Cadabra manual: Metric

Metric

Makes a two-tensor a metric.

Labels the object as a symmetric tensor, and optionally gives it the indicated signature through the signature parameter.

g_{m n}::Metric(signature=1). ex:= g_{m n} A^{n p}; eliminate_metric(_);

\(\displaystyle{}g_{m n} A^{n p}\)

g_{m n} A^{n p}

\(\displaystyle{}A_{m}\,^{p}\)

A_{m}^{p}

Objects declared as Metric can be used to automatically raise or lower indices using the eliminate_metric algorithm, as above.