radical of an ideal

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

using radical

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