cadabra 1.39-0.2ubuntu2 / usr / share / doc / cadabra / algorithms / rewrite_indices.tex

\cdbalgorithm{rewrite\_indices}{}

Rewrite indices on an object by contracting it with a second object
which contains indices of both the old and the new type (a vielbein,
in other words, or a metric). A vielbein example is
\begin{screen}{1,2,3,4}
{m,n,p}::Indices(flat).
{\mu,\nu,\rho}::Indices(curved).
T_{m n p};
@rewrite_indices!(%){ T_{\mu\nu\rho} }{ e_{\mu}^{n} };
T_{\mu \nu \rho} e_{\mu}^{m} e_{\nu}^{n} e_{\rho}^{p};
\end{screen}
If you want to raise or lower an index with a metric, this can also be
done with as an index rewriting command, as the following example shows:
\begin{screen}{1,2,3}
{m,n,p,q,r,s}::Indices(curved, position=fixed).
H_{m n p};
@rewrite_indices!(%){ H^{m n p} }{ g_{m n} };
H^{q r s} g_{m q} g_{n r} g_{p s};
\end{screen}
As these examples show, the desired form of the tensor should be given
as the first argument, and the conversion object (metric, vielbein) as
the second object. 

\cdbseealgo{split_index}