\cdbalgorithm{riemann\_index\_regroup}{}

Given a set (or multiple sets) of indices in which to anti-symmetrise,
this routine determines whether the indicated Riemann tensor has an
index distribution with two of the anti-symmetrised indices on two
different pairs. If so, it performs the substitution
\begin{equation*}
R_{m [p|\, n|q]} \rightarrow \frac{1}{2}R_{m n p q}\, ,
\end{equation*}
which is valid by virtue of the Riccy cyclic identity $R_{m [npq]}=0$.
The example above translates to
\begin{screen}{1,2,3,4}
R_{m n p q}::RiemannTensor.
A^{m n}::AntiSymmetric.
R_{m p n q} A^{p q};
@riemann_index_regroup!(%);
 1/2 R_{m n p q} A^{p q};
\end{screen}
Note that this also works on Weyl tensors.

\cdbseealgo{young_project_tensor}
