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integralClosure(..., Strategy => ...) -- control the algorithm used

Synopsis

Description

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.

AllCodimensions tels the algorithm to bypass the computation of the S2-ification, but in each iteration of the algorithm, use the radical of the extended Jacobian ideal from the previous step, instead of using only the codimension 1 components of that. This is useful when for some reason the S2-ification is hard to compute, or if the probabilistic algorithm for computing it fails. In general though, this option slows down the computation for many examples.
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 0.735888 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 0.584911 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 0.59091 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 0.751886 seconds

o8 = R'

o8 : QuotientRing

Further information