> namely, just contract on the inner indices. That is, arr(n1, ..., nk, m) @ arr(m, p1, ... pl) = arr(n1, ..., nk, p1, ..., pl).
No. This is what a mathematician might assume the PEP proposes without actually reading it. It instead proposes an entirely non-obvious definition which not equivalent to what you wrote.
I know it is not equivalent—that is why I proposed it as a sensible alternative to what the PEP proposes (which I quoted). The punctuation may have made it unclear, but what I was trying to say was:
> … a sensible alternative to [PEP proposal]; namely, just contract on the inner indices.
and not
> … a sensible alternative to contracting on the inner indices.
My argument for why it's sensible is precisely what you mentioned, namely, that it is what a mathematician would expect.
No. This is what a mathematician might assume the PEP proposes without actually reading it. It instead proposes an entirely non-obvious definition which not equivalent to what you wrote.
In particular consider this example from the PEP.