/***************************************************************************
                          rational.h  -  description
                             -------------------
    begin                : Mon Jan 17 19:41:58 CST 2004
    copyright            : (C) 2003 by Daniel Eric Smith
    email                : 
 ***************************************************************************/

/***************************************************************************
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU General Public License as published by  *
 *   the Free Software Foundation; either version 2 of the License, or     *
 *   (at your option) any later version.                                   *
 *                                                                         *
 ***************************************************************************/


#include <cmath>
#include <iomanip>
using namespace std;


/*Don't think I need this any longer
long int abs(long int u)
{
  if(u<0) {return -1*u;}
  else {return u;}
}
*/

long int gcd(long int u,long int v)
{
  long int t;
  while(u>0)
    {
      if(u<v)
	{
	  t=u;
	  u=v;
	  v=t;
	}
      u=u-v;
    }
  return v;
}


long int lpow(long int b, long int n)
{
  long int a=1;

  for(int i=1;i<=n;i++) a *= b;

  return a;
}

class rational{
  long int num,den; //num=numerator, den=denominator of fraction
 public:
  rational() {num=0; den=1;} 
  rational(long int x) {num=x; den=1;}
  rational(long int n, long int d) {num=n; den=d;}  //parameterized construtor
  void set(long int n, long int d);                 //initializes r
  void show();                            //displays the rational number
  double decimal();                       //returns the decimal approx. of r
  void reduce();                          //reduces r
  long int getnum();
  long int getden();
/*
ARITIMETIC
*/
  rational operator+(rational r); //rational addition r+s
  rational operator-(rational r);
  rational operator*(rational r);
  rational operator/(rational r);
/*
SHORTCUT OPERATORS
*/
  rational operator+=(rational r);
  rational operator-=(rational r);
  rational operator*=(rational r);
  rational operator/=(rational r);
/*
RELATIONAL OPERATORS
*/
  bool operator== (rational q);
  bool operator!= (rational q);
  bool operator< (rational q);
  bool operator> (rational q);
  bool operator<= (rational q);
  bool operator>= (rational q);
/*
INPUT/OUTPUT
*/
  friend istream& operator>>(istream& s, rational& r);
  friend ostream& operator<<(ostream& s, rational r);
/*
OTHER
*/  
  friend rational pow(rational r, long int n);
};







void rational::set(long int n, long int d)
{
  num=n;
  den=d;
}

void rational::show()
{
  cout <<num<<"/"<<den<<endl;
}

double rational::decimal()
{
  return (double)num/(double)den;
}
void rational::reduce()
{
  long int g;

  g=gcd(labs(num),labs(den));

  num=num/g;
  den=den/g;
}

long int rational::getnum()
{
  return num;
}
long int rational::getden()
{
  return den;
}



/************
* ARITMETIC *
************/

/****************
*               *
* r+s  ADDITION * 
*               *
****************/
rational rational::operator+(rational r)
{
  rational t;

  t.num=num*r.den+den*r.num;
  t.den=den*r.den;

  t.reduce();

  return t;	
}
/******************
*                 *
* r-s SUBTRACTION *
*                 *
******************/
rational rational::operator-(rational r)
{
  rational t;

  t.num=num*r.den-den*r.num;
  t.den=den*r.den;

  t.reduce();

  return t;	
}
/*********************
*                    *
* r*s MULTIPLICATION *
*                    *
*********************/
rational rational::operator*(rational r)
{
  rational t;

  t.num=num*r.num;
  t.den=den*r.den;

  t.reduce();

  return t;
}
/***************
*              *
* r/s DIVISION *
*              *
***************/
rational rational::operator/(rational r)
{
  rational t;

  t.num=num*r.den;
  t.den=den*r.num;

  t.reduce();

  return t;
}

/*********************
* SHORTCUT OPERATORS *
*********************/
rational rational::operator+=(rational r)
{
  *this=*this+r;
  return(*this);
}
rational rational::operator-=(rational r)
{
  *this=*this-r;
  return(*this);
}
rational rational::operator*=(rational r)
{
  *this=*this*r;
  return(*this);
}
rational rational::operator/=(rational r)
{
  *this=*this/r;
  return(*this);
}

/***********************
* RELATIONAL OPERATORS *
***********************/
bool rational::operator== (rational q)
{
  return(num*q.den==den*q.num);
}

bool rational::operator!= (rational q)
{
  return(num*q.den!=den*q.num);
}
bool rational::operator< (rational q)
{
  return(num*q.den < den*q.num);
}
bool rational::operator> (rational q)
{
  return(num*q.den > den*q.num);
}
bool rational::operator<= (rational q)
{
  return(num*q.den <= den*q.num);
}
bool rational::operator>= (rational q)
{
  return(num*q.den >= den*q.num);
}








/***************
* INPUT/OUTPUT *
***************/
istream& operator>>(istream& s, rational& r)
{
  s>>r.num>>r.den;
  return s;
}

ostream& operator<<(ostream& s, rational r)
{
  if(r.den == 1)
    {
      s <<r.num;
    }
  else
    {
      s<<r.num<<"/"<<r.den;
    }
  return s;
}

/********
* OTHER *
********/
rational pow(rational r, long int n)
{
  rational t;

  r.reduce();

  t.num=lpow(r.num,n);
  t.den=lpow(r.den,n);

  return t;
}