/// <summary>
/// Returns the inverse of the specified element.
/// </summary>
/// <param name="element">The element.</param>
/// <returns>The inverse of element (-element)</returns>
/// <exception cref="InvalidCastException">When the cast to DirectSum from interface was not possible</exception>
public DirectSum <T, TGroup> Inverse(DirectSum <T, TGroup> element)
{
var tuple = element.InverseElement() as DirectSum <T, TGroup>;
if (tuple == null)
{
throw new InvalidCastException();
}
return(tuple);
}
/// <summary>
/// Returns a vector with ones as values.
/// </summary>
/// <returns>The vector.</returns>
/// <param name="dimension">The dimension.</param>
/// <typeparam name="T">The type parameter.</typeparam>
/// <typeparam name="TStruct">The underlying structure.</typeparam>
/// <returns>The zerovector with dimension.</returns>
public DirectSum <T, TStruct> OneTuple <T, TStruct> (UInt32 dimension)
where TStruct : IRing <T>, new()
{
var tuple = new DirectSum <T, TStruct> (dimension);
var baseStructure = new TStruct();
for (UInt32 i = 0; i < tuple.Dimension; i++)
{
tuple [i] = baseStructure.One;
}
return(tuple);
}
/// <summary>
/// Multiplication of the specified leftElement and rightElement.
/// </summary>
/// <param name="leftElement">Left element.</param>
/// <param name="rightElement">Right element.</param>
/// <returns>The multiplication of the leftElement and rightElement (leftElement * rightElement)</returns>
/// <exception cref="InvalidCastException">Thrown when the cast was not possible.</exception>
public DirectSum <T, TRing> Multiplication(
DirectSum <T, TRing> leftElement,
DirectSum <T, TRing> rightElement)
{
var tuple = leftElement.Multiply(rightElement) as DirectSum <T, TRing>;
if (tuple == null)
{
throw new InvalidCastException();
}
return(tuple);
}
/// <summary>
/// Addition of the specified leftElement and rightElement.
/// </summary>
/// <param name="leftElement">Left element.</param>
/// <param name="rightElement">Right element.</param>
/// <returns>The addition of the leftElement and rightElement (leftElement + rightElement)</returns>
/// <exception cref="InvalidCastException">When the cast was not possible.</exception>
/// <exception cref="NotSupportedException">When the dimension of the parameters is not equal to the set dimension of the instance.</exception>
public DirectSum <T, TMonoid> Addition(
DirectSum <T, TMonoid> leftElement,
DirectSum <T, TMonoid> rightElement)
{
if (leftElement.Dimension != this.Dimension)
{
throw new NotSupportedException("The dimension is not set right");
}
var tuple = leftElement.Add(rightElement) as DirectSum <T, TMonoid>;
if (tuple == null)
{
throw new InvalidCastException();
}
return(tuple);
}
/// <summary>
/// Determines whether the specified <see cref="DirectSum{T,TStruct}"/> is equal to the current <see cref="DirectSum{T,TStruct}"/>.
/// </summary>
/// <param name="other">The <see cref="DirectSum{T,TStruct}"/> to compare with the current <see cref="DirectSum{T,TStruct}"/>.</param>
/// <returns><c>true</c> if the specified <see cref="DirectSum{T,TStruct}"/> is equal to the current
/// <see cref="DirectSum{T,TStruct}"/>otherwise, <c>false</c>.</returns>
public Boolean Equals(DirectSum <T, TStruct> other)
{
if (other == null)
{
return(false);
}
if (Object.ReferenceEquals(this, other))
{
return(true);
}
for (UInt32 i = 0; i < this._entries.Count; i++)
{
if (!this[i].Equals(other[i]))
{
return(false);
}
}
return(true);
}
