TestIdeals : Index
- adicDigit -- digit of the non-terminating expansion of a number in [0,1] in a given base
- adicDigit(ZZ,ZZ,List) -- digit of the non-terminating expansion of a number in [0,1] in a given base
- adicDigit(ZZ,ZZ,QQ) -- digit of the non-terminating expansion of a number in [0,1] in a given base
- adicDigit(ZZ,ZZ,ZZ) -- digit of the non-terminating expansion of a number in [0,1] 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 -- finds the smallest phi-stable ideal containing a given ideal in a quotient of a polynomial ring.
- ascendIdeal(..., AscentCount => ...) -- return how many times it took before the ascent of the ideal stabilized
- ascendIdeal(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- ascendIdeal(ZZ,BasicList,BasicList,Ideal) -- finds the smallest phi-stable ideal containing a given ideal in a quotient of a polynomial ring.
- ascendIdeal(ZZ,RingElement,Ideal) -- finds the smallest phi-stable ideal containing a given ideal in a quotient of a polynomial ring.
- ascendIdeal(ZZ,ZZ,RingElement,Ideal) -- finds the smallest phi-stable ideal containing a given ideal in a quotient of a polynomial ring.
- AscentCount -- an option for ascendIdeal
- AssumeCM -- make assumptions about your ring
- AssumeDomain -- an option to assume a ring is a domain
- AssumeNormal -- make assumptions about your ring
- AssumeReduced -- make assumptions about your ring
- canonicalIdeal -- given a ring, produces an ideal isomorphic to the canonical module
- canonicalIdeal(..., MTries => ...) -- how many times to try to embed a canonical module as an ideal
- canonicalIdeal(Ring) -- given a ring, produces an ideal isomorphic to the canonical module
- CanonicalStrategy -- an option for isFinjective
- compatibleIdeals -- finds all ideals compatibly Frobenius split ideals
- compatibleIdeals(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- compatibleIdeals(RingElement) -- finds all ideals compatibly Frobenius split ideals
- decomposeFraction -- decompose a rational number into a/(p^b(p^c-1))
- decomposeFraction(..., NoZeroC => ...) -- decompose a rational number into a/p^b(p^c-1) and force c not equal to zero
- decomposeFraction(ZZ,QQ) -- decompose a rational number into a/(p^b(p^c-1))
- decomposeFraction(ZZ,ZZ) -- decompose a rational number into a/(p^b(p^c-1))
- fastExponentiation -- computes powers of elements in rings of positive characteristic quickly
- fastExponentiation(ZZ,RingElement) -- computes powers of elements in rings of positive characteristic quickly
- floorLog -- floor of a logarithm
- floorLog(ZZ,ZZ) -- floor of a logarithm
- frobenius -- computes Frobenius powers of ideals and matrices
- frobenius(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- frobeniusPower -- computes the (generalized) Frobenius power of an ideal
- frobeniusPower(..., FrobeniusPowerStrategy => ...) -- control strategy for frobeniusPower
- frobeniusPower(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- frobeniusPower(QQ,Ideal) -- computes the (generalized) Frobenius power of an ideal
- frobeniusPower(ZZ,Ideal) -- computes the (generalized) Frobenius power of an ideal
- FrobeniusPowerStrategy -- an option for frobeniusPower
- frobeniusRoot -- computes I^[1/p^e] in a polynomial ring over a perfect field
- frobeniusRoot(..., FrobeniusRootStrategy => ...) -- controls what strategy Frobenius root uses.
- frobeniusRoot(ZZ,Ideal) -- computes I^[1/p^e] in a polynomial ring over a perfect field
- frobeniusRoot(ZZ,List,List) -- computes I^[1/p^e] in a polynomial ring over a perfect field
- frobeniusRoot(ZZ,List,List,Ideal) -- computes I^[1/p^e] in a polynomial ring over a perfect field
- frobeniusRoot(ZZ,Matrix) -- computes I^[1/p^e] in a polynomial ring over a perfect field
- frobeniusRoot(ZZ,MonomialIdeal) -- computes I^[1/p^e] in a polynomial ring over a perfect field
- frobeniusRoot(ZZ,ZZ,Ideal) -- computes I^[1/p^e] in a polynomial ring over a perfect field
- frobeniusRoot(ZZ,ZZ,RingElement) -- computes I^[1/p^e] in a polynomial ring over a perfect field
- frobeniusRoot(ZZ,ZZ,RingElement,Ideal) -- computes I^[1/p^e] in a polynomial ring over a perfect field
- FrobeniusRootStrategy -- an option for various functions
- frobeniusTraceOnCanonicalModule -- finds the u, which in a polynomail ring, determines the Frobenius trace on canonical module of a quotient of that ring
- HSLGModule -- computes the submodule of the canonical module stable under the image of the trace of Frobenius
- HSLGModule(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- HSLGModule(Ideal) -- computes the submodule of the canonical module stable under the image of the trace of Frobenius
- HSLGModule(List,List) -- computes the submodule of the canonical module stable under the image of the trace of Frobenius
- HSLGModule(QQ,RingElement) -- computes the submodule of the canonical module stable under the image of the trace of Frobenius
- HSLGModule(Ring) -- computes the submodule of the canonical module stable under the image of the trace of Frobenius
- HSLGModule(Ring,Ideal) -- computes the submodule of the canonical module stable under the image of the trace of Frobenius
- HSLGModule(ZZ,List,List,Ideal) -- computes the submodule of the canonical module stable under the image of the trace of Frobenius
