The zero components of an antisymmetric tensor correctly vanish, but not if I take their derivative (ToCanonical in xCoba)

[Níckolas de Aguiar Alves]

Hi there! 
I'm working with antisymmetric tensors. Let us call it F_ab for now. In the middle of my computation, I evaluate it in components. I noticed that F_00, for example, is simplified to zero when I call ToCanonical, as I would expect. However, this does not happen with \partial_1 F_00. I suppose this simplification is not trivial in the sense that e_1^a e_0^b e_0^c \partial_a F_bc is generally different from e_1^a \partial_a (e_0^b e_0^c F_bc), and perhaps \partial_1 F_00 denotes the first instead of the second? 

What precisely is going on in this case? How can I handle it? 

I am attaching a minimal working example. 

Thanks in advance!

[Juan Margalef]

Hi!

I am no expert on xCoba but if you use PDsph[{1, -sph}][Faraday[{0, -sph}, {0, -sph}]] // SeparateBasis[], you would see that, indeed, it is  e_1^a e_0^b e_0^c \partial_a F_bc and not  e_1^a \partial_a (e_0^b e_0^c F_bc). You can also check PDsph[{1, -sph}][Faraday[{0, -sph}, {0, -sph}]] // SeparateBasis[] // ContractBasis that returns  e_0^a e_1^b \partial_1 F_bc

If you evaluate somehow the argument, it reduces to zero PDsph[{1, -sph}][Faraday[{0, -sph}, {0, -sph}] // Simplification]. I think the notation is quite dangerous so maybe someone with more knowledge quite chip in and explain a bit more.

Best,

Juan