Cadabra
a field-theory motivated approach to computer algebra

decompose

Decompose a tensor monomial on a given basis of monomials.
The basis should be given in the second argument. All tensor symmetries, including those implied by Young tableau Garnir symmetries, are taken into account. Example,
{m,n,p,q}::Indices(vector). {m,n,p,q}::Integer(0..10). R_{m n p q}::RiemannTensor. ex:=R_{m n q p} R_{m p n q};
\(\displaystyle{}R_{m n q p} R_{m p n q}\)
R_{m n q p} R_{m p n q}
decompose(ex, $R_{m n p q} R_{m n p q}$);
\(\displaystyle{}\left[ - \frac{1}{2}\right]\)
{ - 1/2 }
Note that this algorithm does not yet take into account dimension-dependent identities, but it is nevertheless already required that the index range is specified.
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