initialize_Z_mod()

bool Z_mod::initialize_Z_mod ( int p )

protected

Definition at line 15 of file ZZp.cpp.

{
  initialize_ring(p);
  P = p;
 
  declare_field();
  int i, j, q, n;
 
  if (P == 2)
    _minus_one = 0;
  else
    _minus_one = (P - 1) / 2;
 
  if (P == 2)
    _prim_root = 1;
  else
    {
      j = 1;
      for (i = 2; (i < P && j < P - 1); i++)
        for (q = i, j = 1; (q != 1 && j < P); q = (q * i) % P, j++)
          ;
      _prim_root = i - 1;
    }
 
  // cerr << "z_mod_p: creating table for P = " << P << endl;
  _log_table = newarray_atomic(int, P);
  _exp_table = newarray_atomic(int, P);
  for (i = 0, n = 1; i < P - 1; i++, n = (n * _prim_root) % P)
    {
      _log_table[n] = i;  // i = log_(base _prim_root)(n)
      _exp_table[i] = n;  // n = (_prim_root)^i
    }
  _ZERO = P - 1;
  _exp_table[_ZERO] = 0;
  _log_table[0] = _ZERO;
 
  _P1 = P - 1;
 
  zeroV = from_long(0);
  oneV = from_long(1);
  minus_oneV = from_long(-1);
 
  coeffR = new CoefficientRingZZp(P, _log_table, _exp_table);
  aringZZp = new M2::ARingZZp(P);  // WARNING: this uses that the primitive
                                   // element is the SAME as computed above!!
  // Remove this warning once Z_mod is not in existence any longer.
  return true;
}

References _exp_table, _log_table, _minus_one, _P1, _prim_root, _ZERO, aringZZp, coeffR, Ring::declare_field(), from_long(), Ring::initialize_ring(), Ring::minus_oneV, newarray_atomic, Ring::oneV, P, p, and Ring::zeroV.