public override RingElement Multiply(RingElement el)
{
Matrix <T> B = el as Matrix <T>;
if (B == null)
{
throw new Exception("Ring element cannot be cast as Matrix!");
}
if (N != B.M)
{
throw new Exception("Invalid dimensions for matrix multiplication!");
}
T[][] newElements = new T[M][];
for (int i = 0; i < M; i++)
{
newElements[i] = new T[B.N];
for (int j = 0; j < B.N; j++)
{
RingElement sum = elements[0][0].Zero();
for (int k = 0; k < N; k++)
{
sum += elements[i][k] * B.GetElement(k, j);
}
newElements[i][j] = (T)sum;
}
}
return(new Matrix <T>(newElements));
}
public override bool Equals(RingElement el)
{
Rational q = el as Rational;
if (q == null)
{
throw new Exception("RingElement cannot be cast as Rational!");
}
return(Numerator == q.Numerator && Denominator == q.Denominator);
}
public override RingElement Multiply(RingElement el)
{
Rational q = el as Rational;
if (q == null)
{
throw new Exception("RingElement cannot be cast as Rational!");
}
return(new Rational(Numerator * q.Numerator, Denominator * q.Denominator));
}
public override RingElement Add(RingElement el)
{
Matrix <T> B = el as Matrix <T>;
if (B == null)
{
throw new Exception("Ring element cannot be cast as Matrix!");
}
if (B.M != M || B.N != N)
{
throw new Exception("Invalid dimensions for matrix addition!");
}
T[][] newElements = new T[M][];
for (int i = 0; i < M; i++)
{
newElements[i] = new T[N];
for (int j = 0; j < N; j++)
{
newElements[i][j] = (T)(elements[i][j] + B.GetElement(i, j));
}
}
return(new Matrix <T>(newElements));
}
public override bool Equals(RingElement el)
{
return(true);
}