In Chapter 1, Section 4 of Cox et al "Ideals, Varieties and Algorithms, Exercise 3(c) reads as follows:

Prove the following equality of ideals in $\displaystyle \mathbb{Q}[x,y] $:

$\displaystyle < 2x^2 + 3y^2 -11, x^2 - y^2 - 3> \ = \ <x^2 - 4, y^2 - 1> $

Any help with this problem would be appreciated.

Peter