LIB "solve.lib";
ring r4n = (0,n),(x,y,z),dp;
poly p1 = z^2*x^2*y^2-y^2-x^2;
poly p2 = -n+n*x+3*n*z^2*x^2-2*n*z^2*x^3+51*z^3*x^6-2*z^3*x^7;
poly p3 = -n+n*y+3*n*z^2*y^2-2*n*z^2*y^3+51*z^3*y^6-2*z^3*y^7;
ideal i1 = p1,p2,p3;
ideal si1 = std(i1);
printf("standard ideal should be zero, it is: %2s",dim(si1));
printf("number of complex solutions is: %2s",vdim(si1)); // it is 62
option(redSB);
ideal maxI=maxideal(1);
ideal jnumbers = sat(si1,maxI)[1];  // this takes about 10 seconds
printf("number of non-zero solutions: %2s",vdim(jnumbers)); //still 62
// triangulate
ring T4n = (0,n),(x,y,z),lp;
print("calling fglm"); // the last line printed in the actual run
ideal j4n = fglm(r4n,jnumbers);
print("calling triangl");
list Sol4n = triangMH(j);
print("DONE!, %s components",size(Sol4n));