Function randomElement

factory/cfModGcd.cc:379–418

compute a random element a of \f$ F_{p}(\alpha ) \f$ , 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

/// 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
static inline CanonicalForm
randomElement (const CanonicalForm & F, const Variable & alpha, CFList & list,
               bool & fail)
{
  fail= false;
  Variable x= F.mvar();
  AlgExtRandomF genAlgExt (alpha);
  FFRandom genFF;
  CanonicalForm random, mipo;
  mipo= getMipo (alpha);
  int p= getCharacteristic ();
  int d= degree (mipo);
  double bound= pow ((double) p, (double) d);
  do
  {
    if (list.length() == bound)
    {
      fail= true;
      break;
    }
    if (list.length() < p)
    {
      random= genFF.generate();
      while (find (list, random))
        random= genFF.generate();
    }
    else
    {
      random= genAlgExt.generate();
      while (find (list, random))
        random= genAlgExt.generate();
    }
    if (F (random, x) == 0)
    {
      list.append (random);
      continue;
    }
  } while (find (list, random));
  return random;
}

static inline
Variable chooseExtension (const Variable & alpha)