software with a routine for the vanishing ideal of a finite set of points

Question

I am looking for an algebraic software package that provides a routine that computes the vanishing ideal of a finite set of points. So far i am working with Macaulay2 but i have not been able to find any such routine. Does anyone know otherwise? Is anyone familiar with some other software that provides this feature?

Answer 1

Maple has the VanishingIdeal command in the PolynomialIdeals package. E.g. for the points {[5,4,4], [4,0,2], [6,4,1]} in [x,y,z] you would do:

with(PolynomialIdeals):
J := VanishingIdeal({[5,4,4], [4,0,2], [6,4,1]}, [x,y,z]);
Simplify(PrimeDecomposition(J));  # check