private BigFloat Factor()
{
//factoring can be very slow. So use only when neccessary (ToString, and comparisons)
if (denominator == 1)
{
return(this);
}
//factor numerator and denominator
BigInteger factor = BigInteger.GreatestCommonDivisor(numerator, denominator);
numerator /= factor;
denominator /= factor;
return(this);
}
public BigRational(BigInteger numerator, BigInteger denominator)
{
if (denominator.IsZero)
{
numerator = numerator.Sign;
}
else if (numerator.IsZero)
{
denominator = BigInteger.One;
}
else
{
var pgcd = BigInteger.GreatestCommonDivisor(numerator, denominator);
if (denominator.Sign < 0)
{
pgcd = -pgcd;
}
numerator /= pgcd;
denominator /= pgcd;
}
Numerator = numerator;
Denominator = denominator;
}
// Least Common Denominator (LCD)
//
// The LCD is the least common multiple of the two denominators. For instance, the LCD of
// {1/2, 1/4} is 4 because the least common multiple of 2 and 4 is 4. Likewise, the LCD
// of {1/2, 1/3} is 6.
//
// To find the LCD:
//
// 1) Find the Greatest Common Divisor (GCD) of the denominators
// 2) Multiply the denominators together
// 3) Divide the product of the denominators by the GCD
public static BigInteger LeastCommonDenominator(BigRational x, BigRational y)
{
// LCD( a/b, c/d ) == (bd) / gcd(b,d)
return (x.Denominator * y.Denominator) / BigInteger.GreatestCommonDivisor(x.Denominator, y.Denominator);
}
