RadicalCodim1 chooses an alternate, often much faster, sometimes much slower, algorithm for computing the radical of ideals. This will often produce a different presentation for the integral closure.
i1 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); |
i2 : time R' = integralClosure(R, Strategy=>{RadicalCodim1}) -- used 0.812691 seconds o2 = R' o2 : QuotientRing |
i3 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); |
i4 : time R' = integralClosure(R) -- used 0.599271 seconds o4 = R' o4 : QuotientRing |
i5 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); |
i6 : time R' = integralClosure(R, Strategy=>{AllCodimensions}) -- used 0.701286 seconds o6 = R' o6 : QuotientRing |
i7 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); |
i8 : time R' = integralClosure(R, Strategy=>{RadicalCodim1, AllCodimensions}) -- used 0.70855 seconds o8 = R' o8 : QuotientRing |