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/