radical of an ideal

radical of an ideal

There are two main ways to find the radical of an ideal. The first is to use the function radical and the second is to find the intersection of the minimal prime ideals. On some large examples the second method is faster.

Sections:

using radical

using minimal prime ideals

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 minimal prime ideals

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 decompose. Then use intersect.

i4 : intersect decompose I



                           3    2

o4 = ideal (-y*z, -x*z, - x  + y )



o4 : Ideal of S