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NoetherianOperators : Index
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AllVisible
-- numerically determine if the point is an embedded component of the scheme
amult
-- Computes the arithmetic multiplicity of a module
amult(Ideal)
-- Computes the arithmetic multiplicity of a module
amult(Module)
-- Computes the arithmetic multiplicity of a module
colon
-- colon of a (truncated) dual space
colon(...,Tolerance=>...)
-- colon of a (truncated) dual space
colon(DualSpace,Ideal)
-- colon of a (truncated) dual space
colon(DualSpace,RingElement)
-- colon of a (truncated) dual space
coordinateChangeOps
-- induced Noetherian operators under coordinate change
coordinateChangeOps(Matrix,DiffOp)
-- induced Noetherian operators under coordinate change
coordinateChangeOps(Matrix,List)
-- induced Noetherian operators under coordinate change
coordinateChangeOps(RingMap,DiffOp)
-- induced Noetherian operators under coordinate change
coordinateChangeOps(RingMap,List)
-- induced Noetherian operators under coordinate change
DependentSet
-- option for computing Noetherian operators
differentialPrimaryDecomposition
-- compute a differential primary decomposition
differentialPrimaryDecomposition(Ideal)
-- compute a differential primary decomposition
differentialPrimaryDecomposition(Module)
-- compute a differential primary decomposition
DiffOp
-- differential operator
diffOp
-- create a differential operator
DiffOp Matrix
-- apply a differential operator
DiffOp RingElement
-- apply a differential operator
diffOp(Matrix)
-- create a differential operator
diffOp(RingElement)
-- create a differential operator
diffOpRing
-- create and cache the ring of differential operators
eliminatingDual
-- eliminating dual space of a polynomial ideal
eliminatingDual(...,Tolerance=>...)
-- optional argument for numerical tolerance
eliminatingDual(AbstractPoint,Ideal,List,ZZ)
-- eliminating dual space of a polynomial ideal
eliminatingDual(AbstractPoint,Matrix,List,ZZ)
-- eliminating dual space of a polynomial ideal
evaluate(DiffOp,AbstractPoint)
-- evaluate coefficients of a differential operator
evaluate(DiffOp,Matrix)
-- evaluate coefficients of a differential operator
gCorners
-- generators of the initial ideal of a polynomial ideal
gCorners(...,StandardBasis=>...)
-- generators of the initial ideal of a polynomial ideal
gCorners(...,Tolerance=>...)
-- optional argument for numerical tolerance
gCorners(AbstractPoint,Ideal)
-- generators of the initial ideal of a polynomial ideal
gCorners(AbstractPoint,Matrix)
-- 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
getIdealFromNoetherianOperators(List,Ideal)
-- Computes a primary ideal corresponding to a list of Noetherian operators and a prime ideal
getModuleFromNoetherianOperators
-- Computes a primary submodule corresponding to a list of Noetherian operators and a prime ideal
getModuleFromNoetherianOperators(Ideal,List)
-- Computes a primary submodule corresponding to a list of Noetherian operators and a prime ideal
hilbertFunction(DualSpace)
hilbertFunction(List,DualSpace)
hilbertFunction(ZZ,DualSpace)
IntegralStrategy
-- strategy for computing Noetherian operators
InterpolationDegreeLimit
-- Noetherian operators via numerical interpolation
InterpolationTolerance
-- Noetherian operators via numerical interpolation
isPointEmbedded
-- numerically determine if the point is an embedded component of the scheme
isPointEmbedded(...,AllVisible=>...)
-- numerically determine if the point is an embedded component of the scheme
isPointEmbedded(AbstractPoint,Ideal,List)
-- numerically determine if the point is an embedded component of the scheme
isPointEmbeddedInCurve
-- numerically determine if the point is an embedded component of a 1-dimensional scheme
isPointEmbeddedInCurve(...,Regularity=>...)
-- numerically determine if the point is an embedded component of a 1-dimensional scheme
isPointEmbeddedInCurve(AbstractPoint,Ideal)
-- numerically determine if the point is an embedded component of a 1-dimensional scheme
joinIdeals
-- Computes the join of two ideals
joinIdeals(Ideal,Ideal)
-- Computes the join of two ideals
KernelStrategy
-- strategy for computing Noetherian operators
localHilbertRegularity
-- regularity of the local Hilbert function of a polynomial ideal
localHilbertRegularity(...,Tolerance=>...)
