Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
Can't write down the vanishing ideal directly? – Martin Brandenburg Oct 4 '13 at 21:13
@MartinBrandenburg: I can write it abstractly; it is the intersection of the vanishing ideals of all points. But computing it, e.g. finding a Groebner basis, is far from trivial in terms of computational complexity. For example, a simple for loop in Macaulay2 that computes this intersection (which is the same as the product) incrementally, gets stuck after 50 points in $\mathbb{Q}^3$. What i want, is to be able to compute the vanishing ideal of as many as 500 points in an ambient space as big as $\mathbb{Q}^7$. – Manos Oct 4 '13 at 21:31

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:

J := VanishingIdeal({[5,4,4], [4,0,2], [6,4,1]}, [x,y,z]);
Simplify(PrimeDecomposition(J));  # check
share|cite|improve this answer
Thanks. Do you have any idea how fast this routine is? What if we have 100 points in $\mathbb{R}^3$? How fast does it do the computation? – Manos Oct 7 '13 at 14:48

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.