Peano Numbers

Peano Numbers

using System;

namespace PeanoNumbers
{
	public class PeanoNumber
	{
		private PeanoNumber _base;
		public PeanoNumber ():this(null)
		{

		}

		public PeanoNumber (PeanoNumber x)
		{
			this._base = x;
		}

		public PeanoNumber (int x)
		{
			if(x >= 0)
				this._base = new PeanoNumber(x-1);		
		}

		public bool IsZero{ get { return this._base == null; } }

		public bool IsOne{ get { return !IsZero && this._base.IsZero; } }

		public static PeanoNumber Zero{ get { return new PeanoNumber (); } }

		public int ToNatural(){
			if (this._base == null)
				return 0;
			else
				return 1 + this._base.ToNatural ();
		}

		public PeanoNumber Sum(PeanoNumber y){
			if (y.IsZero)
				return this;
			if (this.IsZero)
				return y;

			return new PeanoNumber(this + y._base);
		}

		public static PeanoNumber operator +(PeanoNumber p1, PeanoNumber p2) 
		{
			return p1.Sum (p2);
		}

		public PeanoNumber Difference(PeanoNumber y){

						if (this.IsZero && !y.IsZero)
				throw new Exception("Peano doesnt have negative numbers");
			if (y.IsZero)
				return this;

			return this._base - y._base;
		}

		public static PeanoNumber operator -(PeanoNumber p1, PeanoNumber p2) 
		{
			return p1.Difference(p2);
		}


		public PeanoNumber Product(PeanoNumber y){
			if (this.IsZero || y.IsZero)
				return Zero;
			return this + this* y._base;
		}

		public static PeanoNumber operator *(PeanoNumber p1, PeanoNumber p2) 
		{
			return p1.Product(p2);
		}

		public PeanoNumber Division(PeanoNumber y){
			if (this.IsZero)
				return Zero;
			if (y.IsZero)
				throw new Exception ("Division by zero doesnt exists");

			return new PeanoNumber ((this._base - y._base) / y);
		}

		public static PeanoNumber operator /(PeanoNumber p1, PeanoNumber p2) 
		{
			return p1.Division(p2);
		}

		public override bool Equals(object y){
			if (!(y is PeanoNumber))
				return false;
			var toCompare = y as PeanoNumber;

			if (toCompare.IsZero && !this.IsZero)
				return false;
			else if (!toCompare.IsZero && this.IsZero)
				return false;
			else
				return this._base.Equals (toCompare._base);
		}
	}
}