ICfractions Ring -- Compute the fractions integral over a domain.

ICfractions Ring -- Compute the fractions integral over a domain.

Synopsis:

Usage: M = ICfractions R

Function: ICfractions

Input:

R, an instance of class Ring: affine domain

Output:

M, an instance of class RingMap: returns a matrix of fractions that generate the integral closure of R over R.

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

i2 : S = ICfractions R



o2 = | x3/z2 x2/z x y z |



                  1            5

o2 : Matrix frac R  <--- frac R

i3 : integralClosure(R,Variable => a)



                  QQ [w , w , x, y, z]

                       7   6

o3 = ---------------------------------------------

       2                    2         2    2    2

     (x  - w z, w x - w z, w  - w x, w  - y  - z )

            6    6     7    6    7    7



o3 : QuotientRing

Thus the new variables a_7 and a_6 correspond to the fractions respectively. 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.