-- optional argument for numerical tolerance
localHilbertRegularity(AbstractPoint,Ideal)
-- regularity of the local Hilbert function of a polynomial ideal
localHilbertRegularity(AbstractPoint,Matrix)
-- regularity of the local Hilbert function of a polynomial ideal
mapToPunctualHilbertScheme
-- maps an ideal into a point in a certain punctual Hilbert scheme
mapToPunctualHilbertScheme(Ideal)
-- maps an ideal into a point in a certain punctual Hilbert scheme
NoetherianDegreeLimit
-- Noetherian operators via numerical interpolation
NoetherianOperators
-- algorithms for computing local dual spaces and sets of Noetherian operators
noetherianOperators
-- Noetherian operators
noetherianOperators(Ideal)
-- Noetherian operators of a primary ideal
noetherianOperators(Ideal,Ideal)
-- Noetherian operators of a primary component
noetherianOperators(Module)
-- Noetherian operators of a primary submodule
noetherianOperators(Module,Ideal)
-- Noetherian operators of a primary component
noethOpsFromComponents
-- merge Noetherian operators for non-primary ideals
noethOpsFromComponents(List)
-- merge Noetherian operators for non-primary ideals
normalize
-- rescale a differential operator
normalize(DiffOp)
-- rescale a differential operator
numericalNoetherianOperators
-- Noetherian operators via numerical interpolation
numericalNoetherianOperators(Ideal)
-- Noetherian operators via numerical interpolation
orthogonalInSubspace
-- Orthogonal of a space
orthogonalInSubspace(DualSpace,PolySpace,Number)
-- Orthogonal of a space
orthogonalInSubspace(PolySpace,PolySpace,Number)
-- Orthogonal of a space
pairingMatrix
-- Applies dual space functionals to polynomials
pairingMatrix(PolySpace,DualSpace)
-- Applies dual space functionals to polynomials
pairingMatrix(PolySpace,PolySpace)
-- Applies dual space functionals to polynomials
pairingMatrix(PolySpace,RingElement)
-- Applies dual space functionals to polynomials
pairingMatrix(RingElement,DualSpace)
-- Applies dual space functionals to polynomials
pairingMatrix(RingElement,RingElement)
-- Applies dual space functionals to polynomials
Rational
-- Noetherian operators of a primary component
rationalInterpolation
-- numerically interpolate rational functions
rationalInterpolation(...,Tolerance=>...)
-- optional argument for numerical tolerance
rationalInterpolation(List,List,Matrix)
-- numerically interpolate rational functions
rationalInterpolation(List,List,Matrix,Matrix)
-- numerically interpolate rational functions
rationalInterpolation(List,List,Ring)
-- numerically interpolate rational functions
Regularity
-- numerically determine if the point is an embedded component of a 1-dimensional scheme
Sampler
-- optional sampler function
solvePDE
-- solve linear systems of PDE with constant coefficients
solvePDE(Ideal)
-- solve linear systems of PDE with constant coefficients
solvePDE(Matrix)
-- solve linear systems of PDE with constant coefficients
solvePDE(Module)
-- solve linear systems of PDE with constant coefficients
specializedNoetherianOperators
-- Noetherian operators evaluated at a point
specializedNoetherianOperators(Ideal,AbstractPoint)
-- Noetherian operators evaluated at a point
specializedNoetherianOperators(Ideal,Matrix)
-- Noetherian operators evaluated at a point
StandardBasis
-- generators of the initial ideal of a polynomial ideal
Strategy => "Hybrid"
-- strategy for computing Noetherian operators
Strategy => "MacaulayMatrix"
-- strategy for computing Noetherian operators
Strategy => "PunctualQuot"
-- strategy for computing Noetherian operators
Tolerance (NoetherianOperators)
-- optional argument for numerical tolerance
truncate(DualSpace,List,ZZ)
-- truncate a polynomial space or dual space
truncate(DualSpace,ZZ)
-- truncate a polynomial space or dual space
truncate(PolySpace,List,ZZ)
-- truncate a polynomial space or dual space
truncate(PolySpace,ZZ)
-- truncate a polynomial space or dual space
truncatedDual
-- truncated dual space of a polynomial ideal
truncatedDual(...,Tolerance=>...)
-- optional argument for numerical tolerance
truncatedDual(AbstractPoint,Ideal,ZZ)
-- truncated dual space of a polynomial ideal
truncatedDual(AbstractPoint,Matrix,ZZ)
-- truncated dual space of a polynomial ideal
truncatedDual(Matrix,Ideal,ZZ)
-- truncated dual space of a polynomial ideal
truncatedDual(Matrix,Matrix,ZZ)
-- truncated dual space of a polynomial ideal
TrustedPoint
-- Noetherian operators via numerical interpolation
zeroDimensionalDual
-- dual space of a zero-dimensional polynomial ideal
zeroDimensionalDual(...,Tolerance=>...)
-- optional argument for numerical tolerance
zeroDimensionalDual(AbstractPoint,Ideal)
-- dual space of a zero-dimensional polynomial ideal
zeroDimensionalDual(AbstractPoint,Matrix)
-- dual space of a zero-dimensional polynomial ideal
zeroDimensionalDual(Matrix,Ideal)
-- dual space of a zero-dimensional polynomial ideal
zeroDimensionalDual(Matrix,Matrix)
-- dual space of a zero-dimensional polynomial ideal