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/usr/share/doc/cadabra/reserved/prod.tex is in cadabra 1.46-4.

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\cdbreserved{prod}{}

Denotes a generic product of objects. The parser translates objects
separated by whitespace or by a ``\verb|*|'' symbol to products. 

The default properties of \verb|\prod| are
\begin{verbatim}
\prod{#}::Distributable.
\prod{#}::IndexInherit.
\prod{#}::CommutingAsProduct.
\prod{#}::DependsInherit.
\prod{#}::WeightInherit(label=all, type=Multiplicative).
\prod{#}::NumericalFlat.
\end{verbatim}
~

\cdbseeprop{AntiCommuting}
\cdbseeprop{NonCommuting}
\cdbseealgo{prodsort}