Compute the radical of an ideal with
radical.
i1 : R = QQ[x,y,z];
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i2 : radical ideal(z^4+2*z^2+1)
2
o2 = ideal(z + 1)
o2 : Ideal of R
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A somewhat more complicated example:
i3 : I = ideal"xyz,x2,y4+y5"
2 5 4
o3 = ideal (x*y*z, x , y + y )
o3 : Ideal of R
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i4 : radical I
2
o4 = ideal (x, y + y)
o4 : Ideal of R
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The index of nilpotency. We compute the minimal integer $k$ such that $(y^2+y)^k \in I$.
i5 : k = 0;
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i6 : while (y^2+y)^k % I != 0 do k = k+1;
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i7 : k
o7 = 4
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The index of nilpotency is 4.