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
• 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
• 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
• 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
• frobeniusPreimage -- finds the ideal of elements mapped into a given ideal, under all $p^{-e}$-linear maps
• frobeniusPreimage(ZZ,Ideal) -- finds the ideal of elements mapped into a given ideal, under all $p^{-e}$-linear maps
• 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(...,AtOrigin=>...) -- 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(...,AtOrigin=>...) -- whether a ring is F-injective
• isFInjective(...,CanonicalStrategy=>...) -- whether a ring is F-injective
• isFInjective(...,FrobeniusRootStrategy=>...) -- whether a ring is F-injective
• isFInjective(Ring) -- whether a ring is F-injective
• isFPure -- whether a ring is F-pure
• isFPure(...,AtOrigin=>...) -- whether a ring is F-pure
• isFPure(...,FrobeniusRootStrategy=>...) -- 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(...,AtOrigin=>...) -- whether a ring is F-rational
• isFRational(...,FrobeniusRootStrategy=>...) -- 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(...,AtOrigin=>...) -- 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(...,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
• 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