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IntegralClosure :: integralClosure(..., Strategy => ...)

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.
R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);
time R' = integralClosure(R, Strategy=>{RadicalCodim1})
R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);
time R' = integralClosure(R)
R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);
time R' = integralClosure(R, Strategy=>{AllCodimensions})
R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);
time R' = integralClosure(R, Strategy=>{RadicalCodim1, AllCodimensions})

Further information