/// <summary>
/// Subtracts the right group element from the left one: Left+(-Right)
/// </summary>
/// <param name="Left">Left element.</param>
/// <param name="Right">Right element.</param>
/// <returns>Result, if understood, null otherwise.</returns>
public override sealed IGroupElement RightSubtract(IGroupElement Left, IGroupElement Right)
{
IAbelianGroupElement L = Left as IAbelianGroupElement;
IAbelianGroupElement R = Right as IAbelianGroupElement;
if (L is null || R is null)
{
return(base.RightSubtract(Left, Right));
}
/// <summary>
/// Tries to add an element to the current element, from the left.
/// </summary>
/// <param name="Element">Element to add.</param>
/// <returns>Result, if understood, null otherwise.</returns>
public override ISemiGroupElement AddLeft(ISemiGroupElement Element)
{
IAbelianGroupElement E = Element as IAbelianGroupElement;
if (E is null)
{
return(null);
}
else
{
return(E.Add(this));
}
}
/// <summary>
/// Subtracts the left group element from the right one: (-Left)+Right.
/// </summary>
/// <param name="Left">Left element.</param>
/// <param name="Right">Right element.</param>
/// <returns>Result, if understood, null otherwise.</returns>
public override sealed IGroupElement LeftSubtract(IGroupElement Left, IGroupElement Right)
{
IAbelianGroupElement L = Left as IAbelianGroupElement;
IAbelianGroupElement R = Right as IAbelianGroupElement;
if (L == null || R == null)
{
return(base.LeftSubtract(Left, Right));
}
else
{
return(this.Subtract(R, L));
}
}
/// <summary>
/// Tries to add an element to the current element.
/// </summary>
/// <param name="Element">Element to add.</param>
/// <returns>Result, if understood, null otherwise.</returns>
public override IAbelianGroupElement Add(IAbelianGroupElement Element)
{
ComplexNumber E = Element as ComplexNumber;
if (E is null)
{
DoubleNumber D = Element as DoubleNumber;
if (D is null)
{
return(null);
}
else
{
return(new ComplexNumber(this.value + D.Value));
}
}
else
{
return(new ComplexNumber(this.value + E.value));
}
}
/// <summary>
/// Tries to add an element to the current element.
/// </summary>
/// <param name="Element">Element to add.</param>
/// <returns>Result, if understood, null otherwise.</returns>
public override IAbelianGroupElement Add(IAbelianGroupElement Element)
{
if (Element is RationalNumber Q)
{
return(this + Q);
}
if (Element is Integer i)
{
return(this + i.Value);
}
if (Element is DoubleNumber D)
{
return(new DoubleNumber(this.ToDouble() + D.Value));
}
if (Element is ComplexNumber z)
{
return(new ComplexNumber(this.ToDouble() + z.Value));
}
return(null);
}
/// <summary>
/// Subtracts the right group element from the left one: Left-Right
/// </summary>
/// <param name="Left">Left element.</param>
/// <param name="Right">Right element.</param>
/// <returns>Result, if understood, null otherwise.</returns>
public virtual IAbelianGroupElement Subtract(IAbelianGroupElement Left, IAbelianGroupElement Right)
{
return(this.Add(Left, Right.Negate()) as IAbelianGroupElement);
}
