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NumericalImplicitization : Index
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Z
AttemptZZ
-- finds implicit equations in a fixed degree for the image of a variety
ConvertToCone
-- specifies whether to convert image to a cone
DoRefinements
-- computes a pseudo-witness set for the image of a variety
DoTraceTest
-- computes a pseudo-witness set for the image of a variety
extractImageEquations
-- finds implicit equations in a fixed degree for the image of a variety
extractImageEquations(...,AttemptZZ=>...)
-- finds implicit equations in a fixed degree for the image of a variety
extractImageEquations(...,Threshold=>...)
-- finds implicit equations in a fixed degree for the image of a variety
extractImageEquations(List,Ideal,ZZ)
-- finds implicit equations in a fixed degree for the image of a variety
extractImageEquations(Matrix,Ideal,ZZ)
-- finds implicit equations in a fixed degree for the image of a variety
extractImageEquations(NumericalInterpolationTable)
-- finds implicit equations in a fixed degree for the image of a variety
extractImageEquations(RingMap,Ideal,ZZ)
-- finds implicit equations in a fixed degree for the image of a variety
generalCombinations
-- the class of all pseudo-witness sets
hilbertFunctionArgument
-- the class of all NumericalInterpolationTables
hilbertFunctionValue
-- the class of all NumericalInterpolationTables
imagePoints
-- the class of all NumericalInterpolationTables
imageSlice
-- the class of all pseudo-witness sets
Initial
-- samples a real point on a variety
interpolationBasis
-- the class of all NumericalInterpolationTables
interpolationMatrix
-- the class of all NumericalInterpolationTables
interpolationSVD
-- the class of all NumericalInterpolationTables
isCompletePseudoWitnessSet
-- the class of all pseudo-witness sets
isOnImage
-- tests whether a point lies on the image of a variety
isOnImage(...,MaxThreads=>...)
-- specifies the maximum number of processor threads
isOnImage(...,Software=>...)
-- specify software for homotopy continuation
isOnImage(...,Threshold=>...)
-- computes a pseudo-witness set for the image of a variety
isOnImage(...,Verbose=>...)
-- display detailed output
isOnImage(List,Ideal,Point)
-- tests whether a point lies on the image of a variety
isOnImage(Matrix,Ideal,Point)
-- tests whether a point lies on the image of a variety
isOnImage(PseudoWitnessSet,Point)
-- tests whether a point lies on the image of a variety
isOnImage(RingMap,Ideal,Point)
-- tests whether a point lies on the image of a variety
lineSearch
-- samples a real point on a variety
lineSearch(...,Iterations=>...)
-- samples a real point on a variety
lineSearch(...,Tolerance=>...)
-- samples a real point on a variety
lineSearch(Ideal,Matrix)
-- samples a real point on a variety
MaxAttempts
-- computes a pseudo-witness set for the image of a variety
MaxPoints
-- computes a pseudo-witness set for the image of a variety
MaxThreads
-- specifies the maximum number of processor threads
net(NumericalInterpolationTable)
-- the class of all NumericalInterpolationTables
net(PseudoWitnessSet)
-- the class of all pseudo-witness sets
numericalHilbertFunction
-- computes the values of the Hilbert function for the image of a variety
numericalHilbertFunction(...,ConvertToCone=>...)
-- specifies whether to convert image to a cone
numericalHilbertFunction(...,Precondition=>...)
-- computes numerical kernel dimension of a matrix
numericalHilbertFunction(...,Software=>...)
-- specify software for homotopy continuation
numericalHilbertFunction(...,SVDGap=>...)
-- computes numerical kernel dimension of a matrix
numericalHilbertFunction(...,UseSLP=>...)
-- computes the values of the Hilbert function for the image of a variety
numericalHilbertFunction(...,Verbose=>...)
-- display detailed output
numericalHilbertFunction(List,Ideal,List,ZZ)
-- computes the values of the Hilbert function for the image of a variety
numericalHilbertFunction(List,Ideal,ZZ)
-- computes the values of the Hilbert function for the image of a variety
numericalHilbertFunction(Matrix,Ideal,List,ZZ)
-- computes the values of the Hilbert function for the image of a variety
numericalHilbertFunction(Matrix,Ideal,ZZ)
-- computes the values of the Hilbert function for the image of a variety
numericalHilbertFunction(RingMap,Ideal,List,ZZ)
-- computes the values of the Hilbert function for the image of a variety
numericalHilbertFunction(RingMap,Ideal,ZZ)
-- computes the values of the Hilbert function for the image of a variety
numericalImageDegree
-- computes the degree of the image of a variety
numericalImageDegree(...,DoRefinements=>...)
-- computes a pseudo-witness set for the image of a variety
numericalImageDegree(...,DoTraceTest=>...)
-- computes a pseudo-witness set for the image of a variety
numericalImageDegree(...,MaxAttempts=>...)
-- computes a pseudo-witness set for the image of a variety
numericalImageDegree(...,MaxPoints=>...)
-- computes a pseudo-witness set for the image of a variety
numericalImageDegree(...,MaxThreads=>...)
-- specifies the maximum number of processor threads
numericalImageDegree(...,Repeats=>...)
-- computes a pseudo-witness set for the image of a variety
numericalImageDegree(...,Software=>...)
-- specify software for homotopy continuation
numericalImageDegree(...,Threshold=>...)
-- computes a pseudo-witness set for the image of a variety
numericalImageDegree(...,TraceThreshold=>...)
-- computes a pseudo-witness set for the image of a variety
numericalImageDegree(...,Verbose=>...)
