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

Problem:

Solution:

a) $(y^2z)x^5 + (-y^3)x^4 + (z)x^2 + (y + 2)x + (y^5 - y^3z - 5z + 3)$
b) $y^5 + (-x^4 - z)y^3 + (x^5z + x)y + (x^2z + 2x - 5z + 3)$
c) $(x^5y^2 + x^2 -y^3 - 5)z + (x^4y^3 + y^5 + xy + 2x + 3)$

A rather straightforward problem, terms in the brackets are the coefficients.