TestIdeals is a package for basic computations of F-singularities. It is focused on computing test ideals and related objects. It does this via
frobeniusRoot which computes
I[1/pe] as introduced by Blickle-Mustata-Smith (this is equivalent to the image of an ideal under the Cartier operator in a polynomial ring).
We describe some notable functions below.
Notable functions:- testIdeal compute the test ideal of a normal Q-Gorenstein ring or pair.
- testModule compute the parameter test module of a ring or pair.
- parameterTestIdeal compute the parameter test ideal of a Cohen-Macaulay ring.
- HSLGModule compute the stable image of the trace of Frobenius on the canonical module.
- isFregular checks if a normal Q-Gorenstein ring or pair is F-regular.
- isFpure checks if a ring is F-pure.
- isFrational checks if a ring is F-rational.
- isFinjective checks if a ring is F-injective.
- compatibleIdeals finds the compatibly F-split ideals with a (near) F-splitting.
Acknowledgements:The authors would like to thank David Eisenbud, Daniel Grayson, Anurag Singh, Greg Smith, and Mike Stillman for useful conversations and comments on the development of this package.