refactor ProductLog - avoid StackOverflow because of recursion

- introduce new EvalEngine#evalNumericFunction() method

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

@@ -2120,12 +2120,55 @@ public void setUp(final ISymbol newSymbol) {
 
     @Override
     public IExpr e1ObjArg(final IExpr o) {
+      IExpr temp = functionExpandLogArg(o);
+      if (temp.isPresent()) {
+        return temp;
+      }
       if (o.equals(F.C0) || o.equals(F.CD0)) {
         return F.C0;
       }
       return F.NIL;
     }
 
+    private static IExpr functionExpandLogArg(final IExpr o) {
+      if (o.isTimes() && o.first().isFraction() && o.argSize() == 3) {
+        // ProductLog(Rational(k_,n_)*b_^Rational(c_,n_)*Log(b_)) :=
+        // Module( {a, v},
+        // a = N( (n*ProductLog((b^(c/n)*k*Log(b))/n))/Log(b) );
+        // v = Rationalize(a);
+        // v*Log(b)/n
+        // /; IntegerQ(v) && v >= 1 && PossibleZeroQ( (((-b^(c/n))*k + b^(v/n)*v)*Log(b))/n ))
+        IAST times = (IAST) o;
+        if (times.arg2().isPower() && times.arg3().isLog()) {
+          IAST power = (IAST) times.arg2();
+          if (power.base().isInteger() && power.base().equals(times.arg3().first())
+              && power.exponent().isFraction()) {
+            IInteger b = (IInteger) times.arg3().first();
+            IFraction arg1 = (IFraction) times.arg1();
+            IInteger k = arg1.numerator();
+            IInteger n = arg1.denominator();
+            IFraction powExponent = (IFraction) power.exponent();
+            if (n.equals(powExponent.denominator())) {
+              EvalEngine engine = EvalEngine.get();
+              IExpr a = engine
+                  .evalNumericFunction(F.Times(n, F.ProductLog(F.Times(arg1, F.Power(b, powExponent), F.Log(b))),
+                      F.Power(F.Log(b), F.CN1)));
+              IExpr v = engine.evaluate(F.Rationalize(a));
+              if (v.isInteger() && ((IInteger) v).isGE(F.C1)) {
+                IFraction resultFactor = F.QQ((IInteger) v, n);
+                IExpr isZero = engine.evaluate(F.Plus(F.Times(k.negate(), F.Power(b, powExponent)),
+                    F.Times(v, F.Power(b, resultFactor))));
+                if (isZero.isZero()) {
+                  return engine.evaluate(F.Times(resultFactor, F.Log(b)));
+                }
+              }
+            }
+          }
+        }
+      }
+      return F.NIL;
+    }
+
     @Override
     public IExpr e2ObjArg(IExpr k, IExpr z) {
       int ki = Integer.MIN_VALUE;

symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/eval/EvalEngine.java

@@ -787,8 +787,8 @@ private IAST endTrace() {
    *
    * @param result0 store the result of the evaluation in the i-th argument of the ast in <code>
    *     result0[0]</code>. <code>result0[0]</code> should be <code>F.NIL</code> if no evaluation
-   *        occured.
-   * @param ast the original <code>ast</code> for whixh the arguments should be evaluated
+   *        occurred.
+   * @param ast the original <code>ast</code> for which the arguments should be evaluated
    * @param arg the i-th argument of <code>ast</code>
    * @param i <code>arg</code> is the i-th argument of <code>ast</code>
    * @param isNumericFunction if <code>true</code> the <code>NumericFunction</code> attribute is set
@@ -1671,14 +1671,14 @@ public final int evalInt(final IExpr expr) throws ArgumentTypeException {
       result = expr.toIntDefault();
     }
     if (expr.isNumericFunction(true)) {
-      IExpr numericResult = evalN(expr);
+      IExpr numericResult = evalNumericFunction(expr);
       if (numericResult.isReal()) {
         result = numericResult.toIntDefault();
       }
     } else {
       IExpr temp = evaluateNIL(expr);
       if (temp.isNumericFunction(true)) {
-        IExpr numericResult = evalN(temp);
+        IExpr numericResult = evalNumericFunction(temp);
         if (numericResult.isReal()) {
           result = numericResult.toIntDefault();
         }
@@ -2093,6 +2093,26 @@ private void printOnOffTrace(IExpr unevaledExpr, IExpr evaledExpr) {
     }
   }
 
