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
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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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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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