icFractions -- Compute the fractions integral over a domain.

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

i2 : integralClosure(R,Variable => a)
            +----------------+
choices are |(1, 1, x)       |
            +----------------+
            |        2     3 |
            |(3, 2, y z + z )|
            +----------------+
            +----------------+
choices are |(1, 1, x)       |
            +----------------+
            |(1, 1, a )      |
            |        0       |
            +----------------+
            |        2     3 |
            |(3, 2, y z + z )|
            +----------------+
            +----------------+
choices are |(1, 1, x)       |
            +----------------+
            |(1, 1, a )      |
            |        2       |
            +----------------+
            |(1, 1, a )      |
            |        1       |
            +----------------+
            |        2     3 |
            |(3, 2, y z + z )|
            +----------------+
            +----------+
choices are |(1, 1, x) |
            +----------+
            |(1, 1, a )|
            |        5 |
            +----------+
            |(1, 1, a )|
            |        4 |
            +----------+
            |(1, 1, a )|
            |        3 |
            +----------+
            +----------+
choices are |(1, 1, x) |
            +----------+
            |(1, 1, a )|
            |        3 |
            +----------+
            |(1, 1, a )|
            |        6 |
            +----------+
            +----------+
choices are |(1, 1, x) |
            +----------+
            |(1, 1, a )|
            |        6 |
            +----------+

                  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