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