WIP #1146 add ConditionalExpression solutions without cross-check

- see `SolveData#solveTimesAST()`

Author: axkr

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

@@ -5,7 +5,6 @@
 import java.util.function.Predicate;
 import java.util.function.Supplier;
 import org.matheclipse.core.basic.Config;
-import org.matheclipse.core.basic.OperationSystem;
 import org.matheclipse.core.builtin.Algebra;
 import org.matheclipse.core.builtin.BooleanFunctions;
 import org.matheclipse.core.builtin.RootsFunctions;

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

@@ -708,6 +708,7 @@ private static IExpr solveNumeric(IExpr expr, boolean isNumeric, EvalEngine engi
      *
      * @param termsEqualZeroList a list of expressions which equals zero.
      * @param variable the variable which should be eliminated in the term
+     * @param multipleValues if <code>true</code> multiple results are returned as list of values
      * @param numeric evaluate in numericMode
      * @param engine
      * @return
@@ -984,7 +985,7 @@ private IASTMutable solveTimesEquationsRecursively(IASTMutable termsEqualZero,
           IExpr termEQZero = termsEqualZero.get(i);
           if (termEQZero.isTimes()) {
             solveTimesAST((IAST) termEQZero, termsEqualZero, inequationsList, numericFlag,
-                variables, multipleValues, engine, subSolutionSet, i);
+                variables, multipleValues, subSolutionSet, i, engine);
           } else {
             if (termEQZero.isAST()) {
               // try factoring
@@ -1006,7 +1007,7 @@ private IASTMutable solveTimesEquationsRecursively(IASTMutable termsEqualZero,
                 termEQZero = S.Factor.of(engine, termEQZero);
                 if (termEQZero.isTimes()) {
                   solveTimesAST((IAST) termEQZero, termsEqualZero, inequationsList, numericFlag,
-                      variables, multipleValues, engine, subSolutionSet, i);
+                      variables, multipleValues, subSolutionSet, i, engine);
                 }
               }
             }
@@ -1106,9 +1107,24 @@ private static IASTMutable crossChecking(IASTMutable termsEqualZero, IASTMutable
       return result;
     }
 
+    /**
+     * Analyze the <code>Time(..., ...)</code> expression in the given list of equations. If the
+     * expression is of the form <code>Times(..., ...) == 0</code>, set each factor equal to
+     * <code>0</code> and solve the resulting equations recursively.
+     * 
+     * @param times the <code>Times(..., ...)</code> expression
+     * @param termsEqualZeroList the list of expressions, which should equal <code>0</code>
+     * @param inequationsList a list of inequality constraints
+     * @param numericFlag if <code>true</code>, try to find a numeric solution
+     * @param variables the variables for which the equations should be solved
+     * @param multipleValues if <code>true</code> multiple results are returned as list of values
+     * @param subSolutionSet a set of rules which should solve the terms
+     * @param i the index of the current equation in the list
+     * @param engine the evaluation engine
+     */
     private void solveTimesAST(IAST times, IAST termsEqualZeroList, IAST inequationsList,
-        boolean numericFlag, IAST variables, boolean multipleValues, EvalEngine engine,
-        Set<IExpr> subSolutionSet, int i) {
+        boolean numericFlag, IAST variables, boolean multipleValues, Set<IExpr> subSolutionSet,
+        int i, EvalEngine engine) {
       IAST temp;
       for (int j = 1; j < times.size(); j++) {
         if (!times.get(j).isFree(Predicates.in(variables), true)) {
@@ -1127,6 +1143,9 @@ private void solveTimesAST(IAST times, IAST termsEqualZeroList, IAST inequations
                 if (replaceAll.isPlusTimesPower() && //
                     S.PossibleZeroQ.ofQ(engine, replaceAll)) {
                   subSolutionSet.add(solution);
+                } else if (!solution.isFree(S.ConditionalExpression)) {
+                  // TODO create some cross-check for C(1),... variables?
+                  subSolutionSet.add(solution);
                 }
               }
             }

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

@@ -1511,7 +1511,8 @@ public void testSolveHO4() {
     // TODO check result
     check(
         "Solve(Cos(x)+ Cos(x)^3 + Cos(x)^5 - 3*Cos(x)*Sin(x)^2 - 10*Cos(x)^3*Sin(x)^2 + 5*Cos(x)*Sin(x)^4 ==0,x)", //
-        "{{x->ConditionalExpression(Pi/8+2*Pi*C(1),C(1)∈Integers)}}");
+        "{{x->ConditionalExpression(-Pi/2+2*Pi*C(1),C(1)∈Integers)},{x->ConditionalExpression(Pi/\n"
+            + "8+2*Pi*C(1),C(1)∈Integers)},{x->ConditionalExpression(Pi/2+2*Pi*C(1),C(1)∈Integers)}}");
   }
 
   @Test
@@ -1924,11 +1925,13 @@ public void testSolveTrigs() {
     // \end{aligned}
     checkSolveLatex("9 \\sin x+6 \\cos x-3 \\sin 2 x+\\cos 2 x=8",
         "Cos(2*x)+6*Cos(x)+9*Sin(x)-3*Sin(2*x)==8",
-        "{{x->ConditionalExpression(-ArcTan(3)+2*Pi*C(1),C(1)∈Integers)}}");
+        "{{x->ConditionalExpression(Pi*(1/2+2*C(1)),C(1)∈Integers)},{x->ConditionalExpression(-ArcTan(\n" //
+            + "3)+2*Pi*C(1),C(1)∈Integers)}}");
 
     checkSolveLatex("\\sin 2 x-\\cos 2 x=3 \\sin x+\\cos x-2",
         "-Cos(2*x)+Sin(2*x)==-2+Cos(x)+3*Sin(x)",
-        "{{x->ConditionalExpression(Pi*(-1/4+2*C(1)),C(1)∈Integers)}}");
+        "{{x->ConditionalExpression(Pi*(-1/4+2*C(1)),C(1)∈Integers)},{x->ConditionalExpression(Pi*(\n"
+            + "1/6+2*C(1)),C(1)∈Integers)},{x->ConditionalExpression(Pi*(5/6+2*C(1)),C(1)∈Integers)}}");
 
     // TODO: wrong parsed input
     // checkSolveLatex("1+\\cot 2 x=\\frac{1-\\cos 2 x}{\\sin ^2 2 x}",
@@ -2275,6 +2278,16 @@ public void testSolveInverseMultivaluedArcSin() {
         "{{x->0}}");
   }
 
+  @Test
+  public void testSolveGithub1147() {
+    // issue 1147
+    check("Solve(-2*x*Sin(x^2)==0, x)", //
+        "{{x->0},{x->ConditionalExpression(Sqrt(2*Pi)*Sqrt(C(1)),C(1)∈Integers)},{x->ConditionalExpression(-Sqrt(\n" //
+            + "2*Pi)*Sqrt(C(1)),C(1)∈Integers)},{x->ConditionalExpression(-Sqrt(Pi+2*Pi*C(1)),C(\n" //
+            + "1)∈Integers)},{x->ConditionalExpression(Sqrt(Pi+2*Pi*C(1)),C(1)∈Integers)}}");
+
+  }
+
 
   /** The JUnit setup method */
   @Override