cadabra 1.39-0.2 / usr / share / doc / cadabra / algorithms / impose_bianchi.tex

\cdbalgorithm{impose\_bianchi}{}

Removes terms which are proportional to the (Garnir generalised)
Bianchi identity. It removes all products for which a set of indices
in Garnir hook form is contracted with an anti-symmetric set. Here is
a simple example with a Riemann tensor,
\begin{screen}{1,2,3,4}
A^{m n p}::AntiSymmetric.
R_{m n p q}::RiemannTensor.
R_{m n p q} A^{m n p};
@impose_bianchi!(%);
0;
\end{screen}
Here is a more complicated one using a \subsprop{TableauSymmetry}
property,
\begin{screen}{1,2,3,4}
\epsilon^{m n p q}::EpsilonTensor.
B_{m n p}::TableauSymmetry(shape={2,1}, indices={0,1,2}).
\epsilon^{m n p q} B_{m n p};
@impose_bianchi!(%);
0;
\end{screen}
An alternative way to obtain the same result is to project each tensor
using the generic \subscommand{young\_project\_tensor} algorithm, and
then use \subscommand{distribute} followed by \subscommand{canonicalise}, but that
generically takes much more time.

\cdbseeprop{RiemannTensor}
\cdbseeprop{TableauSymmetry}
\cdbseealgo{young_project_tensor}
\cdbseealgo{canonicalise}