Cadabra
a field theory motivated approach to computer algebra

young_project_product

Project all tensors in a product with their Young tableau projector.
Project all tensors in a product with their Young tableau projector. Each factor is projected in turn, after which the product is distributed and then canonicalised. This is often faster and more memory-efficient than first projecting every factor and then distributing. Young projection can be used to find equalities between tensor polynomials which are due to multi-term symmetries, such as the Ricci identity in the example below.
{a,b,c,d}::Indices. R_{a b c d}::RiemannTensor. ex:=2 R_{a b c d} R_{a c b d} - R_{a b c d} R_{a b c d};
\(\displaystyle{}2R_{a b c d} R_{a c b d}-R_{a b c d} R_{a b c d}\)
young_project_product(_);
\(\displaystyle{}0\)
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