new example for incomplete primdecSY() decomposition

[kroeker@…]

LIB("primdec.lib");
LIB("ehv.lib");
ring rng = (5,vv),(xx,yy,zz,ww),dp;
minpoly = (vv^2-2);
ideal I = (2*vv)*xx*yy+(vv)*xx*ww+zz,(-vv)*xx^2*zz+2*zz;
list L1, L2;
int i ;

// despite using fixed random seed, primdecSY() sometime succeeds. (why?)
for (i=0; i<20; i++)
{
    system("random",1803001481);
    L1 = primdecGTZ (I);
    L2 = primdecSY (I);
    "i";i;
    "L1";L1;   
    "L2";L2;
    ASSUME(0, primDecsAreEquivalent (L1,L2) ) ; // will fail!
}

output:

L1
[1]
   [1]
      _[1]=zz
      _[2]=yy-2*ww
   [2]
      _[1]=zz
      _[2]=yy-2*ww
[2]
   [1]
      _[1]=zz
      _[2]=xx
   [2]
      _[1]=zz
      _[2]=xx
[3]
   [1]
      _[1]=xx*zz-yy+2*ww
      _[2]=yy^2+(-vv)*zz^2+yy*ww-ww^2
      _[3]=xx*yy-2*xx*ww+(-vv)*zz
      _[4]=xx^2+(-vv)
   [2]
      _[1]=xx*zz-yy+2*ww
      _[2]=yy^2+(-vv)*zz^2+yy*ww-ww^2
      _[3]=xx*yy-2*xx*ww+(-vv)*zz
      _[4]=xx^2+(-vv)
L2
[1]
   [1]
      _[1]=xx*yy-2*xx*ww+(-vv)*zz
      _[2]=xx*zz^2-yy*zz+2*zz*ww
      _[3]=yy^2*zz+(-vv)*zz^3+yy*zz*ww-zz*ww^2
      _[4]=xx^2*zz+(-vv)*zz
      _[5]=xx^3+(-vv)*xx
   [2]:
      _[1]=zz
      _[2]=xx
[2]
   [1]
      _[1]=zz
      _[2]=yy-2*ww
   [2]
      _[1]=zz
      _[2]=yy-2*ww

[hannes]

fixed with 3106b37eea17482acd0b02cc99f0d0d2f1419894