-- -*- M2-comint -*- hash: 11672546221254882638

i1 : R = CC[s,t]

o1 = R

o1 : PolynomialRing

i2 : F = basis(3, R)

o2 = | s3 s2t st2 t3 |

             1      4
o2 : Matrix R  <-- R

i3 : numericalHilbertFunction(F, ideal 0_R, 4)
Sampling image points ...
     -- used .0119582 seconds
Creating interpolation matrix ...
     -- used .0112966 seconds
Performing normalization preconditioning ...
     -- used .00686926 seconds
Computing numerical kernel ...
     -- used .00075998 seconds

o3 = a "numerical interpolation table", indicating
     the space of degree 4 forms in the ideal of the image has dimension 22

o3 : NumericalInterpolationTable

i4 : R = CC[x_(1,1)..x_(2,4)];

i5 : F = (minors(2, genericMatrix(R, 2, 4)))_*;

i6 : S = numericalImageSample(F, ideal 0_R, 60);

i7 : numericalHilbertFunction(F, ideal 0_R, S, 2, UseSLP => true)
Creating interpolation matrix ...
     -- used .00306346 seconds
Performing normalization preconditioning ...
     -- used .00812204 seconds
Computing numerical kernel ...
     -- used .00092891 seconds

o7 = a "numerical interpolation table", indicating
     the space of degree 2 forms in the ideal of the image has dimension 1

o7 : NumericalInterpolationTable

i8 : 
