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

integralClosure(..., Limit => ...) -- do a partial integral closure

Synopsis

Description

The integral closure algorithm proceeds by finding a suitable ideal J, and then computing HomR(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     
o3 = ideal (t   x - y z  - z  - z, t   y z  + t   z  - x y  - x z , t   z -
             1,1                    1,1        1,1                   1,1   
     ------------------------------------------------------------------------
      4 2     4 3    4   3      3 4 2     3 2 4    3 6     3 2      3 3    3
     x y z - x z  - x , t    - x y z  - 2x y z  - x z  - 2x y z - 2x z  - x )
                         1,1

o3 : Ideal of QQ[t   , x, y, z]
                  1,1
i4 : icFractions R

       2 2    4
      y z  + z  + z
o4 = {-------------, x, y, z}
            x

o4 : List

Further information