/usr/share/doc/cadabra/properties/SatisfiesBianchi.tex is in cadabra 1.46-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | \cdbproperty{SatisfiesBianchi}{}
Indicates that an object satisfies a (generalised) Bianchi
identity. This is often used to link a derivative operator to a
curvature tensor, as in
\begin{screen}{1,2,3,4,5,6,8}
R_{m n p q}::RiemannTensor;
D{#}::Derivative.
D_{m}{ R_{n p q r} }::SatisfiesBianchi.
A^{m n p q}::AntiSymmetric.
D_{m}{ R_{n p q r} } A^{m n p q};
@canonicalise!(%);
(-1) D_{m}{ R_{r n p q} } A^{m n p q};
@impose_bianchi!(%);
0;
\end{screen}
This general method allows one to handle more than one type of
derivative object.
\cdbseeprop{RiemannTensor}
\cdbseealgo{canonicalise}
\cdbseealgo{impose_bianchi}
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