There are two main ways to find the radical of an ideal. On some large examples the second method is faster.

 i1 : S = ZZ/101[x,y,z] o1 = S o1 : PolynomialRing i2 : I = ideal(x^3-y^2,y^2*z^2) 3 2 2 2 o2 = ideal (x - y , y z ) o2 : Ideal of S i3 : radical I 3 2 o3 = ideal (y*z, x*z, x - y ) o3 : Ideal of S

## using theminimal primes of an ideal

An alternate way to find the radical of an ideal I is to take the intersection of its minimal prime ideals. To find the minimal primes of an ideal I use the function minimalPrimes. Then use intersect.

 i4 : intersect minimalPrimes I 3 2 o4 = ideal (y*z, x*z, x - y ) o4 : Ideal of S