The integral closure algorithm proceeds by finding a suitable ideal $J$, and then computing $Hom_R(J,J)$, and repeating these steps. This optional argument limits the number of such steps to perform.
The result is an integral extension, but is not necessarily integrally closed.
i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4-z^3); |
i2 : R' = integralClosure(R, Variable => symbol t, Limit => 2) o2 = R' o2 : QuotientRing |
i3 : trim ideal R' 2 2 4 2 2 4 5 2 5 2 2 4 2 4 3 4 3 3 4 2 3 2 4 3 6 o3 = ideal (t x - y z - z - z, t y z + t z - x y - x z , t z - x y z - x z - x , t - x y z - 2x y z - x z - 1,1 1,1 1,1 1,1 1,1 ---------------------------------------------------------------------------------------------------------------------------- 3 2 3 3 3 2x y z - 2x z - x ) o3 : Ideal of QQ[t , x..z] 1,1 |
i4 : icFractions R 2 2 4 y z + z + z o4 = {-------------, x, y, z} x o4 : List |