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+1 vote

I have the following example, where i want the partial derivative index be raised up by metric, but eliminate_metric does nothing:

{\mu, \nu}::Indices(position=independent).
g_{\mu \nu}::Metric.
g^{\mu \nu}::InverseMetric.
g_{\mu \nu}::Depends(\partial{#}).
g^{\mu \nu}::Depends(\partial{#}).
expr:=g^{\mu \nu}\partial_{\nu}{A_{\mu}}.

This results the same expression. Is there a way to raise up partial derivative index?

in General questions by (130 points)

1 Answer

0 votes

Interestingly, if you write the metric inside the derivative the desired result,

expr:=\partial_{\nu}{ g^{\mu \nu} A_{\mu}};

I think that the behaviour differs because you cannot take in/out freely the metric from the expression.

Personally, I find your question very interesting!

by (10.9k points)