  Let $R$ be a ring of prime characteristic $p$, and let $F^e_* R$ denote $R$
viewed as an $R$-module via the $e$th iterated Frobenius map. Given a
surjective map $\phi : F^e_* R \to R$ (for example a Frobenius splitting), we
exhibit an algorithm which produces all the $\phi$-compatible ideals.
  We also explore a variant of this algorithm under the hypothesis that $\phi$
is not necessarily a Frobenius splitting (or even surjective). This algorithm,
and the original, have been implemented in Macaulay2.
