--Poly. Ring
R=QQ[x,y]
I=ideal(x^2,x*y)

K=ideal(x)

J1=ideal(x^2,x*y,y^2)
J2=ideal(x^2,y)
--both are primary decompositons
I==intersect(K,J1)
I==intersect(K,J2)
J1==J2
--both are minimal since
radical J1
--is not x
radical J2
--is not x
--and neither compnent contains the other in both cases
--i.e.
isSubset(K,J1)
--however 
radical(J1)==radical(J2)
--which makes sense becuase the decomposition for vareiteis, i.e
--for radical ideals, is unique

--we can find primary components using
primaryDecomposition I
--and assoicated primes, i.e. radicals of each primary component
associatedPrimes I

--I:K is done using
quotient(I,K)
--and I:K^{\infty} , i.e I satuate K, is
saturate(I,K)