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\cdbalgorithm{lr\_tensor}{}
Compute the tensor product of two tableaux or filled tableaux. The
algorithm acts on objects which have the \subsprop{Tableau}
or \subsprop{FilledTableau} property, through which it is possible to
set the dimension. The standard Littlewoord-Richardson algorithm is
used to construct the tableaux in the tensor product. An example
with \subsprop{Tableau} objects is given below.
\begin{screen}{1,2,3}
\tableau{#}::Tableau(dimension=10).
\tableau{2}{2} \tableau{2}{2};
@lr_tensor!(%);
\tableau{4 4} + \tableau{4 3 1} + \tableau{4 2 2}
+ \tableau{3 3 1 1} + \tableau{3 2 2 1}
+ \tableau{2 2 2 2};
\end{screen}
In the graphical interface the output will show up as proper Young tableaux,
\begin{equation}
\tableau{4 4} + \tableau{4 3 1} + \tableau{4 2 2} + \tableau{3 3 1 1} + \tableau{3 2 2 1} + \tableau{2 2 2 2};
\end{equation}
The same example, but now with \subsprop{FilledTableau} objects, is
\begin{screen}{1,2,3}
\tableau{#}::FilledTableau(dimension=10).
\tableau{0,0}{1,1} \tableau{a,a}{b,b}:
@lr_tensor!(%);
\end{screen}
This will again output a sum of \verb|\tableau| objects. In the graphical
interface they will be typeset as
\begin{equation}
\ftableau{{0}{0}{a}{a},{1}{1}{b}{b}} + \ftableau{{0}{0}{a}{a},{1}{1}{b},{b}} + \ftableau{{0}{0}{a}{a},{1}{1},{b}{b}} + \ftableau{{0}{0}{a},{1}{1}{b},{a},{b}} + \ftableau{{0}{0}{a},{1}{1},{a}{b},{b}} + \ftableau{{0}{0},{1}{1},{a}{a},{b}{b}};
\end{equation}
\cdbseeprop{Tableau}
\cdbseeprop{FilledTableau}
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