# Singular

#### D.4.25.2 normalI

Procedure from library `reesclos.lib` (see reesclos_lib).

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

Return:
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.

Display:
The procedure displays more comments for higher printlevel.

Example:
 ```LIB "reesclos.lib"; ring R=0,(x,y),dp; ideal I = x2,xy4,y5; list J = normalI(I); 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 ```