the result, and test its symmetry with TensorSymmetry. The result is not correspond to the Weyl Tensor's symmetry. I think there is something wrong.

More tries

Besides, inspired by your work, I programmed a package for Mathematica for Differential Geometry, too. I used two different ways to calculate the Weyl Tensor, but they give different results. One looks like the one OGRe gives, the other is None Tensor.

Oh, The metric I used is Robertson-Walker Metric:
$\text{g}_{\mu \nu }(t,r,\theta ,\phi )\text{ = }\left(
\begin{array}{cccc}
-1 & 0 & 0 & 0 \
0 & \frac{a(t)^2}{1-k r^2} & 0 & 0 \
0 & 0 & a(t)^2 r^2 & 0 \
0 & 0 & 0 & a(t)^2 r^2 \sin ^2(\theta ) \
\end{array}
\right)$

Share my work

In the end, I want to share my package with you, which is not as good as yours, but I added something more to my taste.[Jayce-Ping/SpTm: Space-Time - A Differential Geometry Calculations Package for Wolfram Mathematica. (github.com)](https://github.com/Jayce-Ping/SpTm)

I read your documentation but did not find operators to down or up index and obtain an object of OGRe. For example, to obtain a contravariant metric as the OGRe object I use TNewTensor["svu", "sv", "co", {1, 1}, TGetComponents["sv", {1, 1}, "co"], "svu"], where "sv" is the metric {-1,-1}, which was defined at the beginning, "co" is my coordinates. After this operation, the OGRe object {1,1} appears with the name svu. But this is rather long and inconvenient. If I use TGetComponents["sv", {1, 1}, "co"], this is not an object of OGRe, but a simple List of Mathematica. Maybe possible to make an operator with more simple syntax than I showed above? Something like TDown and TUp with marking the number of indexes that have to be down or up.

First of all, thank you very much for all of your efforts in developing this easy-to-use and powerful tool.

I'm working with a specific metric, the one proposed by Hadad and Zakharov in the following article: https://www.sciencedirect.com/science/article/pii/S0393044014000266#s000020. I can get the various useful tensors (Riemann, Ricci, Weyl etc.) but when I tried to compute the Kretschmann scalar things get complicated.

I use the method presented in your article to contract the Riemann tensor by itself. The code seems to run as the progress bars advance, but at a final stage nothing appear. It's as if the code fall into an infinite loop. The strange thing is that there was no problem when trying to calculate this scalar for common metrics (Schwarschild, FLRW).

The notebook can be found here: https://github.com/benoit-gay/Hadad-Zakharov/

I don't know if this problem can be solved, but I'd like to take the liberty of throwing this bottle into the sea.

Thank you very much for your attention and your help.

B.

I couldn't figure if there is a way to convert tensors to usual Mathematica functions so that we could use them in other packages like VariationalD.

By default, the output of the calculation is in the DisplayFormula style. The copy-paste as Latex format in this style is very strange. For example, the copying of component of tensor Riemann R^t_{tutu} (in Mathematica notebook looks very beautiful) gives \text{R}_{\text{t}\text{u}\text{t}\text{u}}^{\text{t}\text{u}\text{t}\text{u}} in the latex file, which is wrang. You wrote in the documentation that it is possible to change output by using Edit StyleSheet. I tried but unsuccessfully. Maybe better to make some operator like TSetOutput by using which one could change style at the beginning? I tried to change DisplayFormula to Output inside of your OGRe.m file. The output changed but the same problem of copy-paste to Latex.

The calculation of Laplace/d'Alembert operators for scalar/vector/tensor fields is very common in GR research. Can you add them to your package?

Can you add the Weyl tensor to this package?