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

Synopsis

Description

Note that if an integrally closed ring is given as input, the identity 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

This finite map is needed to compute the conductor of the integral closure into the original ring.

See also

Ways to use ICmap :