--Poly. Ring
R=QQ[x,y]
--V(x^2,y^2)=V(x,y) but (x^2,y^2) is not equal to (x,y)
I=ideal(x^2,y^2)
K=ideal(x,y)
I==K
--Ideal membership:
--x is in K... can think of % as modulo, i.e. working in R/K
(x)%K==0
--but not in I
(x)%I==0
--K contains I
isSubset(I,K)
--I does not contain K
isSubset(K,I)
--Nullstellensatz:
--radical(x^2,y^2)=I(V((x^2,y^2)))...We will learn how this works
--in Ch.4 
radical(I)==K
ideal radical I