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D.4.25.2 normalI

Procedure from library reesclos.lib (see reesclos_lib).

normalI (I [,p [,r [,l]]]); I an ideal, p, r, and l optional integers

the integral closure of I, ..., I^p, where I is an ideal in the polynomial ring R=k[x(1),...x(n)]. If p is not given, or p==0, compute the closure of all powers up to the maximum degree in t occurring in the closure of R[It] (so this is the last power whose closure is not just the sum/product of the smaller). If r is given and r==1, normalI starts with a check whether I is already a radical ideal.
If l==1 then locNormal instead of normal is used to compute normalization. The result is a list containing the closure of the desired powers of I as ideals of the basering.

The procedure displays more comments for higher printlevel.

LIB "reesclos.lib";
ring R=0,(x,y),dp;
ideal I = x2,xy4,y5;
list J = normalI(I);
==> I[1]=x2
==> I[2]=xy4
==> I[3]=y5
J;                             // J[1] is the integral closure of I
==> [1]:
==>    _[1]=x2
==>    _[2]=xy4
==>    _[3]=y5
==>    _[4]=xy3