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NumericalImplicitization :: NumericalInterpolationTable

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:

  • hilbertFunctionArgument: the argument, d, to the Hilbert function
  • hilbertFunctionValue: the value of the Hilbert function at d
  • imagePoints: a (vertical) list of sample points on the image
  • interpolationBasis: a matrix consisting of the degree d monomials
  • interpolationSVD: the singular value decomposition of the interpolation matrix
  • interpolationMatrix: the matrix obtained by evaluating degree d monomials at the sample points
  • map: the map F, of which the image is under consideration
i1 : R = CC[x_(1,1)..x_(3,5)];
i2 : F = (minors(3, genericMatrix(R, 3, 5)))_*;
i3 : T = numericalHilbertFunction(F, ideal 0_R, 2, Verbose => false)
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)

o3 = a numerical interpolation table, indicating
     the space of degree 2 forms in the ideal of the image has dimension 5

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

o4 = (2, 5)

o4 : Sequence

See also

Functions and methods returning a numerical interpolation table :

Methods that use a numerical interpolation table :

For the programmer

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