noethOpsFromComponents L
Let $I$ be an unmixed ideal in a polynomial ring $R = K[x_1, ..., x_n]$, with primary decomposition $I = Q_1 \cap ... \cap Q_s$, where $Q_i$ is $P_i$-primary. If $N_i$ is a set of Noetherian operators for $Q_i$, then one can construct a set of differential operators $N$ for $I$ which satisfies the Noetherian operator condition: given $f \in R$, one has $f \in I$ iff $D(f) \in\sqrt{I}$ for all $D \in N$.
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Note that this construction justifies the focus of Noetherian operators on the case that the ideal I is primary: in order to get a useful membership test for a non-primary (but still unmixed) ideal, it suffices to compute Noetherian operators on each primary component, and then combine them in the way given above.
The object noethOpsFromComponents is a method function.