RationalNumbers.cs

using System;
using System.Numerics;
using Waher.Script.Abstraction.Sets;
using Waher.Script.Abstraction.Elements;
 
namespace Waher.Script.Objects
{
    public sealed class RationalNumbers : Field, IOrderedSet
    {
        internal static readonly RationalNumber zero = new RationalNumber(BigInteger.Zero);
        internal static readonly RationalNumber one = new RationalNumber(BigInteger.One);
        private static readonly int hashCode = typeof(RationalNumbers).FullName.GetHashCode();
 
        public RationalNumbers()
        {
        }
 
        public override ICommutativeRingWithIdentityElement One
        {
            get { return one; }
        }
 
        public override IAbelianGroupElement Zero
        {
            get { return zero; }
        }
 
        public override bool Contains(IElement Element)
        {
            if (Element is RationalNumber)
                return true;
 
            object Obj = Element.AssociatedObjectValue;
            return Obj is BigInteger || Obj is double;
        }
 
        public override bool Equals(object obj)
        {
            return obj is RationalNumbers;
        }
 
        public override int GetHashCode()
        {
            return hashCode;
        }
 
        public static readonly RationalNumbers Instance = new RationalNumbers();
 
        public override string ToString()
        {
            return "ℚ";
        }
 
        public static int CompareNumbers(IElement x, IElement y)
        {
            BigInteger n1, d1;
            BigInteger n2, d2;
 
            if (x is RationalNumber q1)
            {
                n1 = q1.Numerator;
                d1 = q1.Denominator;
            }
            else if (x.AssociatedObjectValue is BigInteger i1)
            {
                n1 = i1;
                d1 = BigInteger.One;
            }
            else
            {
                n1 = BigInteger.Zero;
                d1 = BigInteger.One;
            }
 
            if (y is RationalNumber q2)
            {
                n2 = q2.Numerator;
                d2 = q2.Denominator;
            }
            else if (y.AssociatedObjectValue is BigInteger i2)
            {
                n2 = i2;
                d2 = BigInteger.One;
            }
            else
            {
                n2 = BigInteger.Zero;
                d2 = BigInteger.One;
            }
 
            BigInteger l = n1 * d2;
            BigInteger r = n2 * d1;
 
            return l.CompareTo(r);
        }
 
        public int Compare(IElement x, IElement y)
        {
            return CompareNumbers(x, y);
        }
    }
}