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Ring Normalization - Sturmfels example

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

V = { wy-vz=0 , vx-uy=0 , tv-sw=0 , su-bv=0 , tuy-bvz=0 }
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:

$\displaystyle K[t_1,\dots,t_6]^2
\oplus K[b,s,t,u,v,w,x,y,z]\big/\langle wy\!-\!vz,
ty\!-\!sz, \dots, tu\!-\!bw, su\!-\!bv\rangle $

Lille, 08-07-02 http://www.singular.uni-kl.de