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FrobeniusRootStrategy -- an option for various functions

Description

An option for various functions, and in particular for frobeniusRoot. The valid values are Substitution and MonomialBasis.

Functions with optional argument named FrobeniusRootStrategy:

  • ascendIdeal(...,FrobeniusRootStrategy=>...) -- see ascendIdeal -- find the smallest ideal containing a given ideal which is compatible with a given Cartier linear map
  • compatibleIdeals(...,FrobeniusRootStrategy=>...) -- see compatibleIdeals -- find all prime ideals compatible with a Frobenius near-splitting
  • descendIdeal(...,FrobeniusRootStrategy=>...) -- see descendIdeal -- finds the maximal F-pure Cartier submodule of an ideal viewed as a Cartier module
  • FPureModule(...,FrobeniusRootStrategy=>...) -- see FPureModule -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
  • frobenius(...,FrobeniusRootStrategy=>...) -- see frobenius -- compute a Frobenius power of an ideal or a matrix
  • frobeniusPower(...,FrobeniusRootStrategy=>...) -- see frobeniusPower -- compute a (generalized) Frobenius power of an ideal
  • frobeniusRoot(...,FrobeniusRootStrategy=>...) -- see frobeniusRoot -- compute a Frobenius root
  • isFInjective(...,FrobeniusRootStrategy=>...) -- see isFInjective -- whether a ring is F-injective
  • isFPure(...,FrobeniusRootStrategy=>...) -- see isFPure -- whether a ring is F-pure
  • isFRational(...,FrobeniusRootStrategy=>...) -- see isFRational -- whether a ring is F-rational
  • isFRegular(...,FrobeniusRootStrategy=>...) -- see isFRegular -- whether a ring or pair is strongly F-regular
  • parameterTestIdeal(...,FrobeniusRootStrategy=>...) -- see parameterTestIdeal -- compute the parameter test ideal of a Cohen-Macaulay ring
  • testIdeal(...,FrobeniusRootStrategy=>...) -- see testIdeal -- compute a test ideal in a Q-Gorenstein ring
  • testModule(...,FrobeniusRootStrategy=>...) -- see testModule -- find the parameter test module of a reduced ring

For the programmer

The object FrobeniusRootStrategy is a symbol.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/TestIdeals/EthRootsDoc.m2:257:0.