-- display detailed output
numericalImageDegree(List,Ideal)
-- computes the degree of the image of a variety
numericalImageDegree(Matrix,Ideal)
-- computes the degree of the image of a variety
numericalImageDegree(PseudoWitnessSet)
-- computes the degree of the image of a variety
numericalImageDegree(RingMap,Ideal)
-- computes the degree of the image of a variety
numericalImageDim
-- computes the dimension of the image of a variety
numericalImageDim(...,Software=>...)
-- specify software for homotopy continuation
numericalImageDim(List,Ideal)
-- computes the dimension of the image of a variety
numericalImageDim(List,Ideal,Point)
-- computes the dimension of the image of a variety
numericalImageDim(Matrix,Ideal)
-- computes the dimension of the image of a variety
numericalImageDim(Matrix,Ideal,Point)
-- computes the dimension of the image of a variety
numericalImageDim(RingMap,Ideal)
-- computes the dimension of the image of a variety
numericalImageDim(RingMap,Ideal,Point)
-- computes the dimension of the image of a variety
numericalImageSample
-- samples general points on the image of a variety
numericalImageSample(...,Software=>...)
-- specify software for homotopy continuation
numericalImageSample(List,Ideal)
-- samples general points on the image of a variety
numericalImageSample(List,Ideal,List,ZZ)
-- samples general points on the image of a variety
numericalImageSample(List,Ideal,ZZ)
-- samples general points on the image of a variety
numericalImageSample(Matrix,Ideal)
-- samples general points on the image of a variety
numericalImageSample(Matrix,Ideal,List,ZZ)
-- samples general points on the image of a variety
numericalImageSample(Matrix,Ideal,ZZ)
-- samples general points on the image of a variety
numericalImageSample(RingMap,Ideal)
-- samples general points on the image of a variety
numericalImageSample(RingMap,Ideal,List,ZZ)
-- samples general points on the image of a variety
numericalImageSample(RingMap,Ideal,ZZ)
-- samples general points on the image of a variety
NumericalImplicitization
-- implicitization using numerical algebraic geometry
NumericalInterpolationTable
-- the class of all NumericalInterpolationTables
numericalNullity
-- computes numerical kernel dimension of a matrix
numericalNullity(...,Precondition=>...)
-- computes numerical kernel dimension of a matrix
numericalNullity(...,SVDGap=>...)
-- computes numerical kernel dimension of a matrix
numericalNullity(...,Verbose=>...)
-- display detailed output
numericalNullity(List,Boolean)
-- computes numerical kernel dimension of a matrix
numericalNullity(Matrix)
-- computes numerical kernel dimension of a matrix
numericalNullity(Matrix,Boolean)
-- computes numerical kernel dimension of a matrix
numericalSourceSample
-- samples a general point on a variety
numericalSourceSample(...,Software=>...)
-- specify software for homotopy continuation
numericalSourceSample(Ideal)
-- samples a general point on a variety
numericalSourceSample(Ideal,Point)
-- samples a general point on a variety
numericalSourceSample(Ideal,Thing,ZZ)
-- samples a general point on a variety
numericalSourceSample(Ideal,WitnessSet)
-- samples a general point on a variety
numericalSourceSample(Ideal,ZZ)
-- samples a general point on a variety
optimizeNelderMead
-- samples a real point on a variety
optimizeNelderMead(...,Initial=>...)
-- samples a real point on a variety
optimizeNelderMead(...,Iterations=>...)
-- samples a real point on a variety
optimizeNelderMead(...,Tolerance=>...)
-- samples a real point on a variety
optimizeNelderMead(FunctionClosure,List)
-- samples a real point on a variety
optimizeNelderMead(Ideal)
-- samples a real point on a variety
Precondition
-- computes numerical kernel dimension of a matrix
PseudoWitnessSet
-- the class of all pseudo-witness sets
pseudoWitnessSet
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(...,DoRefinements=>...)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(...,DoTraceTest=>...)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(...,MaxAttempts=>...)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(...,MaxPoints=>...)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(...,MaxThreads=>...)
-- specifies the maximum number of processor threads
pseudoWitnessSet(...,Repeats=>...)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(...,Software=>...)
-- specify software for homotopy continuation
pseudoWitnessSet(...,Threshold=>...)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(...,TraceThreshold=>...)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(...,Verbose=>...)
-- display detailed output
pseudoWitnessSet(List,Ideal)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(List,Ideal,List,Thing)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(List,Ideal,Point)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(Matrix,Ideal)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(Matrix,Ideal,List,Thing)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(Matrix,Ideal,Point)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(RingMap,Ideal)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(RingMap,Ideal,List,Thing)
-- computes a pseudo-witness set for the image of a variety
pseudoWitnessSet(RingMap,Ideal,Point)
-- computes a pseudo-witness set for the image of a variety
realPoint
-- samples a real point on a variety
realPoint(...,Initial=>...)
-- samples a real point on a variety
realPoint(...,Iterations=>...)
-- samples a real point on a variety
realPoint(...,Tolerance=>...)
-- samples a real point on a variety
realPoint(Ideal)
-- samples a real point on a variety
Repeats
-- computes a pseudo-witness set for the image of a variety
sourceEquations
-- the class of all pseudo-witness sets
sourceSlice
-- the class of all pseudo-witness sets
SVDGap
-- computes numerical kernel dimension of a matrix
TraceThreshold
-- computes a pseudo-witness set for the image of a variety
UseSLP
-- computes the values of the Hilbert function for the image of a variety
witnessPointPairs
-- the class of all pseudo-witness sets