For a given partition $[n_{1},...,n_{k}]$ of $N \in \mathbb{N}$ there exists a corresponding nilpotent orbit variety $O_{[n_{1},...,n_{k}]}$ in $\mathfrak{gl}(N)$ which can be represented by a set of polynomial equations relating the conditions on matrices in $\mathfrak{gl}(N)^{\text{nilp}}$. I was wondering if anyone has implemented the computation of nilpotent orbit varieties in Sage or Magma, because otherwise I am going to make my own code for doing so. If you happen to know of any references, that would help!

EDIT: In particular, I am interested in constructing local weak Neron models for the varieties given as output of the program. So, I want to have a some set of polynomial equations to be the output for an integer partition as input. If this isn't already implemented in Sage, Magma, or any other computational language, I would figure out the code myself.