AbelianGroup.cs

using System;
using Waher.Script.Abstraction.Elements;
 
namespace Waher.Script.Abstraction.Sets
{
    public abstract class AbelianGroup : Group, IAbelianGroup
    {
        public AbelianGroup()
            : base()
        {
        }
 
        public override sealed IGroupElement RightSubtract(IGroupElement Left, IGroupElement Right)
        {
            if (Left is IAbelianGroupElement L && Right is IAbelianGroupElement R)
                return this.Subtract(L, R);
            else
                return base.RightSubtract(Left, Right);
        }
 
        public override sealed IGroupElement LeftSubtract(IGroupElement Left, IGroupElement Right)
        {
            if (Left is IAbelianGroupElement L && Right is IAbelianGroupElement R)
                return this.Subtract(R, L);
            else
                return base.LeftSubtract(Left, Right);
        }
 
        public virtual IAbelianGroupElement Subtract(IAbelianGroupElement Left, IAbelianGroupElement Right)
        {
            return this.Add(Left, Right.Negate()) as IAbelianGroupElement;
        }
 
        public override sealed bool IsAbelian
        {
            get
            {
                return true;
            }
        }
 
        public override sealed IGroupElement AdditiveIdentity
        {
            get
            {
                return this.Zero;
            }
        }
 
        public abstract IAbelianGroupElement Zero
        {
            get;
        }
 
    }
}