You may also use [SAGE][1] , (for example, the [Sage online notebook][2] ) Example: The Riemann curvature tensor $R$ lives in the space $Sym^2(\Lambda^2 V)$ (after identifying $V$ with $V^{\vee}$) Decomposing it in Sage: $ s = SFASchur(QQ) $ (let s be the Schur functor) $ s([2])(s([1,1])) $ (compute plethysm $Sym^2 \Lambda^2$) > s[1, 1, 1, 1] + s[2, 2] -- i.e., $\Lambda^4 + s[2,2]$, as it should be $ s([3])(s([1,1])) > s[1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1] + s[3, 3] [1]: http://sagemath.org/ [2]: https://sagenb.kaist.ac.kr/