TestIdeals : Index
- adicDigit -- compute a digit of the non-terminating expansion of a number in the unit interval in a given base
- adicDigit(ZZ,ZZ,List) -- compute a digit of the non-terminating expansion of a number in the unit interval in a given base
- adicDigit(ZZ,ZZ,QQ) -- compute a digit of the non-terminating expansion of a number in the unit interval in a given base
- adicDigit(ZZ,ZZ,ZZ) -- compute a digit of the non-terminating expansion of a number in the unit interval in a given base
- adicExpansion -- compute adic expansion
- adicExpansion(ZZ,ZZ) -- compute adic expansion
- adicExpansion(ZZ,ZZ,QQ) -- compute adic expansion
- adicExpansion(ZZ,ZZ,ZZ) -- compute adic expansion
- adicTruncation -- truncation of a non-terminating adic expansion
- adicTruncation(ZZ,ZZ,List) -- truncation of a non-terminating adic expansion
- adicTruncation(ZZ,ZZ,QQ) -- truncation of a non-terminating adic expansion
- adicTruncation(ZZ,ZZ,ZZ) -- 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
- ascendIdeal(..., AscentCount => ...) -- find the smallest ideal containing a given ideal which is compatible with a given Cartier linear map
- ascendIdeal(..., FrobeniusRootStrategy => ...) -- find the smallest ideal containing a given ideal which is compatible with a given Cartier linear map
- ascendIdeal(ZZ,List,List,Ideal) -- find the smallest ideal containing a given ideal which is compatible with a given Cartier linear map
- ascendIdeal(ZZ,RingElement,Ideal) -- find the smallest ideal containing a given ideal which is compatible with a given Cartier linear map
- ascendIdeal(ZZ,ZZ,RingElement,Ideal) -- 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
- ascendModule(ZZ,Matrix,Matrix) -- find the smallest submodule of free module containing a given submodule which is compatible with a given Cartier linear map
- ascendModule(ZZ,Module,Matrix) -- 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
- 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
- canonicalIdeal(..., Attempts => ...) -- produce an ideal isomorphic to the canonical module of a ring
- canonicalIdeal(Ring) -- 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
- compatibleIdeals(..., FrobeniusRootStrategy => ...) -- find all prime ideals compatible with a Frobenius near-splitting
- compatibleIdeals(RingElement) -- 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
- decomposeFraction(..., NoZeroC => ...) -- decompose a rational number
- decomposeFraction(ZZ,QQ) -- decompose a rational number
- decomposeFraction(ZZ,ZZ) -- 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
- descendIdeal(..., FrobeniusRootStrategy => ...) -- finds the maximal F-pure Cartier submodule of an ideal viewed as a Cartier module
- descendIdeal(ZZ,List,List,Ideal) -- finds the maximal F-pure Cartier submodule of an ideal viewed as a Cartier module
- fastExponentiation -- compute a power of an element in a ring of positive characteristic quickly
- fastExponentiation(ZZ,RingElement) -- compute a power of an element in a ring of positive characteristic quickly
- floorLog -- floor of a logarithm
- floorLog(Number,Number) -- floor of a logarithm
- FPureModule -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
- FPureModule(..., CanonicalIdeal => ...) -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
- FPureModule(..., CurrentRing => ...) -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
- FPureModule(..., FrobeniusRootStrategy => ...) -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
- FPureModule(..., GeneratorList => ...) -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
- FPureModule(List,List) -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
- FPureModule(Number,RingElement) -- compute the submodule of the canonical module stable under the image of the trace of Frobenius
- FPureModule(Ring) -- 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
- frobenius(..., FrobeniusRootStrategy => ...) -- compute a Frobenius power of an ideal or a matrix
- frobeniusPower -- compute a (generalized) Frobenius power of an ideal
- frobeniusPower(..., FrobeniusPowerStrategy => ...) -- compute a (generalized) Frobenius power of an ideal
- frobeniusPower(..., FrobeniusRootStrategy => ...) -- compute a (generalized) Frobenius power of an ideal
- frobeniusPower(QQ,Ideal) -- compute a (generalized) Frobenius power of an ideal
- frobeniusPower(ZZ,Ideal) -- compute a (generalized) Frobenius power of an ideal
- FrobeniusPowerStrategy -- an option for frobeniusPower
- frobeniusRoot -- compute a Frobenius root
- frobeniusRoot(..., FrobeniusRootStrategy => ...) -- compute a Frobenius root
- frobeniusRoot(ZZ,Ideal) -- compute a Frobenius root
- frobeniusRoot(ZZ,List,List) -- compute a Frobenius root
- frobeniusRoot(ZZ,List,List,Ideal) -- compute a Frobenius root
- frobeniusRoot(ZZ,Matrix) -- compute a Frobenius root
