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 $