VectorSpaceElement.cs

using System.Collections.Generic;
using Waher.Script.Abstraction.Sets;
 
namespace Waher.Script.Abstraction.Elements
{
    public abstract class VectorSpaceElement : ModuleElement, IVectorSpaceElement
    {
        public VectorSpaceElement()
        {
        }
 
        public override ILeftModuleElement MultiplyScalarLeft(IRingElement Scalar)
        {
            if (Scalar is IFieldElement FieldElement)
                return this.MultiplyScalar(FieldElement);
            else
                return null;
        }
 
        public override IRightModuleElement MultiplyScalarRight(IRingElement Scalar)
        {
            if (Scalar is IFieldElement FieldElement)
                return this.MultiplyScalar(FieldElement);
            else
                return null;
        }
 
        public override IModuleElement MultiplyScalar(IRingElement Scalar)
        {
            if (Scalar is IFieldElement FieldElement)
                return this.MultiplyScalar(FieldElement);
            else
                return null;
        }
 
        public abstract IVectorSpaceElement MultiplyScalar(IFieldElement Scalar);
 
        public override ISet AssociatedSet => this.AssociatedVectorSpace;
 
        public override ISemiGroup AssociatedSemiGroup => this.AssociatedVectorSpace;
 
        public override IGroup AssociatedGroup => this.AssociatedVectorSpace;
 
        public override IAbelianGroup AssociatedAbelianGroup => this.AssociatedVectorSpace;
 
        public override ILeftModule AssociatedLeftModule => this.AssociatedVectorSpace;
 
        public override IRightModule AssociatedRightModule => this.AssociatedVectorSpace;
 
        public override Sets.IModule AssociatedModule => this.AssociatedVectorSpace;
 
        public abstract IVectorSpace AssociatedVectorSpace
        {
            get;
        }
 
        public abstract int Dimension
        {
            get;
        }
 
        public virtual ICollection<IElement> VectorElements => this.ChildElements;
 
        public abstract IElement GetElement(int Index);
 
        public abstract void SetElement(int Index, IElement Value);
    }
}