Cadabra
a field theory motivated approach to computer algebra

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.
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