private static BigFraction Add(BigFraction left, BigFraction right, bool bReduce = false)
{
if (left.Denominator == right.Denominator)
{
return(new BigFraction(left.Numerator + right.Numerator, left.Denominator));
}
return(new BigFraction(left.Numerator * right.Denominator + right.Numerator * left.Denominator, right.Denominator * left.Denominator));
}
public bool Equals(BigFraction other)
{
BigFraction f1, f2;
if (Denominator == other.Denominator)
{
return(Numerator == other.Numerator);
}
f1 = Reduce(this);
f2 = Reduce(other);
if (f1.Denominator == f2.Denominator)
{
return(f1.Numerator == f2.Numerator);
}
return(false);
}
//Fancy methods
public static BigFraction SqrtConvergent(int iNum, int iConvergent)
{
if (iNum.IsSquare() || iConvergent == 0)
{
return(new BigFraction(iNum.Sqrt(), 1));
}
List <int> liContFrac = Numbers.SqrtContinuedFraction(iNum);
int iPeriod = liContFrac.Count - 1;
iConvergent--;
BigFraction f = new BigFraction(liContFrac[(iConvergent % iPeriod) + 1], 1);
for (int i = iConvergent - 1; i >= 0; i--)
{
f = liContFrac[(i % iPeriod) + 1] + (1 / f);
}
f = liContFrac[0] + (1 / f);
return(f);
}
//Returns Tuple(x,y) for x^2 - Dy^2 = 1;
public static Tuple <BigInteger, BigInteger> SolvePellEquation(int D)
{
BigInteger x, y;
List <int> liSCF = Numbers.SqrtContinuedFraction(D);
int r = Math.Max(liSCF.Count - 2, 1);
BigFraction bf;
if (r % 2 == 0)
{
bf = BigFraction.SqrtConvergent(D, 2 * r + 1);
}
else
{
bf = BigFraction.SqrtConvergent(D, r);
}
bf.Reduce();
x = bf.Numerator;
y = bf.Denominator;
return(new Tuple <BigInteger, BigInteger>(x, y));
}
private static BigFraction Reduce(BigFraction f)
{
f.Reduce();
return(f);
}
private static BigFraction Add(BigFraction f, BigInteger i)
{
return(new BigFraction(f.Numerator + (i * f.Denominator), f.Denominator));
}
