Ring.cs

using Waher.Script.Abstraction.Elements;
 
namespace Waher.Script.Abstraction.Sets
{
    public abstract class Ring : AbelianGroup, IRing
    {
        public Ring()
            : base()
        {
        }
 
        public virtual IRingElement Multiply(IRingElement Left, IRingElement Right)
        {
            IRingElement Result;
 
            Result = Left.MultiplyRight(Right);
            if (!(Result is null))
                return Result;
 
            Result = Right.MultiplyLeft(Left);
            if (!(Result is null))
                return Result;
 
            return null;
        }
 
        public virtual IRingElement RightDivide(IRingElement Left, IRingElement Right)
        {
            IRingElement Inverse = Right.Invert();
            if (Inverse is null)
                return null;
            else
                return this.Multiply(Left, Inverse) as IRingElement;
        }
 
        public virtual IRingElement LeftDivide(IRingElement Left, IRingElement Right)
        {
            IRingElement Inverse = Left.Invert();
            if (Inverse is null)
                return null;
            else
                return this.Multiply(Inverse, Right) as IRingElement;
        }
 
        public abstract bool IsCommutative
        {
            get;
        }
    }
}