# associated primes

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 (c, b), ideal (b - c, a - d), ideal (b + c, a + d)} o3 : List

See primary decomposition for more information about finding primary decompositions. To find just the minimal prime ideals see minimal primes of an ideal.