extern Duple operator- (Duple const &);
extern Duple operator+ (Duple const &, Duple const &);
+extern bool operator== (Duple const &, Duple const &);
extern Duple operator- (Duple const &, Duple const &);
extern Duple operator/ (Duple const &, double);
extern std::ostream & operator<< (std::ostream &, Duple const &);