Given a noetherian ring $R$ and an ideal $I$, we know that if the associated primes of $I$ coincide with its minimal primes (i.e. $\text{Min}(I)=Ass(I)$ ) , then there is a unique irredundant primary decomposition of $I$ and if $Min(I) \subsetneq Ass(I)$ then there are infinitely many irredundant primary decompositions of $I$.
My question: Is there an algorithm for finding infinitely many primary decompositions for a given ideal ?
