I am a software developer writing a library that includes cartesian tensors. I am defining operators on tensors. One such operation is the semicolon derivative (as specified here: http://mathworld.wolfram.com/CovariantDerivative.html).
The mathworld article is about general tensors I think and that due to the simplicity of cartesian tensors I'd think a simple process for its calculation would emerge. Is there a simple algorithm for computing the semicolon derivative for cartesian tensors?
I've done a little research and it seems like a semicolon derivative degenerates into the comma derivative (e.g. partial differentiation) for the euclidean / cartesian case.