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NumericalInterpolationTable -- the class of all NumericalInterpolationTables

Description

This is a type of hash table storing the output of a polynomial interpolation computation, with the following keys:

i1 : R = CC[x_(1,1)..x_(2,4)];
 
i2 : F = (minors(2, genericMatrix(R, 2, 4)))_*;
 
i3 : T = numericalHilbertFunction(F, ideal 0_R, 2, Verbose => false)

o3 = a "numerical interpolation table", indicating
     the space of degree 2 forms in the ideal of the image has dimension 1

o3 : NumericalInterpolationTable
 
i4 : (T.hilbertFunctionArgument, T.hilbertFunctionValue)

o4 = (2, 1)

o4 : Sequence

See also

Functions and methods returning a numerical interpolation table:

  • numericalHilbertFunction(List,Ideal,List,ZZ) -- see numericalHilbertFunction -- computes the values of the Hilbert function for the image of a variety
  • numericalHilbertFunction(List,Ideal,ZZ) -- see numericalHilbertFunction -- computes the values of the Hilbert function for the image of a variety
  • numericalHilbertFunction(Matrix,Ideal,List,ZZ) -- see numericalHilbertFunction -- computes the values of the Hilbert function for the image of a variety
  • numericalHilbertFunction(Matrix,Ideal,ZZ) -- see numericalHilbertFunction -- computes the values of the Hilbert function for the image of a variety
  • numericalHilbertFunction(RingMap,Ideal,List,ZZ) -- see numericalHilbertFunction -- computes the values of the Hilbert function for the image of a variety
  • numericalHilbertFunction(RingMap,Ideal,ZZ) -- see numericalHilbertFunction -- computes the values of the Hilbert function for the image of a variety

Methods that use a numerical interpolation table:

  • extractImageEquations(NumericalInterpolationTable) -- see extractImageEquations -- finds implicit equations in a fixed degree for the image of a variety
  • net(NumericalInterpolationTable)

For the programmer

The object NumericalInterpolationTable is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NumericalImplicitization/doc.m2:485:0.