KK = ZZ / 30097;

R = KK[a,b,c,d,e,f,x_1..x_18];

X1=transpose matrix {{0_R,0,0}};
X2=transpose matrix {{a,0,0}};
X3=transpose matrix {{b,c,0}};
X4=transpose matrix {{d,e,f}};

Y1=transpose matrix {{x_1,x_2,x_3}};
Y2=transpose matrix {{x_4,x_5,x_6}};
Y3=transpose matrix {{x_7,x_8,x_9}};
Y4=transpose matrix {{x_10,x_11,x_12}};
Y5=transpose matrix {{x_13,x_14,x_15}};
Y6=transpose matrix {{x_16,x_17,x_18}};

fun=(X,Y,dum)->(m:=random(R^1,R^1); ideal (transpose(X-Y)*(X-Y)+m));
idfun=(X1,X2,X3,X4,Y,m)->fun(X1,Y,m)+fun(X2,Y,m)+fun(X3,Y,m)+fun(X4,Y,m);

I=idfun(X1,X2,X3,X4,Y1,1)+idfun(X1,X2,X3,X4,Y2,1)+idfun(X1,X2,X3,X4,Y3,1)+idfun(X1,X2,X3,X4,Y4,1)+idfun(X1,X2,X3,X4,Y5,1)+idfun(X1,X2,X3,X4,Y6,1);

print "This script did not remove any symmetries."
print "This usually takes a little time. On my P4 it takes 3minutes"
dim I,degree I