// -*- c++ -*-

 /**

 2 dimensional vector (plainvector) implementation

 */

 #ifndef HUGO_XY_H

 #define HUGO_XY_H

 #include <iostream>

 namespace hugo {

   template<typename T>

     class xy {

     public:

       T x,y;     

       ///Default constructor: both coordinates become 0

       xy() : x(0), y(0) {}

       ///Constructing the instance from coordinates

       xy(T a, T b) : x(a), y(a) { }

       ///Gives back the square of the norm of the vector

       T normSquare(){

 	return x*x+y*y;

       };

       ///Increments the left hand side by u

       xy<T>& operator +=(const xy<T>& u){

 	x += u.x;

 	y += u.y;

 	return *this;

       };

       ///Decrements the left hand side by u

       xy<T>& operator -=(const xy<T>& u){

 	x -= u.x;

 	y -= u.y;

 	return *this;

       };

       ///Multiplying the left hand side with a scalar

       xy<T>& operator *=(const T &u){

 	x *= u;

 	y *= u;

 	return *this;

       };

       ///Dividing the left hand side by a scalar

       xy<T>& operator /=(const T &u){

 	x /= u;

 	y /= u;

 	return *this;

       };

       ///Returns the scalar product of two vectors

       T operator *(const xy<T>& u){

 	return x*u.x+y*u.y;

       };

       ///Returns the sum of two vectors

       xy<T> operator+(const xy<T> &u) const {

 	xy<T> b=*this;

 	return b+=u;

       };

       ///Returns the difference of two vectors

       xy<T> operator-(const xy<T> &u) const {

 	xy<T> b=*this;

 	return b-=u;

       };

       ///Returns a vector multiplied by a scalar

       xy<T> operator*(const T &u) const {

 	xy<T> b=*this;

 	return b*=u;

       };

       ///Returns a vector divided by a scalar

       xy<T> operator/(const T &u) const {

 	xy<T> b=*this;

 	return b/=u;

       };

       ///Testing equality

       bool operator==(const xy<T> &u){

 	return (x==u.x) && (y==u.y);

       };

       ///Testing inequality

       bool operator!=(xy u){

 	return  (x!=u.x) || (y!=u.y);

       };

     };

   ///Reading a plainvector from a stream

   template<typename T>

   inline

   std::istream& operator>>(std::istream &is, xy<T> &z)

   {

     is >> z.x >> z.y;

     return is;

   }

   ///Outputting a plainvector to a stream

   template<typename T>

   inline

   std::ostream& operator<<(std::ostream &os, xy<T> z)

   {

     os << "(" << z.x << ", " << z.y << ")";

     return os;

   }

 } //namespace hugo

 #endif //HUGO_XY_H