loadPackage "SpaceCurves";
p = 3;
r = 1;
q = p^r;
K = GF(q, Variable => a);
d = 1;
S = K[x, y, z, w];
g = x^q*y-x*y^q+z^q*w-z*w^q;
J = ideal(x^q*y-x*y^q, x^q*z-x*z^q, x^q*w-x*w^q, y^q*z-y*z^q, y^q*w-y*w^q, z^q*w-z*w^q);
found = false;
counter = 0;
while not found do
    {
    f = random(q+1+d, J);
    I = ideal(f, g);
    if isSmooth(I) and dim I == 2 then
    {
        print f;
        print counter;
        found = true;
    }
    else counter = counter + 1;
    }
o9 : Ideal of S
 4     3 2    2 3      4    4     3         3     4     3 2    2 3    2 3      4    4     3         3     3         3     4     3 2    2 3    2 3      4
x y - x y  - x y  + x*y  - x z - x y*z + x*y z - y z + x z  + x z  + y z  - x*z  - x w + x y*w - x*y w - x z*w + x*z w - z w - y w  + x w  + z w  + y*w
3177