 ring r = 0,(x,y,z),lp;
ideal i = y3+x2,x2y+x2z2,x3z9,z4y2xz;
ideal j = stdhilb(i); j;
==> j[1]=z10
==> j[2]=yz9
==> j[3]=2y2z4z8
==> j[4]=2y3z32y2z5yz7
==> j[5]=y4+y3z2
==> j[6]=xz+y2z4
==> j[7]=xy2xz4y3z
==> j[8]=x2+y3
ring r1 = 0,(x,y,z),wp(3,2,1);
ideal i = y3+x2,x2y+x2z2,x3z9,z4y2xz; //ideal is homogeneous
ideal j = stdhilb(i,"std"); j;
==> j[1]=y2+xzz4
==> j[2]=x2xyz+yz4
==> j[3]=2xz5z8
==> j[4]=2xyz4yz7+z9
==> j[5]=z10
==> j[6]=2yz9+z11
//this is equivalent to:
intvec v = hilb(std(i),1);
ideal j1 = std(i,v,intvec(3,2,1)); j1;
==> j1[1]=y2+xzz4
==> j1[2]=x2xyz+yz4
==> j1[3]=2xz5z8
==> j1[4]=2xyz4yz7+z9
==> j1[5]=z10
==> j1[6]=yz9
size(NF(j,j1))+size(NF(j1,j)); //j and j1 define the same ideal
==> 0