- HSLGModule(ZZ,RingElement) -- computes the submodule of the canonical module stable under the image of the trace of Frobenius
- isCohenMacaulay -- determines if a ring is Cohen-Macaulay
- isCohenMacaulay(..., IsLocal => ...) -- determines if a ring is Cohen-Macaulay
- isCohenMacaulay(Ring) -- determines if a ring is Cohen-Macaulay
- isFinjective -- whether a ring is F-injective
- isFinjective(..., AssumeCM => ...) -- assumptions to speed up the computation of isFinjective
- isFinjective(..., AssumeNormal => ...) -- assumptions to speed up the computation of isFinjective
- isFinjective(..., AssumeReduced => ...) -- assumptions to speed up the computation of isFinjective
- isFinjective(..., CanonicalStrategy => ...) -- specify a strategy for isFinjective
- isFinjective(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- isFinjective(..., IsLocal => ...) -- controls whether F-injectivity is checked at the origin or everywhere
- isFinjective(Ring) -- whether a ring is F-injective
- isFpure -- whether a ring is F-pure
- isFpure(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- isFpure(..., IsLocal => ...) -- controls whether F-purity is checked at the origin or everywhere
- 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(..., 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(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- isFregular(..., IsLocal => ...) -- controls whether F-regularity is checked at the origin or everywhere
- isFregular(..., MaxCartierIndex => ...) -- sets the maximum Gorenstein index to search for when working with a Q-Gorenstein ambient ring
- isFregular(..., QGorensteinIndex => ...) -- specifies the Q-Gorenstein index of the ring
- isFregular(List,List) -- whether a ring or pair is strongly F-regular
- isFregular(QQ,RingElement) -- whether a ring or pair is strongly F-regular
- isFregular(Ring) -- whether a ring or pair is strongly F-regular
- isFregular(ZZ,RingElement) -- 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 used to specify the maximum possible Cartier index of a divisor
- MonomialBasis -- a valid value for the FrobeniusRootStrategy option
- MTries -- an option to pass through to embedAsIdeal
- 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 -- computes the parameter test ideal of a Cohen-Macaulay ring
- parameterTestIdeal(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- parameterTestIdeal(Ring) -- computes the parameter test ideal of a Cohen-Macaulay ring
- QGorensteinGenerator -- finds an element representing the Frobenius trace map of a Q-Gorenstein ring
- QGorensteinGenerator(Ring) -- finds an element representing the Frobenius trace map of a Q-Gorenstein ring
- QGorensteinGenerator(ZZ,Ring) -- finds an element representing the Frobenius trace map of a Q-Gorenstein ring
- QGorensteinIndex -- an option used to specify the Q-Gorenstein index of the ring
- Safe -- a valid value for the option FrobeniusPowerStrategy
- Substitution -- a valid value for the FrobeniusRootStrategy option
- testElement -- finds a test element of a ring
- testElement(..., AssumeDomain => ...) -- assumes the ring is a domain when finding a test element
- testElement(Ring) -- finds a test element of a ring
- testIdeal -- computes the test ideal of f^t in a Q-Gorenstein ring
- testIdeal(..., AssumeDomain => ...) -- assume the ring is a domain
- testIdeal(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- testIdeal(..., MaxCartierIndex => ...) -- sets the maximum Gorenstein index to search for when working with a Q-Gorenstein ambient ring
- testIdeal(..., QGorensteinIndex => ...) -- specifies the Q-Gorenstein index of the ring
- testIdeal(List,List) -- computes the test ideal of f^t in a Q-Gorenstein ring
- testIdeal(List,List,Ring) -- computes the test ideal of f^t in a Q-Gorenstein ring
- testIdeal(QQ,RingElement) -- computes the test ideal of f^t in a Q-Gorenstein ring
- testIdeal(QQ,RingElement,Ring) -- computes the test ideal of f^t in a Q-Gorenstein ring
- testIdeal(Ring) -- computes the test ideal of f^t in a Q-Gorenstein ring
- testIdeal(ZZ,RingElement) -- computes the test ideal of f^t in a Q-Gorenstein ring
- testIdeal(ZZ,RingElement,Ring) -- computes the test ideal of f^t in a Q-Gorenstein ring
- TestIdeals -- a package for calculations of singularities in positive characteristic
- testModule -- finds the parameter test module of a reduced ring
- testModule(..., AssumeDomain => ...) -- assume the ring is a domain
- testModule(..., FrobeniusRootStrategy => ...) -- controls the strategy for computing the Frobenius root of an ideal within other call
- testModule(List,List) -- finds the parameter test module of a reduced ring
- testModule(List,List,Ideal,List) -- finds the parameter test module of a reduced ring
- testModule(QQ,RingElement) -- finds the parameter test module of a reduced ring
- testModule(QQ,RingElement,Ideal,List) -- finds the parameter test module of a reduced ring
- testModule(Ring) -- finds the parameter test module of a reduced ring
- testModule(Ring,Ideal) -- finds the parameter test module of a reduced ring
- testModule(ZZ,RingElement) -- finds the parameter test module of a reduced ring