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

Let $(x_i,y_i)$ be a finite subset of points of $\mathbb{R}^2$. Find an irreducible polynomials $f(x,y)$ over $\mathbb{R}[x,y]$ such that vanish only in that points.

EDITED: Where $\mathbb{R}$ denoted the Real numbers.

share|cite|improve this question
up vote 1 down vote accepted

Hint: The polynomial $f_i(x,y)=(x-x_i)^2+(y-y_i)^2$ vanishes at $(x_i,y_i)$ but not at any other point. How can you put together a collection of functions $\{f_i\}$ to get a single function which vanishes wherever one of the $f_i$ vanishes?

share|cite|improve this answer

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.