loadPackage "SpaceCurves";
p = 2;
r = 2;
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
 5     4              4 2    4 2    2 4        4             5      5           5       4           4     5         4         4            5       4 2           2 4    2 4          4          4           2 4        5
x z + x y*z + (a + 1)x z  + y z  + x z  + x*y*z  + (a + 1)x*z  + y*z  + (a + 1)x w + a*x y*w + a*x*y w + y w + a*x*z w + a*y*z w + (a + 1)z w + a*x w  + (a + 1)x w  + y w  + a*x*z*w  + a*y*z*w  + (a + 1)z w  + a*x*w
13631