ICmap Ring -- natural map from an affine domain into its integral closure.

ICmap Ring -- natural map from an affine domain into its integral closure.

Synopsis:

Usage: F = ICmap R

Function: ICmap

Input:

R, an instance of class Ring: affine domain

Output:

S, an instance of class RingMap: returns a map from R to its integral closure

Note that if an integrally closed ring is given as input a map from the ring to itself is returned.

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

i2 : ICmap R



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

                           7   6

o2 = map(---------------------------------------------,R,{x, y, z})

           2                    2         2    2    2

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

                6    6     7    6    7    7



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

                               7   6

o2 : RingMap --------------------------------------------- <--- R

               2                    2         2    2    2

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

                    6    6     7    6    7    7