By a classical result of Brodmann, $\text{Ass}(I^k)=\text{Ass}(I^{k+1})$ for all $k\gg0$. We denote the common set $\text{Ass}(I^k)$ for $k\gg0$ by $\text{Ass}^\infty(I)$. A prime ideal $\mathfrak{p}\subset S$ such that $\mathfrak{p}\in \text{Ass}(I^k)$ for all $k \gg 0$ is called a stable prime of $I$. This method computes $\text{Ass}^\infty(I)$, the set of the stable primes of $I$.
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The object stablePrimes is a method function.