StirlingS2(n,k) for int values

Author: axkr

symja_android_library/doc/functions/StirlingS1.md

@@ -1,16 +1,17 @@
 ## StirlingS1
 
-``` 
+```
 StirlingS1(n, k)
-``` 
+```
 
 > returns the Stirling numbers of the first kind. 
  
 See:  
 * [Wikipedia - Stirling numbers of the first kind](https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind)
 
 ### Examples
-``` 
+
+```
 >> StirlingS1(9, 6)
 -4536
 ```

symja_android_library/doc/functions/StirlingS2.md

@@ -1,16 +1,17 @@
 ## StirlingS2
 
-``` 
+```
 StirlingS2(n, k)
-``` 
+```
 
-> returns the Stirling numbers of the second kind. 
+> returns the Stirling numbers of the second kind. `StirlingS2(n,k)` is the number of ways of partitioning an `n`-element set into `k` non-empty subsets.
  
 See:  
 * [Wikipedia - Stirling numbers of the second kind](http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind)
 
 ### Examples
-``` 
+
+```
 >> StirlingS2(10, 6)
 22827
 ```

symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/NumberTheory.java

@@ -5,7 +5,6 @@
 import static org.matheclipse.core.expression.F.C1;
 import static org.matheclipse.core.expression.F.C2;
 import static org.matheclipse.core.expression.F.CN1;
-import static org.matheclipse.core.expression.F.Cos;
 import static org.matheclipse.core.expression.F.Factorial;
 import static org.matheclipse.core.expression.F.Negate;
 import static org.matheclipse.core.expression.F.Plus;
@@ -23,6 +22,8 @@
 import java.util.concurrent.Callable;
 import java.util.concurrent.ExecutionException;
 
+import org.hipparchus.exception.MathRuntimeException;
+import org.hipparchus.util.CombinatoricsUtils;
 import org.matheclipse.core.basic.Config;
 import org.matheclipse.core.convert.JASConvert;
 import org.matheclipse.core.convert.VariablesSet;
@@ -2927,16 +2928,38 @@ public void setUp(final ISymbol newSymbol) {
 	 */
 	private static class StirlingS2 extends AbstractFunctionEvaluator {
 
-		private static IExpr stirlingS2(IInteger nArg1, IInteger kArg2, int k) {
-			IAST temp = F.PlusAlloc(k >= 0 ? k : 0);
-			for (int i = 0; i < k; i++) {
+		/**
+		 * Returns the Stirling number of the second kind, "{@code S(n,k)}", the number of ways of partitioning an
+		 * {@code n}-element set into {@code k} non-empty subsets.
+		 * 
+		 * @param n
+		 *            the size of the set
+		 * @param k
+		 *            the number of non-empty subsets
+		 * @param ki
+		 *            the number of non-empty subsets as int value
+		 * @return {@code S(nArg1,kArg2)}
+		 */
+		private static IExpr stirlingS2(IInteger n, IInteger k, int ki) {
+			try {
+				int ni = n.toIntDefault(0);
+				if (ni != 0 && ni <= 25) {// S(26,9) = 11201516780955125625 is larger than Long.MAX_VALUE
+					return F.ZZ(CombinatoricsUtils.stirlingS2(ni, ki));
+				}
+			} catch (MathRuntimeException mre) {
+				if (Config.DEBUG) {
+					mre.printStackTrace();
+				}
+			}
+			IAST temp = F.PlusAlloc(ki >= 0 ? ki : 0);
+			for (int i = 0; i < ki; i++) {
 				if ((i & 1) == 1) { // isOdd(i) ?
-					temp.append(Times(Negate(Binomial(kArg2, integer(i))), Power(Plus(kArg2, integer(-i)), nArg1)));
+					temp.append(Times(Negate(Binomial(k, integer(i))), Power(Plus(k, integer(-i)), n)));
 				} else {
-					temp.append(Times(Times(Binomial(kArg2, integer(i))), Power(Plus(kArg2, integer(-i)), nArg1)));
+					temp.append(Times(Times(Binomial(k, integer(i))), Power(Plus(k, integer(-i)), n)));
 				}
 			}
-			return Times(Power(Factorial(kArg2), CN1), temp);
+			return Times(Power(Factorial(k), CN1), temp);
 		}
 
 		/** {@inheritDoc} */

symja_android_library/matheclipse-core/src/main/resources/StirlingS1.md

@@ -1,16 +1,17 @@
 ## StirlingS1
 
-``` 
+```
 StirlingS1(n, k)
-``` 
+```
 
 > returns the Stirling numbers of the first kind. 
  
 See:  
 * [Wikipedia - Stirling numbers of the first kind](https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind)
 
 ### Examples
-``` 
+
+```
 >> StirlingS1(9, 6)
 -4536
 ```

symja_android_library/matheclipse-core/src/main/resources/StirlingS2.md

@@ -1,16 +1,17 @@
 ## StirlingS2
 
-``` 
+```
 StirlingS2(n, k)
-``` 
+```
 
-> returns the Stirling numbers of the second kind. 
+> returns the Stirling numbers of the second kind. `StirlingS2(n,k)` is the number of ways of partitioning an `n`-element set into `k` non-empty subsets.
  
 See:  
 * [Wikipedia - Stirling numbers of the second kind](http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind)
 
 ### Examples
-``` 
+
+```
 >> StirlingS2(10, 6)
 22827
 ```

symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java

@@ -6744,6 +6744,7 @@ public void testStirlingS1() {
 	}
 
 	public void testStirlingS2() {
+		check("StirlingS2(6,10)", "0");
 		check("StirlingS2(10,6)", "22827");
 		check("StirlingS2(0,0)", "1");
 		check("StirlingS2(1,1)", "1");