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NoetherianOperators : Table of Contents
NoetherianOperators
-- algorithms for computing local dual spaces and sets of Noetherian operators
amult
-- Computes the arithmetic multiplicity of a module
colon
-- colon of a (truncated) dual space
coordinateChangeOps
-- induced Noetherian operators under coordinate change
DependentSet
-- option for computing Noetherian operators
differentialPrimaryDecomposition
-- compute a differential primary decomposition
DiffOp
-- differential operator
diffOp
-- create a differential operator
DiffOp Matrix
-- apply a differential operator
diffOp(Matrix)
-- create a differential operator
diffOpRing
-- create and cache the ring of differential operators
eliminatingDual
-- eliminating dual space of a polynomial ideal
evaluate(DiffOp,AbstractPoint)
-- 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
getModuleFromNoetherianOperators
-- Computes a primary submodule corresponding to a list of Noetherian operators and a prime ideal
hilbertFunction(ZZ,DualSpace)
isPointEmbedded(AbstractPoint,Ideal,List)
-- numerically determine if the point is an embedded component of the 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
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
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
normalize
-- rescale a differential operator
numericalNoetherianOperators
-- Noetherian operators via numerical interpolation
orthogonalInSubspace
-- Orthogonal of a space
pairingMatrix
-- Applies dual space functionals to polynomials
rationalInterpolation
-- numerically interpolate rational functions
rationalInterpolation(List,List,Ring)
-- numerically interpolate rational functions
Sampler
-- optional sampler function
solvePDE(Module)
-- solve linear systems of PDE with constant coefficients
specializedNoetherianOperators
-- Noetherian operators evaluated at a point
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
truncatedDual
-- truncated dual space of a polynomial ideal
zeroDimensionalDual
-- dual space of a zero-dimensional polynomial ideal