NoetherianOperators : Table of Contents

• NoetherianOperators -- algorithms for computing local dual spaces and sets of Noetherian operators
• - DiffOp -- negation of differential operators
• colon -- colon of a (truncated) dual space
• coordinateChangeOps -- induced Noetherian operators under coordinate change
• DependentSet -- option for computing Noetherian operators
• DiffOp -- differential operator
• diffOp -- create a differential operator
• DiffOp + DiffOp -- addition of differential operators
• DiffOp - DiffOp -- subtraction of differential operators
• DiffOp ? DiffOp -- comparison of differential operators
• DiffOp RingElement -- apply a differential operator
• diffOp(HashTable) -- create a differential operator
• diffOp(Ring,RingElement) -- create a differential operator from a Weyl algebra element
• eliminatingDual -- eliminating dual space of a polynomial ideal
• evaluate(DiffOp,Point) -- evaluate coefficients of a differential operator
• gCorners -- generators of the initial ideal of a polynomial ideal
• getIdealFromNoetherianOperators -- Computes a primary ideal corresponding to a list of Noetherian operators and a prime ideal
• hilbertFunction(ZZ,DualSpace)
• innerProduct -- Applies dual space functionals to polynomials
• InterpolatedDiffOp -- differential operator with interpolated coefficients
• isPointEmbedded(Point,Ideal,List) -- determine if the point is an embedded component of the scheme
• isPointEmbeddedInCurve(Point,Ideal) -- determine if the point is an embedded component of a 1-dimensional scheme
• joinIdeals -- Computes the join of two ideals
• localHilbertRegularity -- regularity of the local Hilbert function of a polynomial ideal
• mapToPunctualHilbertScheme -- maps an ideal into a point in a certain punctual Hilbert scheme
• noetherianOperators -- Noetherian operators
• noetherianOperators(Ideal) -- Noetherian operators of a primary ideal
• noetherianOperators(Ideal,Ideal) -- Noetherian operators of a primary component
• noethOpsFromComponents -- merge Noetherian operators for non-primary ideals
• normalize -- rescale a differential operator to a canonical form
• numericalNoetherianOperators -- Noetherian operators via numerical interpolation
• orthogonalInSubspace -- Orthogonal of a space
• rationalInterpolation -- numerically interpolate rational functions
• rationalInterpolation(List,List,Ring) -- numerically interpolate rational functions
• ring(DiffOp) -- get the ring associated to a differential operator
• RingElement * DiffOp -- scaling of differential operators
• Sampler -- optional sampler function
• specializedNoetherianOperators -- Noetherian operators evaluated at a point
• Strategy => "Hybrid" -- strategy for computing Noetherian operators
• Strategy => "MacaulayMatrix" -- strategy for computing Noetherian operators
• Strategy => "PunctualHilbert" -- strategy for computing Noetherian operators
• substitute(DiffOp,Ring) -- change the ring of a differential operator
• Tolerance (NoetherianOperators) -- optional argument for numerical tolernace
• truncate(DualSpace,List,ZZ) -- truncate a polynomial space or dual space
• truncate(DualSpace,ZZ) -- truncate a polynomial space or dual space
• truncatedDual -- truncated dual space of a polynomial ideal
• ZeroDiffOp -- the zero differential operator of a ring
• zeroDimensionalDual -- dual space of a zero-dimensional polynomial ideal