a field-theory motivated approach to computer algebra

## Tableau

A Young-tableau object with unlabelled boxes.
Declares that the object carrying this property is used to label a Young tableau with unlabelled boxes (Young diagram). The arguments of such objects denote the lenghts of the rows. The dimension argument of the property sets the dimension. Can be used in combination with the lr_tensor and tab_dimension algorithms to compute tensor product representations.
\tableau{#}::FilledTableau(dimension=3); ex:=\tableau{c,c}{c}\tableau{a,a}{b}; lr_tensor(_);
$$\displaystyle{}\text{Attached property FilledTableau to }\ytableaushort{{\#}}.$$
$$\displaystyle{}\ytableaushort{{c}{c},{c}} \otimes \ytableaushort{{a}{a},{b}}$$
\tableau({c, c} , c) \tableau({a, a} , b)
$$\displaystyle{}\ytableaushort{{c}{c}{a}{a},{c}{b}} \oplus \ytableaushort{{c}{c}{a}{a},{c},{b}} \oplus \ytableaushort{{c}{c}{a},{c}{a}{b}} \oplus \ytableaushort{{c}{c}{a},{c}{a},{b}} \oplus \ytableaushort{{c}{c}{a},{c}{b},{a}} \oplus \ytableaushort{{c}{c},{c}{a},{a}{b}}$$
\tableau({c, c, a, a} , {c, b}) + \tableau({c, c, a, a} , c , b) + \tableau({c, c, a} , {c, a, b}) + \tableau({c, c, a} , {c, a} , b) + \tableau({c, c, a} , {c, b} , a) + \tableau({c, c} , {c, a} , {a, b})
q=[int(tab_dimension(t.ex())) for t in ex.top().terms()];
{}$\big[$$27, 10, 10, 8, 8, 1$$\big]$