// a, b, c are just sume dummy variables
// X = \alpha

ring rr = (2,X), (a,b,c), lp;
minpoly = X^4 + X^3 + X^2 + X + 1;

int i,j,k,m;
number beta, p, result;

// number = constant in the ring rr;

for(i = 0; i <= 1; i = i + 1)
{
  for(j = 0; j <= 1; j = j + 1)
  {
    for(k = 0; k <= 1; k = k + 1)
    {
      for(m = 0; m <= 1; m = m + 1)
      {
	beta = i*X^3 + j*X^2 + k*X + m;
	p = beta^4 + beta^3 + 1;
	/* Primitive polynomial; choose beta^4+beta+1 for the other set of solutions */
	if (p == 0)
	{"Primitive element beta = ",beta;
	  result = beta;
	}
      }
    }
  }
}

result = X3+X2+X+1;
"To verify, see that the powers of the element"; result; "are:";

for(i = 1; i < 16; i = i + 1)
{
  result^i;
}