public static void Sample_Sqrt_of_2()
{
//this example shows how to use ContinuedFraction to solve problem
//In the first 1000 expansions of sqrt of 2,
//how many fractions contain a numerator with more digits than denominator?
//(Question from http://projecteuler.net)
var sqrtOf2 = new ContinuedFraction(2);
Console.WriteLine(sqrtOf2.Take(1001).Count(r => r.Numerator.ToString().Length > r.Denominator.ToString().Length));
}
public static void Sequence()
{
//this example shows how to iterate ContinuedFraction
//create ContinuedFraction
var sqrtOf2 = new ContinuedFraction(2);
//ContinuedFraction derived from BaseSequence you can iterate as sequence
foreach (var r in sqrtOf2.Take(10))
{
Console.WriteLine("{0:0.000000}: {1}", (double)r, r);
}
}
public static void Create()
{
//this example shows how to create ContinuedFraction
//you can create continued fraction by new ContinuedFraction(x, y, z)
//where formula is (Sqrt(x) + y) / z
//if you omit y, 0 will be assumed
//if you omit z, 1 will be assumed
var sqrtOf2 = new ContinuedFraction(2);
//show result
Console.WriteLine(sqrtOf2);
}
static List <BigInteger[]> computeQuadratic(BigInteger a, BigInteger b, BigInteger c, int times, Func <Rational, Rational, Rational[]> selector)
{
var a2 = 2 * a;
var s = b * b - 4 * a * c;
Rational[] rt;
var list = new List <BigInteger[]>();
var cf = new ContinuedFraction(s, -b, a2);
foreach (var r in cf.Take(1 + cf.SubQuotients.Count + ((cf.PeriodicLength % 2 == 0) ? 1 : 2) * times * cf.PeriodicLength))
{
if (a * r.Numerator * r.Numerator + b * r.Numerator * r.Denominator + c * r.Denominator * r.Denominator == BigInteger.One)
{
rt = selector(r.Numerator, r.Denominator);
if (rt[0].Denominator == BigInteger.One && rt[1].Denominator == BigInteger.One)
{
list.Add(new[] { rt[0].Numerator, rt[1].Numerator });
break;
}
}
}
foreach (var r in cf.Take(1 + cf.SubQuotients.Count + ((cf.PeriodicLength % 2 == 0) ? 1 : 2) * times * cf.PeriodicLength))
{
if (a * r.Numerator * r.Numerator + b * r.Numerator * r.Denominator + c * r.Denominator * r.Denominator == BigInteger.One)
{
rt = selector(-r.Numerator, -r.Denominator);
if (rt[0].Denominator == BigInteger.One && rt[1].Denominator == BigInteger.One)
{
list.Add(new[] { rt[0].Numerator, rt[1].Numerator });
break;
}
}
}
cf = new ContinuedFraction(s, b, -a2);
foreach (var r in cf.Take(1 + cf.SubQuotients.Count + ((cf.PeriodicLength % 2 == 0) ? 1 : 2) * times * cf.PeriodicLength))
{
if (a * r.Numerator * r.Numerator + b * r.Numerator * r.Denominator + c * r.Denominator * r.Denominator == BigInteger.One)
{
rt = selector(r.Numerator, r.Denominator);
if (rt[0].Denominator == BigInteger.One && rt[1].Denominator == BigInteger.One)
{
list.Add(new[] { rt[0].Numerator, rt[1].Numerator });
break;
}
}
}
foreach (var r in cf.Take(1 + cf.SubQuotients.Count + ((cf.PeriodicLength % 2 == 0) ? 1 : 2) * times * cf.PeriodicLength))
{
if (a * r.Numerator * r.Numerator + b * r.Numerator * r.Denominator + c * r.Denominator * r.Denominator == BigInteger.One)
{
rt = selector(-r.Numerator, -r.Denominator);
if (rt[0].Denominator == BigInteger.One && rt[1].Denominator == BigInteger.One)
{
list.Add(new[] { rt[0].Numerator, rt[1].Numerator });
break;
}
}
}
return(list);
}
