WIP #918 Solve adds wrong zero solution for equation-systems

- Solve#crossChecking() wasn't called for all solution paths

Author: axkr

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

@@ -214,8 +214,7 @@ protected IASTAppendable analyzeSublistRecursive(ArrayList<ExprAnalyzer> analyze
           } else if (numericFlag) {
             listOfRules = findRoot(exprAnalyzer, engine);
             if (listOfRules.isPresent()) {
-              listOfRules =
-                  exprAnalyzer.mapOnOriginal(exprAnalyzer.getOriginalExpr(), listOfRules);
+              listOfRules = exprAnalyzer.mapOnOriginal(exprAnalyzer.getOriginalExpr(), listOfRules);
             }
           }
           if (listOfRules.isPresent()) {
@@ -618,22 +617,23 @@ public IExpr solveRecursive(IASTMutable termsEqualZeroList, IAST inequationsList
         // expensive recursion try
         IExpr firstEquation = termsEqualZeroList.arg1();
 
+        IASTMutable reducedEqualZeroList = termsEqualZeroList.copyAppendable();
         for (int i = 1; i < variables.size(); i++) {
           IExpr variable = variables.get(i);
 
           IAST[] reduced = Eliminate.eliminateOneVariable(F.list(F.Equal(firstEquation, F.C0)),
               variable, true, engine);
           if (reduced != null) {
             variables = variables.splice(i);
-            termsEqualZeroList = termsEqualZeroList.removeAtCopy(1);
+            reducedEqualZeroList = reducedEqualZeroList.removeAtCopy(1);
             // oneVariableRule = ( firstVariable -> reducedExpression )
             IAST oneVariableRule = reduced[1];
-            IExpr replaced = termsEqualZeroList.replaceAll(oneVariableRule);
+            IExpr replaced = reducedEqualZeroList.replaceAll(oneVariableRule);
             if (replaced.isList()) {
               IExpr subResult = solveRecursive((IASTMutable) replaced, inequationsList, numericFlag,
                   variables, engine);
               if (subResult.isListOfLists()) {
-                return F.mapList((IAST) subResult, t -> {
+                IASTMutable result = F.mapList((IAST) subResult, t -> {
                   final IAST listOfRules = (IAST) t;
                   IExpr replaceAllExpr = oneVariableRule.second().replaceAll(listOfRules);
                   if (replaceAllExpr.isPresent()) {
@@ -642,12 +642,13 @@ public IExpr solveRecursive(IASTMutable termsEqualZeroList, IAST inequationsList
                   }
                   return F.NIL;
                 });
+                return crossChecking(termsEqualZeroList, result, engine);
               } else if (subResult.isList()) { // important for NSolve
                 replaced = oneVariableRule.second().replaceAll((IAST) subResult);
                 if (replaced.isPresent()) {
-                  IASTAppendable appendable = ((IAST) subResult).copyAppendable();
-                  appendable.append(F.Rule(variable, replaced));
-                  return appendable;
+                  IASTAppendable result = ((IAST) subResult).copyAppendable();
+                  result.append(F.Rule(variable, replaced));
+                  return crossChecking(termsEqualZeroList, result, engine);
                 }
               }
             }
@@ -941,7 +942,6 @@ private IASTMutable solveTimesEquationsRecursively(IASTMutable termsEqualZero,
                 solveTimesAST((IAST) termEQZero, termsEqualZero, inequationsList, numericFlag,
                     variables, multipleValues, engine, subSolutionSet, i);
               }
-
             }
           }
         }
@@ -1019,6 +1019,10 @@ private static IASTMutable crossChecking(IASTMutable termsEqualZero, IASTMutable
                 break;
               }
             } else {
+              if (possibleZero.isIndeterminate()) {
+                removedPositions[untilPosition++] = j;
+                break;
+              }
               if (!engine.evalTrue(F.PossibleZeroQ(replaceAll))) {
                 removedPositions[untilPosition++] = j;
                 break;

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

@@ -1413,7 +1413,7 @@ public void testSolveIssue130() {
   public void testSolveIssue413() {
     // eval quiet without message
     check("Solve({8.0*E - 9 == x0/x1, x0==x1^4.0},{x0, x1}) ", //
-        "{{x1->-1.16797+I*2.02298,x0->-14.88721+I*25.78541},{x1->-1.16797+I*(-2.02298),x0->-14.88721+I*(-25.78541)},{x1->0.0,x0->0.0},{x1->2.33594,x0->29.77443}}");
+        "{{x1->-1.16797+I*2.02298,x0->-14.88721+I*25.78541},{x1->-1.16797+I*(-2.02298),x0->-14.88721+I*(-25.78541)},{x1->2.33594,x0->29.77443}}");
     // eval quiet without message
     check("Solve({x0^2.0*Sin(x1)==5.0,x1^3.0*Cos(x0)==5.0},{x0,x1}) ", //
         "Solve({x0^2.0*Sin(x1)==5.0,x1^3.0*Cos(x0)==5.0},{x0,x1})");
@@ -2015,10 +2015,29 @@ public void testIssue902() {
 
   @Test
   public void testIssue914() {
+    // TODO
+    // check("Solve(5==35500*(1+x/4)^(4*7),x)", //
+    // "");
     check("Solve({A==20^300,A==26158/5},{A})", //
         "{}");
   }
 
+  // @Test
+  // public void testIssue916() {
+  // TODO
+  // check("ProductLog(-Log(7)/5243338316756303634461458718861951455543)//N", //
+  // "-3.7112*10^-40");
+  // check("Solve(7^x-x==47, x)", //
+  // "{{x->-47},{x->-(47*Log(7)+ProductLog(-1,-Log(7)/\n" //
+  // + "5243338316756303634461458718861951455543))/Log(7)}}");
+  // }
+
+  @Test
+  public void testIssue918() {
+    check("Solve({x==Pi*y^2, 5==x/y}, {x,y})", //
+        "{{y->5/Pi,x->25/Pi}}");
+  }
+
 
   /** The JUnit setup method */
   @Override