Function GFRandomElement

factory/cfModGcd.cc:818–851

compute a random element a of GF, s.t. F(a) \f$ \neq 0 \f$ , F is a univariate polynomial, returns fail if there are no field elements left which have not been used before

/// univariate polynomial, returns fail if there are no field elements left
/// which have not been used before
static inline
CanonicalForm
GFRandomElement (const CanonicalForm& F, CFList& list, bool& fail)
{
  fail= false;
  Variable x= F.mvar();
  GFRandom genGF;
  CanonicalForm random;
  int p= getCharacteristic();
  int d= getGFDegree();
  int bound= ipower (p, d);
  do
  {
    if (list.length() == bound)
    {
      fail= true;
      break;
    }
    if (list.length() < 1)
      random= 0;
    else
    {
      random= genGF.generate();
      while (find (list, random))
        random= genGF.generate();
    }
    if (F (random, x) == 0)
    {
      list.append (random);
      continue;
    }
  } while (find (list, random));
  return random;
}

CanonicalForm
modGCDGF (const CanonicalForm& F, const CanonicalForm& G,