Problem extracting components

[Max Banados]

Hi everyone, I am new to xCoba, hope this is not too trivial:  I want to extract the components of a tensor defined using the covariant derivative; it does not work as expected. 

For example, I create a vector (I don't include here all the preamble, see attached notebook):

 v = CTensor[{2, r[], 5, 4}, {ch}]

and the associated tensor:

T1[a_, b_] = v[a] v[b]

I can extract its components with

T1[{0, ch}, {0, -ch}]

which works fine.  But if the definition of the tensor involves a derivative:

T2[-a_, b_] = cd[-a][v[b]]

The command

T2[{0, -ch}, {0, ch}]

does not deliver the required component.  Details in attached notebook 

Any help? 

(Of course I have a much longer calculation and really need to extract the components.)

Thanks! 

Max

[Jose]

Hi,

This is an issue with pattern matching. When you define something like this:

    T2[-a_, b_] = ...

you are requesting indices that are of the form -a_, and {0, -ch} are not of this form. In other words, the pattern -a_ only matches covariant abstract indices, not covariant component indices.

We could discuss alternative patterns, but I actually recommend changing the definition of T2 to:

   T2 = TensorDerivative[v, cd]

Then T2 will be another CTensor object with all the components you are interested in, and you will be able to extract components as usual.

Cheers,

Jose.