frobeniusTraceOnCanonicalModule(I, canIdeal)
Given $R = S/I$, where $S$ is a polynomial ring over a field of positive characteristic $p$, there is a map $\omega_R^{1/p^e} \to \omega_R$ dual to the Frobenius map on $R$. By embedding $\omega_R$ as an ideal of $R$, one can interpret this map as a $p^{-e}$-linear map on $S$. But every $p^{-e}$-linear map on $S$ is a premultiple of the dual to Frobenius on $S$, by some element of $S$. This function finds such an element.
However, because Macaulay2 does not always properly identify an ideal as principal (even though it is), sometimes the function cannot find this single element, but instead finds a list of elements of $S$, a linear combination of which is the desired one.
The function frobeniusTraceOnCanonicalModule takes as inputs the defining ideal $I$ of $R$, and an ideal $J$ of $S$ whose image in $R$ is a canonical module of $R$.
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The object frobeniusTraceOnCanonicalModule is a method function.
The source of this document is in TestIdeals/parameterTestIdealDoc.m2:74:0.