AbelianGroupElement.cs

using System;
using Waher.Script.Abstraction.Sets;
 
namespace Waher.Script.Abstraction.Elements
{
    public abstract class AbelianGroupElement : GroupElement, IAbelianGroupElement
    {
        public AbelianGroupElement()
        {
        }
 
        public override ISemiGroupElement AddLeft(ISemiGroupElement Element)
        {
            if (Element is IAbelianGroupElement E)
                return E.Add(this);
            else
                return null;
        }
 
        public override ISemiGroupElement AddRight(ISemiGroupElement Element)
        {
            if (Element is IAbelianGroupElement E)
                return this.Add(E);
            else
                return null;
        }
 
        public abstract IAbelianGroupElement Add(IAbelianGroupElement Element);
 
        public override ISet AssociatedSet => this.AssociatedAbelianGroup;
 
        public override ISemiGroup AssociatedSemiGroup => this.AssociatedAbelianGroup;
 
        public override IGroup AssociatedGroup => this.AssociatedAbelianGroup;
 
        public abstract IAbelianGroup AssociatedAbelianGroup
        {
            get;
        }
 
        public abstract IAbelianGroupElement Zero
        {
            get;
        }
    }
}