{a,b,c,d,e}::Indices;
R_{a b c d}::RiemannTensor;
ex:= R_{a b c d} + R_{a c d b} + R_{a d b c};
young_reduce(_);

ex:= R_{a b c d} + R_{a c d b};
young_reduce(_);

ex:= 2 R_{a b c d} R_{a c b d} - R_{a b c d} R_{a b c d};
young_reduce(_);