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\cdbalgorithm{all\_contractions}{}
Construct all full contractions of the given tensors, taking into
account mono-term symmetries. Example,
\begin{screen}{1,2,3,4,5}
A_{m n}::Symmetric.
A_{m n}::Traceless.
{m,n,p,q,r,s,t,u}::Indices(vector).
{m,n,p,q,r,s,t,u}::Integer(0..9).
obj14:= A_{m n} A_{p q} A_{r s} A_{t u};
@all_contractions(%){2};
A_{m n} A_{m n} A_{p q} A_{p q} + A_{m n} A_{m p} A_{n q} A_{p q};
\end{screen}
This command is not entirely correct at the moment: it determines the
total number of singlets correctly, but does not generate parity-odd
contractions (the ones involving an epsilon tensor). It also does not
know about dimension-dependent identities. If this is a problem for
your application, contact the author for an experimental version of
cadabra.
\cdbseeprop{Symmetric}
\cdbseeprop{Traceless}
\cdbseealgo{canonicalise}
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