frobeniusPreimage -- finds the ideal of elements mapped into a given ideal, under all $p^{-e}$-linear maps

Given an ideal $Q$ in a ring $R$, one frequently considers $I_e(Q)$. This is the ideal of elements $x \in R$ such that $\phi(x^{1/p^e}) \in Q$ for all $\phi : R^{1/p^e} \to R$. Sometimes this ideal is called the Frobenius pre-image. In a regular ring, it agrees with the frobenius power $Q^{[p^e]}$.

In the previous example $I_1(Q)$ agrees with $Q^{(p)}$, the $p$th symbolic power of $Q$.