/usr/share/doc/cadabra/algorithms/indexsort.tex is in cadabra 1.39-0.2.
This file is owned by root:root, with mode 0o644.
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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 23 24 25 26 | \cdbalgorithm{indexsort}{}
Lexographically sorts indices of all tensors according to their Young
tableau symmetries. This works in simple symmetric or anti-symmetric
cases as expected:
\begin{screen}{1,2}
A_{m n}::AntiSymmetric.
A_{n m};
@indexsort!(%);
(-1) A_{m n};
\end{screen}
It also sorts index groups in tensors with row exchange
symmetries, such as the Riemann tensor,
\begin{screen}{1,2}
R_{a b c d}::RiemannTensor.
R_{d c a b};
@indexsort!(%);
(-1) R_{a b c d};
\end{screen}
For more complicated canonicalisation algorithms,
see \subscommand{canonicalise} as well as \subscommand{reduce}.
\cdbseealgo{canonicalise}
\cdbseealgo{reduce}
\cdbseeprop{AntiSymmetric}
\cdbseeprop{TableauSymmetry}
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