Merge pull request #2 from GarriJS/combinatorics-functions

Adding combinatorics functions: binomial and permutation.

Author: Nonanti

MathFlow.Core/Combinatorics/CombinatoricsFunctions.cs

@@ -0,0 +1,86 @@
+namespace MathFlow.Core.Combinatorics;
+public static class CombinatoricsFunctions
+{
+	/// <summary>
+	/// Calculates the GCD.
+	/// </summary>
+	public static long GCD(long a, long b)
+	{
+		a = Math.Abs(a);
+		b = Math.Abs(b);
+
+		while (b != 0)
+		{
+			var temp = b;
+			b = a % b;
+			a = temp;
+		}
+
+		return a;
+	}
+
+	/// <summary>
+	/// Calculates the LCM.
+	/// </summary>
+	public static long LCM(long a, long b)
+	{
+		return Math.Abs(a * b) / GCD(a, b);
+	}
+
+	/// <summary>
+	/// Calculates the factorial.
+	/// </summary>
+	public static double Factorial(double n)
+	{
+		if (n < 0 || n != Math.Floor(n))
+			throw new ArgumentException("Factorial is only defined for non-negative integers");
+
+		if (n > 170)
+			return double.PositiveInfinity;
+
+		double result = 1;
+		for (int i = 2; i <= (int)n; i++)
+			result *= i;
+
+		return result;
+	}
+
+	/// <summary>
+	/// Calculates the binomial coefficient.
+	/// </summary>
+	public static double Binomial(double n, double k)
+	{
+		if (n < 0 || n != Math.Floor(n) || k < 0 || k != Math.Floor(k))
+			throw new ArgumentException("Binomial is only defined for non-negative integers");
+
+		if (n < 0 || k < 0 || k > n)
+			return 0;
+
+		if (k > n - k)
+			k = n - k;
+
+		double result = 1;
+		for (int i = 1; i <= k; i++)
+		{
+			result *= n - (k - i);
+			result /= i;
+		}
+
+		return result;
+	}
+
+	/// <summary>
+	/// Calculates the number of permutations.
+	/// </summary>
+	public static double Permutation(double n, double k)
+	{
+		if (n < 0 || n != Math.Floor(n) || k < 0 || k != Math.Floor(k) || k > n)
+			throw new ArgumentException("Permutation is only defined for non-negative integers with k <= n");
+
+		double result = 1;
+		for (int i = 0; i < k; i++)
+			result *= n - i;
+
+		return result;
+	}
+}