public static Fraction Simplify(Fraction fraction)
{
fraction = Normalize(fraction);
long num = fraction.Numerator;
long den = fraction.Denominator;
long g = IntegerMath.GreatestCommonDivisor(num, den);
num /= g;
den /= g;
return(new Fraction(num, den));
}
public static decimal Root(decimal value, long root)
{
if (IntegerMath.IsPowerOfTwo(root) && value < 0.0M)
{
throw new ArgumentOutOfRangeException(nameof(value), ErrorMessages.MustBePositive);
}
else if (value == 0.0M)
{
return(0.0M);
}
try
{
return(NewtonRaphson.Iterate(x => PowSquareLaw(x, root) - value, x => root * PowSquareLaw(x, root - 1), rounding: null));
}
catch (IterationsExceededException <decimal> exc)
{
return(exc.LastValue);
}
}
/// <summary>
/// <para>Defines root as a function</para>
/// <para>i.e. Root(100, 2) = 10 and Root(8, 3) == 2</para>
/// </summary>
/// <param name="value">The value to take the root of</param>
/// <param name="root">The root to apply</param>
/// <returns>The root of the value</returns>
public static double Root(double value, int root)
{
if (IntegerMath.IsPowerOfTwo(root) && value < 0.0)
{
throw new ArgumentOutOfRangeException(nameof(value), ErrorMessages.MustBePositive);
}
else if (value == 0.0)
{
return(0.0);
}
try
{
return(NewtonRaphson.Iterate(x => Math.Pow(x, root) - value, x => root * Math.Pow(x, root - 1), rounding: null));
}
catch (IterationsExceededException <double> exc)
{
return(exc.LastValue);
}
}
public static bool IsSimplified(Fraction fraction)
{
return(IntegerMath.GreatestCommonDivisor(fraction.Numerator, fraction.Denominator) == 1);
}