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icFractions -- Compute the fractions integral over a domain.

Synopsis

Description

i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4);
i2 : integralClosure(R,Variable => a)

                  QQ[a , a , x, y, z]
                      7   6
o2 = ---------------------------------------------
             2                    2   2    2    2
     (a z - x , a z - a x, a x - a , a  - y  - z )
       6         7     6    7     6   7

o2 : QuotientRing
i3 : icFractions R

      a   a    2     3  a   a    2 2    4  a    2 3    5
       3   4  y z + z    2   2  y z  + z    0  y z  + z
o3 = {--, --, --------, --, --, ---------, --, ---------, x, y, z}
      a    x      x      x   z      x       x      x
       6

o3 : List
Thus the new variables a_7 and a_6 in the output from integralClosure correspond to the last two fractions given. The other fractions are those returned in intermediate recursive steps in the computation of the integral closure. a_0 for example corresponds to the first fraction to the left of the original ring variables. The program currently also returns the original variables as part of the matrix. In this way the user can see if any are simplified out of the ring during the process of computing the integral closure.

A future version of icFractions will return only the fractions corresponding to the variables returned by the function integralClosure. Thus the general format will be much easier to use

Ways to use icFractions :