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.