Cadabra manual: Decompose

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.