UTM Ideals Varieties and Algorithm - Chapter 1 Section 5 Exercise 16

Problem:

Solution:

The previous exercises basically outlined the whole algorithm.

First, find the GCD, $g$, of $f_1, \cdots, f_s$. We know that $V(f_1, \cdots, f_s) = V(g)$.

Next, compute $g_{\text{red}} = \frac{g}{GCD(g, g')}$

Now we know $I(V(f_1, \cdots, f_s)) = I(V(g)) = \langle g_{\text{red}} \rangle$