Cadabra manual: Eliminate

eliminate_kronecker

Eliminate Kronecker delta symbols.

Eliminates Kronecker delta symbols by performing index contractions. Also replaces contracted Kronecker delta symbols with the range over which the index runs, if known.

\delta_{m n}::KroneckerDelta. ex:=A_{m p} \delta_{p q} B_{q n}; eliminate_kronecker(_);

\(\displaystyle{}A_{m p} \delta_{p q} B_{q n}\)

\(\displaystyle{}A_{m q} B_{q n}\)

The index range is set as usual with Integer,

{m,n,p,q}::Integer(0..d-1). \delta_{m n}::KroneckerDelta. ex:=\delta_{p q} \delta_{p q}; eliminate_kronecker(_);

\(\displaystyle{}\delta_{p q} \delta_{p q}\)

\(\displaystyle{}d\)

In order to eliminate metric factors (i.e. to 'raise' and 'lower' indices) use the algorithm eliminate_metric.