/// <summary>
/// Finds the greatest common divisor and reduces the fraction by this amount.
/// </summary>
/// <returns>the reduced rational</returns>
private static void Reduce(ref T numerator, ref T denominator)
{
bool reduced = false;
decimal n = Convert.ToDecimal(numerator);
decimal d = Convert.ToDecimal(denominator);
// greatest common divisor
decimal gcd = Rational<T>.GCD(n, d);
if (gcd != Decimal.One && gcd != Decimal.Zero)
{
reduced = true;
n /= gcd;
d /= gcd;
}
// cancel out signs
if (d < Decimal.Zero)
{
reduced = true;
n = -n;
d = -d;
}
if (reduced)
{
numerator = (T)Convert.ChangeType(n, typeof(T));
denominator = (T)Convert.ChangeType(d, typeof(T));
}
}
/// <summary>
/// Lowest Common Denominator
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
private static decimal LCD(decimal a, decimal b)
{
if (a == Decimal.Zero && b == Decimal.Zero)
{
return Decimal.Zero;
}
return (a * b) / Rational<T>.GCD(a, b);
}