Integers.cs

using System;
using System.Numerics;
using Waher.Script.Abstraction.Sets;
using Waher.Script.Abstraction.Elements;
 
namespace Waher.Script.Objects
{
    public sealed class Integers : EuclidianDomain
    {
        internal static readonly Integer zero = new Integer(BigInteger.Zero);
        internal static readonly Integer one = new Integer(BigInteger.One);
        private static readonly int hashCode = typeof(Integers).FullName.GetHashCode();
 
        public Integers()
        {
        }
 
        public override ICommutativeRingWithIdentityElement One
        {
            get { return one; }
        }
 
        public override IAbelianGroupElement Zero
        {
            get { return zero; }
        }
 
        public override bool Contains(IElement Element)
        {
            object Obj = Element.AssociatedObjectValue;
            return (Obj is BigInteger) || (Obj is double d && Math.Truncate(d) == d);
        }
 
        public override bool Equals(object obj)
        {
            return obj is Integers;
        }
 
        public override int GetHashCode()
        {
            return hashCode;
        }
 
        public static readonly Integers Instance = new Integers();
 
        public override string ToString()
        {
            return "ℤ";
        }
 
        public override IEuclidianDomainElement Divide(IEuclidianDomainElement Left, IEuclidianDomainElement Right, out IEuclidianDomainElement Remainder)
        {
            if (Left.AssociatedObjectValue is BigInteger l && 
                Right.AssociatedObjectValue is BigInteger r)
            {
                BigInteger Result = BigInteger.DivRem(l, r, out BigInteger Residue);
                Remainder = new Integer(Residue);
                return new Integer(Result);
            }
            else
            {
                Remainder = null;
                return null;
            }
        }
    }
}