Add elimination rule for logarithmic expressions in EliminateRules

- `Solve(a*x^n+b*Log(c*x)+d==0, x)`

Author: axkr

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

@@ -33,6 +33,9 @@ public static Matcher init2() {
     // elimzeroplus(c_.+Log(b_.*x_)*x_^a_.,x_):=((-a*c)/ProductLog((-a*c)/((1/b))^a))^(1/a)/;FreeQ({a,b,c},x)
 matcher.caseOf($(elimzeroplus,Plus(c_DEFAULT,Times(Log(Times(b_DEFAULT,x_)),Power(x_,a_DEFAULT))),x_),
       Condition(Power(Times(CN1,a,c,Power(ProductLog(Times(CN1,a,Power(Power(Power(b,CN1),a),CN1),c)),CN1)),Power(a,CN1)),FreeQ(list(a,b,c),x)));
+    // elimzeroplus(Log(c_.*x_)*b_.+d_.+a_.*x_^n_.,x_):=((b*ProductLog((a*((1/(E^(d/b)*c)))^n*n)/b))/(a*n))^(1/n)/;FreeQ({a,b,c,d,n},x)
+matcher.caseOf($(elimzeroplus,Plus(Times(Log(Times(c_DEFAULT,x_)),b_DEFAULT),d_DEFAULT,Times(a_DEFAULT,Power(x_,n_DEFAULT))),x_),
+      Condition(Power(Times(b,Power(Times(a,n),CN1),ProductLog(Times(a,Power(b,CN1),Power(Power(Times(Exp(Times(Power(b,CN1),d)),c),CN1),n),n))),Power(n,CN1)),FreeQ(List(a,b,c,d,n),x)));
     // elimzeroplus(w_.*Sqrt(a_.+b_.*x_)+x_*y_.+z_.,x_):={(b*w^2-2*y*z-w*Sqrt(b^2*w^2+4*a*y^2-4*b*y*z))/(2*y^2),(b*w^2-2*y*z+w*Sqrt(b^2*w^2+4*a*y^2-4*b*y*z))/(2*y^2)}/;FreeQ({a,b,w,y,z},x)&&!PossibleZeroQ(y)
 matcher.caseOf($(elimzeroplus,Plus(Times(w_DEFAULT,Sqrt(Plus(a_DEFAULT,Times(b_DEFAULT,x_)))),Times(x_,y_DEFAULT),z_DEFAULT),x_),
       Condition(list(Times(Power(Times(C2,Sqr(y)),CN1),Plus(Times(b,Sqr(w)),Times(CN2,y,z),Times(CN1,w,Sqrt(Plus(Times(Sqr(b),Sqr(w)),Times(C4,a,Sqr(y)),Times(CN4,b,y,z)))))),Times(Power(Times(C2,Sqr(y)),CN1),Plus(Times(b,Sqr(w)),Times(CN2,y,z),Times(w,Sqrt(Plus(Times(Sqr(b),Sqr(w)),Times(C4,a,Sqr(y)),Times(CN4,b,y,z))))))),And(FreeQ(List(a,b,w,y,z),x),Not(PossibleZeroQ(y)))));

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

@@ -2254,6 +2254,8 @@ public void testSolveExp() {
 
   @Test
   public void testSolveLog() {
+    check("Solve(a*x^n+b*Log(c*x)+d==0, x)", //
+        "{{x->((b*ProductLog((a*(1/(c*E^(d/b)))^n*n)/b))/(a*n))^(1/n)}}");
     check("Solve(x^a*Log(b*x)+c==0, x)", //
         "{{x->((-a*c)/ProductLog((-a*c)/((1/b))^a))^(1/a)}}");
     check("Solve(x^c*Log(x)==0, x)", //

symja_android_library/rule_sets/EliminateRules.m

@@ -22,6 +22,9 @@
 elimzeroplus(x_^a_.*Log(b_.*x_)+c_., x_) := (-((a*c)/ProductLog(((-a)*c)/(1/b)^a)))^(1/a)
   /; FreeQ({a,b,c},x),
 
+elimzeroplus(a_.*x_^n_.+b_.*Log(c_.*x_)+d_., x_) := ((b*ProductLog((a*((1/(E^(d/b)*c)))^n*n)/b))/(a*n))^(1/n)
+  /; FreeQ({a,b,c,d,n},x),
+  
 elimzeroplus(y_.*x_+w_.*Sqrt(a_.+b_.*x_)+z_., x_) := {(b*w^2-2*y*z-w*Sqrt(b^2*w^2+4*a*y^2-4*b*y*z))/(2*y^2), 
                                                       (b*w^2-2*y*z+w*Sqrt(b^2*w^2+4*a*y^2-4*b*y*z))/(2*y^2)}  
   /; FreeQ({a,b,w,y,z},x)&&!PossibleZeroQ(y),