1.6.16 Fields, Groups, Rings

Problem: Calculate the reduced Gröbner basis of the ideal \[ I=\left(x^{2}+y^{2}+z^{2}-1, x^{2}+z^{2}-y, x-z\right) \] in \( \mathbb{Q}[x, y, z] \) with lex-ordering \( x>y>z \).