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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 asurjective map $\phi : F^e_* R \to R$ (for example a Frobenius splitting), weexhibit 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.

An algorithm for computing compatibly Frobenius split subvarieties