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ICfractions -- Compute the fractions integral over a domain.

Synopsis

Usage:
ICfractions R
Inputs:
- R, an affine domain
Outputs:
- returns a matrix whose entries are fractions that generate the integral closure of R over R.
Optional inputs:
- Strategy => ...,

Description

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 |

                   QQ [x, y, z]  1             QQ [x, y, z]  5
o2 : Matrix (frac --------------)  <--- (frac --------------)
                   6    2 4    6               6    2 4    6
                  x  - y z  - z               x  - y z  - z

i3 : integralClosure(R,Variable => a)

     QQ [w , w , x, y, z, MonomialOrder => GRevLex => 5]
          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 w_7 and w_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.

Ways to use `ICfractions` :

ICfractions(Ring)