/// <summary>
/// Create a new instance of <see cref="Fraction" /> with a numerator and denominator.
/// </summary>
/// <remarks>
/// When creating an instance of <see cref="Fraction" /> it will always be in its simplest form.
/// </remarks>
/// <param name="numerator">Numerator for the fraction.</param>
/// <param name="denominator">Denominator for the fraction.</param>
public Fraction(int numerator, int denominator = 1)
{
if (denominator == 0)
{
throw new ArgumentException(nameof(denominator));
}
Sign = numerator < 0 ^ denominator < 0 ? -1 : 1;
Numerator = Math.Abs(numerator);
Denominator = Math.Abs(denominator);
var gcd = NumberTheory.GreatestCommonDivisor(Numerator, Denominator);
Numerator /= gcd;
Denominator /= gcd;
if (Denominator == 1)
{
ProperNumerator = 0;
}
else
{
ProperNumerator = Numerator < Denominator ? Numerator : Numerator % Denominator;
}
}
/// <summary>
/// Compare the <see cref="Fraction" /> with another fraction.
/// </summary>
/// <param name="other">The <see cref="Fraction" /> to compare against.</param>
/// <returns>-1 if it is less, 0 if equal, 1 if it is greater.</returns>
public int CompareTo(Fraction other)
{
var lcm = NumberTheory.LeastCommonMultiple(Denominator, other.Denominator);
var leftNumerator = Numerator * lcm / Denominator;
var rightNumerator = other.Numerator * lcm / other.Denominator;
return(leftNumerator.CompareTo(rightNumerator));
}
public static Fraction operator-(Fraction left, Fraction right)
{
var newDenominator = NumberTheory.LeastCommonMultiple(left.Denominator, right.Denominator);
var newNumerator = left.Sign * left.Numerator * newDenominator / left.Denominator
- right.Sign * right.Numerator * newDenominator / right.Denominator;
return(new Fraction(newNumerator, newDenominator));
}