construct a specific second rank tensor

[Shubham Kumar Sinha]

Hi All,

I am using Xtensor for a while and it is very useful in computing complicated tensor structures. Currently I want to construct a tensor field \[Psi][a,b] such that a belongs to manifold M1 and b belongs to manifold M2.  It would be helpful if anyone can tell me that if that is possilble under xact package.

[Jose]

Hi,

Yes, you can define tensor fields with indices in different vector spaces, like two tangent spaces, or a tangent space and an inner space. Do something like this:

DefManifold[M1, 2, {a, b, c, d}]

DefManifold[M2, 3, {A, B, C, D}]

DefTensor[psi[a, A], {M1, M2}]

DefTensor[T[a, b, -A, -B], {M1, M2}, Symmetric[{-A, -B}]]

etc.

Cheers,

Jose.