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Previous: Computing the nonnormal locus
The idea for computing the normalization of is as
follows:
For performance reasons we do not look for a nonzerodivisor in
but choose any nonzero element . If is a zerodivisor then it
gives a splitting of the ring which makes the subsequent computations
easier.
We obtain the following (highly recursive) algorithm for computing the
normalization:
 Input

,
We assume that is a radical ideal.
 Output
 Polynomial rings
, ideals
, and maps
such that
,
induced by
is the normalization map of
.
 Compute an ideal describing the singular locus.
 Compute the radical
.
 Choose
and compute . If
go to 4 (then is a nonzerodivisor
of ). Otherwise, set
and go to 6.
 Compute
and
.
 If then return , otherwise go to 1.
 Suppose
. Then, for each
, set
and go to 1.
Next: Integral closure algorithm
Up: Normalization algorithm
Previous: Computing the nonnormal locus
Christoph Lossen
20010321