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[1]=T(1)`	`==> normap[1]=b`
`==> normap[2]=T(2)`	`==> normap[2]=0`	`==> normap[2]=s`
`==> normap[3]=T(3)`	`==> normap[3]=T(2)`	`==> normap[3]=t`
`==> normap[4]=0`	`==> normap[4]=T(3)`	`==> normap[4]=u`
`==> normap[5]=0`	`==> normap[5]=0`	`==> normap[5]=v`
`==> normap[6]=0`	`==> normap[6]=T(4)`	`==> normap[6]=w`
`==> normap[7]=T(4)`	`==> normap[7]=T(5)`	`==> normap[7]=x`
`==> normap[8]=T(5)`	`==> normap[8]=0`	`==> normap[8]=y`
`==> normap[9]=T(6)`	`==> normap[9]=T(6)`	`==> normap[9]=z`

The normalization (ring) is:

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

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