RiemannYoungProject[expr] projects all Riemann, Weyl, and symmetrized Riemann tensors and their first derivatives in expr onto their respective Young tableaux. |

RiemannYoungProject[expr, cd] only projects curvature tensors of the covariant derivative cd. |

- Only curvature tensors of metric covariant derivatives without torsion are projected.

- The Riemann tensor and the Weyl tensor are projected onto the Young tableau with manifest antisymmetry.

- The symmetrized Riemann tensor is projected onto the Young tableau with manifest symmetry.

- The first derivatives of the Riemann and Weyl tensors, and , are projected onto the Young tableau with manifest antisymmetry.

- The first derivative of the symmetrized Riemann tensor, , is projected onto the sum of the three Young tableaux , , and . This is precisely the right combination of Young tableaux such that their sum has the row-interchange symmetry of the tableaux.