//  Multiplication operator for two polynomials...

Polynomial operator * ( const Polynomial & f, const Polynomial & g )
{
  Polynomial h;
  int i, j;
  for ( i=0; i<f.terms_.size(); ++i )
    for ( j=0; j<g.terms_.size(); ++j ) {
      double coeff = f.terms_[i].coefficient * g.terms_[j].coefficient;
      double expon = f.terms_[i].exponent + g.terms_[j].exponent;
      h.terms_.push_back( PTerm( coeff, expon ) );
    }
  sort( h.terms_.begin(), h.terms_.end() );

  Polynomial h2;
  i=0;
  while ( i<h.terms_.size() ) {
    int expon = h.terms_[i].exponent;
    PTerm pt( 0.0, expon );
    for( ; i < h.terms_.size() && h.terms_[i].exponent == expon; ++i ) {
      pt.coefficient += h.terms_[i].coefficient;
    }
    h2.terms_.push_back( pt );
  }

  return h2;
}