A question about the form of the answers

[Андрей Шушарин]

Hi,

I wanted to check some of my computations using xAct, and I would like the answer to be in a covariant form like $\partial_a j^a$. But the result I get is an explicit sum of the derivatives. It is correct, but very hard to read and to check. In the file below I compute the Ricci scalar, the answer in covariant form is  

6 e^2\tau (\box \tau - (\partial \tau)^2)

Thank you in advance for your responses.

Best regards,

Andrey

[Jose]

Hi,

Once you have performed a computation in a chart, it's generally difficult to re-express it in abstract form. In some cases one knows that the result must be a combination of some collection of possible objects, by symmetry arguments or any other consideration. Then you can introduce an ansatz with free coefficients, create a system of equations, and solve it with WL's Solve. This is a really powerful method, and I've used it a lot in the past. I attach your notebook again, with a first section that implements this for the two objects you were asking for.

Then there are cases that are particularly simple, like the conformal transformation you have. In those cases one can do the computation in xTensor (i.e. without introducing a chart at all). Whenever this is possible, it is generally much better to follow this path. The second part of the notebook uses the option ConformalTo -> {metric, conformalFactor} to achieve what you want in a simple way.

Cheers,

Jose.