Compute the normalization of the following subvariety of P⁸ ( K = Z/32003 Z )

LIB "normal.lib";
ring r=32003,(b,s,t,u,v,w,x,y,z),dp;
ideal i=wy-vz,vx-uy,tv-sw,su-bv,tuy-bvz;
list NN = normal(i); // takes about 6 sec

==>

'normal' created a list of 3 ring(s).

NN[1];

==>

// characteristic : 32003 // number of vars : 6 // block 1 : ordering dp // : names T(1) T(2) T(3) T(4) T(5) T(6) // block 2 : ordering C

def R1=NN[1];		def R2=NN[2];		def R3=NN[3];
setring R1;		setring R2;		setring R3;
norid;		norid;		norid;
==> norid[1]=0		==> norid[1]=0		==> norid[1]=wy-vz norid[2]=ty-sz norid[3]=wx-uz norid[4]=vx-uy norid[5]=tx-bz norid[6]=sx-by norid[7]=tv-sw norid[8]=tu-bw norid[9]=su-bv
normap;		normap;		normap;
==> normap[1]=T(1) normap[2]=T(2) normap[3]=T(3) normap[4]=0 normap[5]=0 normap[6]=0 normap[7]=T(4) normap[8]=T(5) normap[9]=T(6)		==> normap[1]=T(1) normap[2]=0 normap[3]=T(2) normap[4]=T(3) normap[5]=0 normap[6]=T(4) normap[7]=T(5) normap[8]=0 normap[9]=T(6)		==> normap[1]=b normap[2]=s normap[3]=t normap[4]=u normap[5]=v normap[6]=w normap[7]=x normap[8]=y normap[9]=z

The normalization (ring) is: