isFPure(R)
isFPure(I)
Given a ring $R$, this function checks whether the ring is $F$-pure, using Fedder's criterion (by applying frobeniusRoot to $I^{[p]} : I$, where $I$ is the defining ideal of $R$).
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Alternatively, one may pass the defining ideal of a ring.
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The option AtOrigin controls whether $F$-purity is checked at the origin or everywhere. If its value is set to true (the default is false), it will only check $F$-purity at the origin.
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Note that there is a difference in the strategy for the local or non-local computations. In fact, checking $F$-purity globally can sometimes be faster than checking it only at the origin. If AtOrigin is set to false, then isFPure computes the frobeniusRoot of $I^{[p]} : I$, whereas if AtOrigin is set to true, it checks whether $I^{[p]} : I$ is contained in $m^{[p]}$, where $m$ is the maximal ideal generated by the variables.
The option FrobeniusRootStrategy is passed to internal frobeniusRoot calls, and specifies the strategy to be used.
The object isFPure is a method function with options.