public void StirlingNumbers2RowSum()
{
foreach (int n in TestUtilities.GenerateIntegerValues(1, 100, 4))
{
double sum = 0.0;
foreach (double s in AdvancedIntegerMath.StirlingNumbers2(n))
{
sum += s;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(sum, AdvancedIntegerMath.BellNumber(n)));
}
}
public void BellNumberAsPoissonMoment()
{
// The Bell numbers are the moments of the Poisson distribution
// with \mu = 1.
UnivariateDistribution d = new PoissonDistribution(1.0);
foreach (int r in TestUtilities.GenerateIntegerValues(1, 50, 4))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedIntegerMath.BellNumber(r),
d.RawMoment(r)
));
}
}
public void BellNumberRecurrence()
{
// B_{n+1} = \sum_{k=0}^{n} {n \choose k} B_k
foreach (int r in TestUtilities.GenerateIntegerValues(50, 100, 2))
{
double s = 0.0;
IEnumerator <double> b = AdvancedIntegerMath.BinomialCoefficients(r).GetEnumerator();
for (int k = 0; k <= r; k++)
{
b.MoveNext();
s += b.Current * AdvancedIntegerMath.BellNumber(k);
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(s, AdvancedIntegerMath.BellNumber(r + 1)));
}
}