- frobeniusRoot(ZZ,Module) -- compute a Frobenius root
- frobeniusRoot(ZZ,MonomialIdeal) -- compute a Frobenius root
- frobeniusRoot(ZZ,ZZ,Ideal) -- compute a Frobenius root
- frobeniusRoot(ZZ,ZZ,RingElement) -- compute a Frobenius root
- frobeniusRoot(ZZ,ZZ,RingElement,Ideal) -- 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
- frobeniusTraceOnCanonicalModule(Ideal,Ideal) -- 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
- isCohenMacaulay(..., IsLocal => ...) -- whether a ring is Cohen-Macaulay
- isCohenMacaulay(Ring) -- whether a ring is Cohen-Macaulay
- isFInjective -- whether a ring is F-injective
- isFInjective(..., AssumeCM => ...) -- whether a ring is F-injective
- isFInjective(..., AssumeNormal => ...) -- whether a ring is F-injective
- isFInjective(..., AssumeReduced => ...) -- whether a ring is F-injective
- isFInjective(..., CanonicalStrategy => ...) -- whether a ring is F-injective
- isFInjective(..., FrobeniusRootStrategy => ...) -- whether a ring is F-injective
- isFInjective(..., IsLocal => ...) -- whether a ring is F-injective
- isFInjective(Ring) -- whether a ring is F-injective
- isFPure -- whether a ring is F-pure
- isFPure(..., FrobeniusRootStrategy => ...) -- whether a ring is F-pure
- isFPure(..., IsLocal => ...) -- whether a ring is F-pure
- isFPure(Ideal) -- whether a ring is F-pure
- isFPure(Ring) -- whether a ring is F-pure
- isFRational -- whether a ring is F-rational
- isFRational(..., AssumeCM => ...) -- whether a ring is F-rational
- isFRational(..., AssumeDomain => ...) -- whether a ring is F-rational
- isFRational(..., FrobeniusRootStrategy => ...) -- whether a ring is F-rational
- isFRational(..., IsLocal => ...) -- whether a ring is F-rational
- isFRational(Ring) -- whether a ring is F-rational
- isFRegular -- whether a ring or pair is strongly F-regular
- isFRegular(..., AssumeDomain => ...) -- whether a ring or pair is strongly F-regular
- isFRegular(..., DepthOfSearch => ...) -- whether a ring or pair is strongly F-regular
- isFRegular(..., FrobeniusRootStrategy => ...) -- whether a ring or pair is strongly F-regular
- isFRegular(..., IsLocal => ...) -- whether a ring or pair is strongly F-regular
- isFRegular(..., MaxCartierIndex => ...) -- whether a ring or pair is strongly F-regular
- isFRegular(..., QGorensteinIndex => ...) -- whether a ring or pair is strongly F-regular
- isFRegular(List,List) -- whether a ring or pair is strongly F-regular
- isFRegular(Number,RingElement) -- whether a ring or pair is strongly F-regular
- isFRegular(Ring) -- whether a ring or pair is strongly F-regular
- IsLocal -- an option used to specify whether to only work locally
- 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
- multiplicativeOrder(ZZ,ZZ) -- 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
- parameterTestIdeal(..., FrobeniusRootStrategy => ...) -- compute the parameter test ideal of a Cohen-Macaulay ring
- parameterTestIdeal(Ring) -- compute the parameter test ideal of a Cohen-Macaulay ring
- QGorensteinGenerator -- find an element representing the Frobenius trace map of a Q-Gorenstein ring
- QGorensteinGenerator(Ring) -- find an element representing the Frobenius trace map of a Q-Gorenstein ring
- QGorensteinGenerator(ZZ,Ring) -- 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
- testElement(..., AssumeDomain => ...) -- find a test element of a ring
- testElement(Ring) -- find a test element of a ring
- testIdeal -- compute a test ideal in a Q-Gorenstein ring
- testIdeal(..., AssumeDomain => ...) -- compute a test ideal in a Q-Gorenstein ring
- testIdeal(..., FrobeniusRootStrategy => ...) -- compute a test ideal in a Q-Gorenstein ring
- testIdeal(..., MaxCartierIndex => ...) -- compute a test ideal in a Q-Gorenstein ring
- testIdeal(..., QGorensteinIndex => ...) -- compute a test ideal in a Q-Gorenstein ring
- testIdeal(List,List) -- compute a test ideal in a Q-Gorenstein ring
- testIdeal(Number,RingElement) -- compute a test ideal in a Q-Gorenstein ring
- testIdeal(Ring) -- compute a test ideal in a Q-Gorenstein ring
- TestIdeals -- a package for calculations of singularities in positive characteristic
- testModule -- find the parameter test module of a reduced ring
- testModule(..., AssumeDomain => ...) -- find the parameter test module of a reduced ring
- testModule(..., CanonicalIdeal => ...) -- find the parameter test module of a reduced ring
- testModule(..., CurrentRing => ...) -- find the parameter test module of a reduced ring
- testModule(..., FrobeniusRootStrategy => ...) -- find the parameter test module of a reduced ring
- testModule(..., GeneratorList => ...) -- find the parameter test module of a reduced ring
- testModule(List,List) -- find the parameter test module of a reduced ring
- testModule(Number,RingElement) -- find the parameter test module of a reduced ring
- testModule(Ring) -- find the parameter test module of a reduced ring