An effective method to compute closure ordering for nilpotent orbits of $\theta$-representations

We develop an algorithm for computing the closure of a given nilpotent $G_0$-orbit in ${\text{g}}_1$, where ${\text{g}}_1$ and $G_0$ are coming from a $\mathbb{Z}$ or a $\mathbb{Z}\mathrm{/}m\mathbb{Z}$-grading $\text{g}=⨁{\text{g}}_i$ of a simple complex Lie algebra $\text{g}$.