I have a problem regarding the physics package, which concerns, more specifically, the Define command.
It seems to be the case that it provides the wrong answer, and blatantly so, and I can't see what I am doing wrong for the life of me.
I want to build a fast way of doing coordinate transformations in general relativity, for which the basis vectors are called E[mu,~nu]. XX[~alpha] is the old coordinates expressed in terms of the new (in this case, the spherical coordinates are expressed in terms of cylindrical ones, i.e. [t,r, theta, phi]->[t, rho, phi,z].) As can be seen, only the first component in XX depends on time, but E contains weird elements (look at, for example, E[1,~2].) But when I do the calculation manually, it returns the expected results.
What am I doing wrong? I really appreciate any help you can provide.