Cadabra manual: InverseMetric

InverseMetric

Make a two-tensor an inverse metric.

This property is the partner of Metric. It makes the associated two-tensor symmetric and also indicates that it can be used to raise or lower indices.

g^{m n}::InverseMetric. g_{m n}::Metric. ex:=g_{m q} g^{m n} A_{n p};

\(\displaystyle{}g_{m q} g^{m n} A_{n p}\)

eliminate_metric(_);

\(\displaystyle{}g_{q}\,^{n} A_{n p}\)

For more information, see Metric.