public static BigRational ComputeP(int k, int n, int p)
{
// the P(n) equation
BigRational pnNumerator = BigRational.Pow(p, n);
BigRational pnDenominator = BigRational.Pow(k, (n - k)) * Factorial(k);
// the P(0) equation
//---the right side of "+" sign in Denominator
BigRational pk = BigRational.Pow(p, k);
BigRational factorialK = Factorial(k);
// CHANGED: Don't cast to double here (loses precision)
BigRational lastPart = (BigRational.Subtract(1, BigRational.Divide(p, k)));
BigRational factorialAndLastPart = BigRational.Multiply(factorialK, lastPart);
BigRational fullRightSide = BigRational.Divide(pk, factorialAndLastPart);
//---the left side of "+" sign in Denominator
BigRational series = Series(k, p);
BigRational p0Denominator = series + fullRightSide;
BigRational p0Result = BigRational.Divide(1, p0Denominator);
BigRational pNResult = BigRational.Divide((pnNumerator * p0Result), pnDenominator);
return(pNResult);
}
public void TestSubtraction()
{
BigRational sevenTwoths = new BigRational(3, 1, 2);
BigRational sevenFifths = new BigRational(1, 2, 5);
BigRational expected = new BigRational(2, 1, 10);
BigRational result = BigRational.Subtract(sevenTwoths, sevenFifths);
Assert.AreEqual(expected, result);
}
public void TestMullersRecurrenceConvergesOnFive()
{
// Set an upper limit to the number of iterations to be tried
int n = 100;
// Precreate some constants to use in the calculations
BigRational c108 = new BigRational(108);
BigRational c815 = new BigRational(815);
BigRational c1500 = new BigRational(1500);
BigRational convergencePoint = new BigRational(5);
// Seed the initial values
BigRational X0 = new BigRational(4);
BigRational X1 = new BigRational(new Fraction(17, 4));
BigRational Xprevious = X0;
BigRational Xn = X1;
// Get the current distance to the convergence point, this should be constantly
// decreasing with each iteration
BigRational distanceToConvergence = BigRational.Subtract(convergencePoint, X1);
int count = 1;
for (int i = 1; i < n; ++i)
{
BigRational Xnext = c108 - (c815 - c1500 / Xprevious) / Xn;
BigRational nextDistanceToConvergence = BigRational.Subtract(convergencePoint, Xnext);
Assert.IsTrue(nextDistanceToConvergence < distanceToConvergence);
Xprevious = Xn;
Xn = Xnext;
distanceToConvergence = nextDistanceToConvergence;
if ((double)Xn == 5d)
{
break;
}
++count;
}
Assert.AreEqual((double)Xn, 5d);
Assert.IsTrue(count == 70);
}
public void big_rational_static_methods()
{
Assert.True(0.5 == BigRational.Abs(0.5d));
Assert.True(0.5 == BigRational.Abs(-0.5d));
Assert.False(0.5 == BigRational.Abs(-1));
Assert.False(0.5 == BigRational.Abs(1));
Assert.True(-0.5 == BigRational.Negate(0.5d));
Assert.True(0.5 == BigRational.Negate(-0.5d));
Assert.False(0.5 == BigRational.Negate(-1));
Assert.False(-0.5 == BigRational.Negate(1));
//Doesn't work great... testing with equals doubles fails
Assert.True(new BigRational(1, 2) == BigRational.Invert(new BigRational(2, 1)));
Assert.True(new BigRational(2, 1) == BigRational.Invert(new BigRational(1, 2)));
Assert.True(new BigRational(-1, 2) == BigRational.Invert(new BigRational(-2, 1)));
Assert.True(new BigRational(-2, 1) == BigRational.Invert(new BigRational(-1, 2)));
Assert.True(new BigRational(BigInteger.One) + new BigRational(BigInteger.One) == 2);
Assert.True(BigRational.Add(new BigRational(BigInteger.One), new BigRational(BigInteger.One)) == 2);
//Not working for me
//BigRational big1 = new BigRational(1.0);
//big1++;
//Assert.AreEqual(new BigRational(2, 1), big1);
//Not working for me
//BigRational big2 = new BigRational(1.0);
//big2--;
//Assert.True(0 == big2);
Assert.True(new BigRational(BigInteger.One) - new BigRational(BigInteger.One) == 0);
Assert.True(BigRational.Subtract(new BigRational(BigInteger.One), new BigRational(BigInteger.One)) == 0);
BigRational big3 = new BigRational(1.0);
Assert.True(-1.0 == -big3);
BigRational big4 = new BigRational(1.0);
Assert.True(1.0 == +big3);
Assert.True(new BigRational(BigInteger.One) * new BigRational(BigInteger.One) == 1);
Assert.True(BigRational.Multiply(new BigRational(BigInteger.One), new BigRational(BigInteger.One)) == 1);
Assert.True(new BigRational(BigInteger.One) * new BigRational(2.0) == 2.0);
Assert.True(BigRational.Multiply(new BigRational(BigInteger.One), new BigRational(2.0)) == 2.0);
Assert.True(new BigRational(BigInteger.One) / new BigRational(BigInteger.One) == 1);
Assert.True(BigRational.Divide(new BigRational(BigInteger.One), new BigRational(BigInteger.One)) == 1);
Assert.AreEqual(new BigRational(1, 2), new BigRational(new BigInteger(1)) / new BigRational(new BigInteger(2))); //Again, mixing consructors doesn't work well.
Assert.AreEqual(new BigRational(1, 2), BigRational.Divide(new BigRational(new BigInteger(1)), new BigRational(new BigInteger(2)))); //Again, mixing consructors doesn't work well. Testing with equals double 0.5 fails
//Assert.True(new BigRational(BigInteger.One) < new BigRational(2.0)); //Don't mix the constructors for comparison!!!
Assert.True(new BigRational(1.0) < new BigRational(2.0));
Assert.False(new BigRational(2.0) < new BigRational(1.0));
Assert.False(new BigRational(1.0) < new BigRational(1.0));
Assert.True(new BigRational(1.0) <= new BigRational(2.0));
Assert.True(new BigRational(1.0) <= new BigRational(1.0));
Assert.False(new BigRational(2.0) <= new BigRational(1.0));
Assert.True(new BigRational(1.0) == new BigRational(1.0));
Assert.True(new BigRational(1.0) != new BigRational(2.0));
Assert.False(new BigRational(1.0) > new BigRational(2.0));
Assert.True(new BigRational(2.0) > new BigRational(1.0));
Assert.False(new BigRational(BigInteger.One) > new BigRational(BigInteger.One));
Assert.False(new BigRational(1.0) >= new BigRational(2.0));
Assert.True(new BigRational(BigInteger.One) >= new BigRational(BigInteger.One));
Assert.True(new BigRational(2.0) >= new BigRational(1.0));
//Modulus doesn't seem to work well
//Assert.AreEqual(BigRational.Zero, new BigRational(2.0) % new BigRational(1.0));
//Assert.AreEqual(BigRational.One, new BigRational(3.0) % new BigRational(2.0));
//Assert.True(new BigRational(1.5) % new BigRational(1.0) == new BigRational(0.5));
//Assert.True(new BigRational(1.0) % new BigRational(2.0) == 0);
}
