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.
using radical
i1 : S = ZZ/101[x,y,z]
o1 = S
o1 : PolynomialRing
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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
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i3 : radical I
3 2
o3 = ideal (y*z, x*z, x - y )
o3 : Ideal of S
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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
minimalPrimes. Then use
intersect.
i4 : intersect minimalPrimes I
3 2
o4 = ideal (y*z, x*z, - x + y )
o4 : Ideal of S
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