LocalRings : Index

• baseRing(LocalRing) -- produce the ring from which a ring was formed
• char(LocalRing) -- computes the characteristic of the ring or field
• coefficientRing(LocalRing) -- get the coefficient ring
• degreeLength(LocalRing) -- the length of the degree vector
• degrees(LocalRing) -- degrees of generators
• dim(LocalRing) -- compute the Krull dimension
• frac(LocalRing) -- construct a fraction field
• generators(LocalRing) -- the list of generators of a ring
• hilbertSamuelFunction -- Computes the Hilbert-Samuel Function of Modules over Local Rings
• hilbertSamuelFunction(Ideal,Module,ZZ) -- Computes the Hilbert-Samuel Function of Modules over Local Rings
• hilbertSamuelFunction(Ideal,Module,ZZ,ZZ) -- Computes the Hilbert-Samuel Function of Modules over Local Rings
• hilbertSamuelFunction(Module,ZZ) -- Computes the Hilbert-Samuel Function of Modules over Local Rings
• hilbertSamuelFunction(Module,ZZ,ZZ) -- Computes the Hilbert-Samuel Function of Modules over Local Rings
• isCommutative(LocalRing) -- whether a ring is commutative
• isWellDefined(LocalRing) -- whether a local ring is well defined
• liftUp -- Lifts various objects over R_P to R.
• liftUp(Ideal,Ring) -- Lifts various objects over R_P to R.
• liftUp(Matrix,Ring) -- Lifts various objects over R_P to R.
• liftUp(Module,Ring) -- Lifts various objects over R_P to R.
• liftUp(MutableMatrix,Ring) -- Lifts various objects over R_P to R.
• liftUp(RingElement,Ring) -- Lifts various objects over R_P to R.
• liftUp(Thing) -- Lifts various objects over R_P to R.
• localComplement -- find the splitting of the target of a map
• localComplement(Matrix) -- find the splitting of the target of a map
• localMingens -- finds a minimal set of generators
• localMingens(Matrix) -- finds a minimal set of generators
• localModulo -- find the pre-image (pullback) of image of a map over a local ring
• localModulo(Matrix,Matrix) -- find the pre-image (pullback) of image of a map over a local ring
• localPrune -- find a minimal presentation
• localPrune(Module) -- find a minimal presentation
• localResolution -- find a resolution over a local ring
• localResolution(...,DegreeLimit=>...) -- find a resolution over a local ring
• localResolution(...,FastNonminimal=>...) -- find a resolution over a local ring
• localResolution(...,HardDegreeLimit=>...) -- find a resolution over a local ring
• localResolution(...,LengthLimit=>...) -- find a resolution over a local ring
• localResolution(...,PairLimit=>...) -- find a resolution over a local ring
• localResolution(...,SortStrategy=>...) -- find a resolution over a local ring
• localResolution(...,StopBeforeComputation=>...) -- find a resolution over a local ring
• localResolution(...,Strategy=>...) -- find a resolution over a local ring
• localResolution(...,SyzygyLimit=>...) -- find a resolution over a local ring
• localResolution(Ideal) -- find a resolution over a local ring
• localResolution(Module) -- find a resolution over a local ring
• LocalRing -- The class of all local rings
• localRing -- Constructor for local rings
• localRing(EngineRing,Ideal) -- Constructor for local rings
• localRing(Ring,Ideal) -- Constructor for local rings
• LocalRings -- Localizations of polynomial rings at prime ideals
• localsyz -- find syzygies
• localsyz(Matrix) -- find syzygies
• max(LocalRing) -- The class of all local rings
• maxIdeal -- The class of all local rings
• numgens(LocalRing) -- number of generators of a polynomial ring
• PolynomialRing _ Ideal -- Constructor for local rings
• PolynomialRing _ RingElement -- Constructor for local rings
• replacements for functions from version 1.0
• residueMap -- The class of all local rings
• setMaxIdeal -- set the maximal ideal for local ring methods
• setMaxIdeal(Ideal) -- set the maximal ideal for local ring methods