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I noticed recently that

  • the dependence of an object only includes the given position of the index and also that
  • objects with derivatives cannot change their index-position if the index position is given as fixed.

For example, the Exp in the following gives zero, because only A with an upper index depends on the derivative:


Exp:= \partial^{\mu}{A_\nu};

Of course I could just make A dependent on \partial for lowercase indices as well or just for every index position via


but it still strikes me as odd.

Secondly, once I have defined objects with derivatives, the index position does not change through the use of canonicalise. So for example

Exp:= \partial_{\mu}{A^\mu} - \partial^{\mu}{A_\mu};

gives not zero as expected. And even if I derive a scalar, its index is fixed, so

Exp:= A^\mu \partial_{\mu}{B} - A_\mu \partial^{\mu}{B};

does not give zero.

I usually don't want to think about the position of dummy indices. So if it would be possible to give the index positions of derivatives a bit more freedom I would be very grateful!

Cheers, Karim

in Bug reports by (300 points)

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