The function associatedPrimes returns a list of the associated prime ideals for a given ideal I. The associated prime ideals correspond to the irreducible components of the variety associated to I. They are useful in many applications in commutative algebra, algebraic geometry and combinatorics.
i1 : R = ZZ/101[a..d];
i2 : I = ideal(a*b-c*d, (a*c-b*d)^2);
o2 : Ideal of R
i3 : associatedPrimes I
o3 = {ideal (d, a), ideal (b + c, a + d), ideal (c, b), ideal (b - c, a - d)}
o3 : List