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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 $Hom_R(J,J)$, 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     
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..z]
                  1,1
i4 : icFractions R

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

o4 : List

Further information

Functions with optional argument named Limit :