using System;

namespace TPClasses
{
	class Rationnel
	{
		
		/*Exercice 1*/
		public long num, den;
		
		/*Exercice 2*/
		public String toString()
		{
			return "" + num + "/" + den;
		}
		
		public static Rationnel create(long num, long den)
		{
			Rationnel r = new Rationnel();
			r.num = num;
			r.den = den;
			r.reduce();
			return r;
		}
		
		public Rationnel copy()
		{
			return create (num, den);
		}
		
		public Rationnel opposite()
		{
			return create(-num, den);
		}
		
		public Rationnel inverse()
		{
			return create(den, num);
		}
		
		public void reduce()
		{
			long p = num, q = den;
			while(q != 0)
			{
				long r = p%q;
				p = q;
				q = r;
			}
			num /= p;
			den /= p;
		}
		
		public bool isPositive()
		{
			return num >= 0 && den >= 0 || num < 0 && den < 0;
		}
		
		
		public Rationnel add(Rationnel other)
		{
			return create(num*other.den + den*other.num, den*other.den);
		}
		
		public void addTo(Rationnel other)
		{
			num = num*other.den + den*other.num;
			den = den*other.den;
		}
		
		
		public Rationnel sub(Rationnel other)
		{
			return add(other.opposite());
		}
		
		public Rationnel multiply(Rationnel other)
		{
			return create(num*other.num, den*other.den);
		}
		
		public Rationnel divide(Rationnel other)
		{
			return multiply(other.inverse());
		}
		
		public bool equals(Rationnel other)
		{
			return num*other.den == den*other.num;
		}
		
		public int compareTo(Rationnel other)
		{
			if (equals(other))
				return 0;
			Rationnel s = sub(other);
			if (s.isPositive())
				return 1;
			else 
				return -1;					
		}
		
		/*********************************************/
		
		public static void Main (string[] args)
		{
			/*Exercice 1*/
			Rationnel unDemi = new Rationnel();
			unDemi.num = 1;
			unDemi.den = 2;
			Rationnel quatreTiers = new Rationnel();
			quatreTiers.num = 4;
			quatreTiers.den = 3;
			/*Exercice 2*/
			Console.WriteLine("4/3 = " + quatreTiers.toString());
			Console.WriteLine("5/2 = " + create(5, 2).toString());
			Console.WriteLine("4/3 = " + quatreTiers.copy().toString());
			Console.WriteLine("-4/3 = " + quatreTiers.opposite().toString());
			Console.WriteLine("3/4 = " + quatreTiers.inverse().toString());
			Rationnel quatreTiersBis = create(40, 30);
			quatreTiersBis.reduce();
			Console.WriteLine("4/3 = " + quatreTiersBis.toString());
			Console.WriteLine("4/3 is " + ((quatreTiersBis.isPositive())?"positive":"negative"));
			Console.WriteLine("-4/3 is " + ((quatreTiersBis.opposite().isPositive())?"positive":"negative"));
			Console.WriteLine("4/3 + 1/2 = " + quatreTiers.add(unDemi).toString());
			quatreTiersBis.addTo(unDemi);
			Console.WriteLine("4/3 + 1/2 = " + quatreTiersBis.toString());
			Console.WriteLine("4/3 - 1/2 = " + quatreTiers.sub(unDemi).toString());
			Console.WriteLine("4/3 * 1/2 = " + quatreTiers.multiply(unDemi).toString());
			Console.WriteLine("(4/3) / (1/2) = " + quatreTiers.divide(unDemi).toString());
			Console.WriteLine("(4/3) == (8/4) = " + quatreTiers.equals(create(8, 4)));
			Console.WriteLine("(4/3) == (8/6) = " + quatreTiers.equals(create(8, 6)));
			Console.WriteLine("(4/3) > (8/4) = " + quatreTiers.compareTo(create(8, 4)));
			Console.WriteLine("(8/4) > (4/3) = " + create(8, 4).compareTo(quatreTiers));
			Console.WriteLine("(4/3) == (8/6) = " + quatreTiers.compareTo(create(8, 6)));
		}
	}
}