betterNormalizationMap -- normalizes non domains

Synopsis

Usage:

phi = betterNormalizationMap(S)
Inputs:
- S, a ring,
Optional inputs:
- Strategy => ..., default value {}, controls what strategy is used in calls to integralClosure
- Variable => ..., default value Yy, set the name for new variables created by the function
Outputs:
- phi, a ring map, the map from the ring to its normalization

Description

Given a reduced ring $S$, this returns the normalization map $S \to S^N$. It works by computing the normalization after modding out by each minimal prime, and then taking the product of the rings. This should be compared to the function icMap built into Macaulay2.

i1 : R = QQ[x,y]/ideal(x*y);

i2 : icMap(R);

o2 : RingMap R <-- R

i3 : h2 = betterNormalizationMap(R);

                       QQ[Yy0, Yy1, Yy2]
o3 : RingMap ------------------------------------ <-- R
                 2
             (Yy2  - Yy2, Yy1*Yy2 - Yy1, Yy0*Yy2)

i4 : RN = target h2

o4 = RN

o4 : QuotientRing

i5 : radical ideal singularLocus RN

o5 = ideal 1

o5 : Ideal of QQ[Yy0, Yy1, Yy2]

Ways to use betterNormalizationMap :

betterNormalizationMap(Ring)

For the programmer

The object betterNormalizationMap is a method function with options.