TestIdeals : Table of Contents

• TestIdeals -- a package for calculations of singularities in positive characteristic
• adicDigit -- compute a digit of the non-terminating expansion of a number in the unit interval in a given base
• adicExpansion -- compute adic expansion
• adicTruncation -- truncation of a non-terminating adic expansion
• ascendIdeal -- find the smallest ideal containing a given ideal which is compatible with a given Cartier linear map
• ascendModule -- find the smallest submodule of free module containing a given submodule which is compatible with a given Cartier linear map
• AscentCount -- an option for ascendIdeal
• AssumeCM -- an option to assume a ring is Cohen-Macaulay
• AssumeDomain -- an option to assume a ring is a domain
• AssumeNormal -- an option to assume a ring is normal
• AssumeReduced -- an option to assume a ring is reduced
• AtOrigin -- an option used to specify whether to only work locally
• CanonicalIdeal -- an option to specify that a certain ideal be used as the canonical ideal
• canonicalIdeal -- produce an ideal isomorphic to the canonical module of a ring
• CanonicalStrategy -- an option for isFInjective
• compatibleIdeals -- find all prime ideals compatible with a Frobenius near-splitting
• CurrentRing -- an option to specify that a certain ring is used
• decomposeFraction -- decompose a rational number
• DepthOfSearch -- an option to specify how hard to search for something
• descendIdeal -- finds the maximal F-pure Cartier submodule of an ideal viewed as a Cartier module
• floorLog -- floor of a logarithm
• FPureModule -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
• frobenius -- compute a Frobenius power of an ideal or a matrix
• frobeniusPower -- compute a (generalized) Frobenius power of an ideal
• FrobeniusPowerStrategy -- an option for frobeniusPower
• frobeniusPreimage -- finds the ideal of elements mapped into a given ideal, under all $p^{-e}$-linear maps
• frobeniusRoot -- compute a Frobenius root
• FrobeniusRootStrategy -- an option for various functions
• frobeniusTraceOnCanonicalModule -- find an element of a polynomial ring that determines the Frobenius trace on the canonical module of a quotient of that ring
• GeneratorList -- an option to specify that a certain list of elements is used to describe a Cartier action
• isCohenMacaulay -- whether a ring is Cohen-Macaulay
• isFInjective -- whether a ring is F-injective
• isFPure -- whether a ring is F-pure
• isFRational -- whether a ring is F-rational
• isFRegular -- whether a ring or pair is strongly F-regular
• Katzman -- a valid value for the option CanonicalStrategy
• MaxCartierIndex -- an option to specify the maximum number to consider when computing the Cartier index of a divisor
• MonomialBasis -- a valid value for the option FrobeniusRootStrategy
• multiplicativeOrder -- multiplicative order of an integer modulo another
• Naive -- a valid value for the option FrobeniusPowerStrategy
• NoZeroC -- an option for decomposeFraction
• parameterTestIdeal -- compute the parameter test ideal of a Cohen-Macaulay ring
• QGorensteinGenerator -- find an element representing the Frobenius trace map of a Q-Gorenstein ring
• QGorensteinIndex -- an option to specify the index of the canonical divisor, if known
• Safe -- a valid value for the option FrobeniusPowerStrategy
• Substitution -- a valid value for the option FrobeniusRootStrategy
• testElement -- find a test element of a ring
• testIdeal -- compute a test ideal in a Q-Gorenstein ring
• testModule -- find the parameter test module of a reduced ring