/usr/share/doc/cadabra/algorithms/sym.tex is in cadabra 1.39-0.2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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{sym}{}
Symmetrise a product or tensor in the indicated objects. This works
both with normal objects, as in
\begin{screen}{1,2}
A B C;
@sym!(%){A,B,C};
1/6 A B C + 1/6 A C B + 1/6 B A C
+ 1/6 B C A + 1/6 C A B + 1/6 C B A;
\end{screen}
as well as with indices. When used with indices, remember to also
indicate whether you want to symmetrise upper or lower indices, as in
the example below.
\begin{screen}{1,2}
A_{m n} B_{p};
@sym!(%){ _{m}, _{n}, _{p} };
1/6 A_{m n} B_{p} + 1/6 A_{m p} B_{n} + 1/6 A_{n m} B_{p}
+ 1/6 A_{n p} B_{m} + 1/6 A_{p m} B_{n} + 1/6 A_{p n} B_{m};
\end{screen}
Anti-symmetrisation (i.e.~introducing a sign depending on the
permutation of each term) is handled by the \subscommand{asym}
algorithm.
\cdbseealgo{asym}
\cdbseealgo{young_project}
\cdbseealgo{young_project_tensor}
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