+  public final IExpr evalNumericFunction(final IExpr expr) {
+    if (expr.isNumericFunction(true)) {
+      final boolean oldNumericMode = isNumericMode();
+      final long oldDigitPrecision = getNumericPrecision();
+      final int oldSignificantFigures = getSignificantFigures();
+      try {
+        setNumericMode(true, oldDigitPrecision, oldSignificantFigures);
+        IExpr temp = evalWithoutNumericReset(expr);
+        if (temp.isListOrAssociation() || temp.isRuleAST()) {
+          return ((IAST) temp).mapThread(arg -> evalNumericFunction(arg));
+        }
+        return temp;
+      } finally {
+        setNumericMode(oldNumericMode);
+        setNumericPrecision(oldDigitPrecision);
+      }
+    }
+    return expr;
+  }
+
   /**
    * Evaluates <code>expr</code> numerically.
    *

symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/ProductLogRules.java

@@ -13,7 +13,7 @@ public class ProductLogRules {
    * <li>index 0 - number of equal rules in <code>RULES</code></li>
 	 * </ul>
 	 */
-  final public static int[] SIZES = { 12, 5 };
+  final public static int[] SIZES = { 12, 4 };
 
   final public static IAST RULES = List(
     IInit(ProductLog, SIZES),
@@ -64,9 +64,6 @@ public class ProductLogRules {
       Condition(x,GreaterEqual(x,CN1))),
     // ProductLog(-1,E^x_*x_):=x/;x<=-1
     ISetDelayed(ProductLog(CN1,Times(Exp(x_),x_)),
-      Condition(x,LessEqual(x,CN1))),
-    // ProductLog(Log(b_)*k_/n_*b_^(c_/n_)):=Module({a,v},a=N((n*ProductLog((b^(c/n)*k*Log(b))/n))/Log(b));v=Rationalize(a);v*Log(b)/n/;IntegerQ(v)&&v>=1&&PossibleZeroQ(((-b^(c/n)*k+b^(v/n)*v)*Log(b))/n))
-    ISetDelayed(ProductLog(Times(Log(b_),Rational(k_,n_),Power(b_,Rational(c_,n_)))),
-      Module(list(a,v),CompoundExpression(Set(a,N(Times(n,Power(Log(b),CN1),ProductLog(Times(Power(b,Times(c,Power(n,CN1))),k,Power(n,CN1),Log(b)))))),Set(v,Rationalize(a)),Condition(Times(v,Power(n,CN1),Log(b)),And(IntegerQ(v),GreaterEqual(v,C1),PossibleZeroQ(Times(Power(n,CN1),Plus(Times(CN1,Power(b,Times(c,Power(n,CN1))),k),Times(Power(b,Times(Power(n,CN1),v)),v)),Log(b))))))))
+      Condition(x,LessEqual(x,CN1)))
   );
 }

symja_android_library/rules/ProductLogRules.m

@@ -21,13 +21,5 @@
 ProductLog(x_*E^x_) := x 
   /; x>=-1,
 ProductLog(-1, x_*E^x_) := x 
-  /; x<=-1,
-ProductLog(Rational(k_,n_)*b_^Rational(c_,n_)*Log(b_)) :=
-  Module( {a, v},
-    a = N( (n*ProductLog((b^(c/n)*k*Log(b))/n))/Log(b) );
-	v = Rationalize(a);
-	v*Log(b)/n
-      /; IntegerQ(v) && 
-         v >= 1 &&
-	     PossibleZeroQ( (((-b^(c/n))*k + b^(v/n)*v)*Log(b))/n ))   
+  /; x<=-1  
 }