initialize_GF()

bool GF::initialize_GF ( const RingElement * prim )

protected

Definition at line 39 of file GF.cpp.

{
  // set the GF ring tables.  Returns false if there is an error.
  _primitive_element = prim;
  _originalR = prim->get_ring()->cast_to_PolynomialRing();
  initialize_ring(_originalR->characteristic(),
                  PolyRing::get_trivial_poly_ring());
 
  declare_field();
 
  int i, j;
 
  if (_originalR->n_quotients() != 1)
    {
      throw exc::engine_error(
          "rawGaloisField expected an element of a quotient ring of the form "
          "ZZ/p[x]/(f)");
    }
  ring_elem f = _originalR->quotient_element(0);
  Nterm *t = f;
  int n = _originalR->getMonoid()->primary_degree(t->monom);
 
  Q_ = static_cast<int>(characteristic());
  for (i = 1; i < n; i++) Q_ *= static_cast<int>(characteristic());
 
  Qexp_ = n;
  Q1_ = Q_ - 1;
  _ZERO = 0;
  _ONE = Q1_;
  _MINUS_ONE = (characteristic() == 2 ? _ONE : Q1_ / 2);
 
  // Get ready to create the 'one_table'
  VECTOR(ring_elem) polys;
  polys.push_back(_originalR->from_long(0));
  ring_elem primelem = prim->get_value();
  polys.push_back(_originalR->copy(primelem));
 
  ring_elem oneR = _originalR->one();
 
  _x_exponent = -1;
  ring_elem x = _originalR->var(0);
  if (_originalR->is_equal(primelem, x)) _x_exponent = 1;
  for (i = 2; i < Q_; i++)
    {
      ring_elem g = _originalR->mult(polys[i - 1], primelem);
      polys.push_back(g);
      if (_originalR->is_equal(g, oneR)) break;
      if (_originalR->is_equal(g, x)) _x_exponent = i;
    }
 
  if (polys.size() != Q_)
    {
      throw exc::engine_error("GF: primitive element expected");
    }
 
  assert(_x_exponent >= 0);
 
  // Set 'one_table'.
  _one_table = newarray_atomic(int, Q_);
  _one_table[0] = Q_ - 1;
  for (i = 1; i <= Q_ - 1; i++)
    {
      if (system_interrupted()) return false;
      ring_elem f1 = _originalR->add(polys[i], oneR);
      for (j = 1; j <= Q_ - 1; j++)
        if (_originalR->is_equal(f1, polys[j])) break;
      _one_table[i] = j;
    }
 
  // Create the Z/P ---> GF(Q) inclusion map
  _from_int_table = newarray_atomic(int, characteristic());
  int a = _ONE;
  _from_int_table[0] = _ZERO;
  for (i = 1; i < characteristic(); i++)
    {
      _from_int_table[i] = a;
      a = _one_table[a];
    }
 
  zeroV = from_long(0);
  oneV = from_long(1);
  minus_oneV = from_long(-1);
 
  return true;
}

References _from_int_table, _MINUS_ONE, _ONE, _one_table, _originalR, _primitive_element, _x_exponent, _ZERO, Ring::cast_to_PolynomialRing(), Ring::characteristic(), Ring::declare_field(), from_long(), RingElement::get_ring(), PolyRing::get_trivial_poly_ring(), RingElement::get_value(), Ring::initialize_ring(), Ring::minus_oneV, Nterm::monom, newarray_atomic, Ring::oneV, Q1_, Q_, Qexp_, system_interrupted(), VECTOR, x, and Ring::zeroV.