Improve rule Limit(x_^(a_.*(x_^n_.)), x_Symbol->Infinity)

axkr · Aug 3, 2024 · 568bab0 · 568bab0
1 parent 3806b84
commit 568bab0
Show file tree

Hide file tree

Showing 2 changed files with 12 additions and 12 deletions.
diff --git a/...theclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/LimitRules.java b/...theclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/LimitRules.java
@@ -23,18 +23,18 @@ public class LimitRules {
     // Limit(x_/(x_!)^(1/x_),x_Symbol->Infinity):=E
     ISetDelayed(Limit(Times(Power(Factorial(x_),Negate(Power(x_,CN1))),x_),Rule(x_Symbol,oo)),
       E),
-    // Limit(x_^(b_.+a_.*x_^n_.),x_Symbol->0):=With({r=ConditionalExpression(1,a∈Reals&&b>0&&n>0)},r/;r=!=Undefined)
+    // Limit(x_^(b_.+a_.*x_^n_.),x_Symbol->0):=With({r=ConditionalExpression(1,a∈Reals&&b>0&&n>0)},r/;r=!=Undefined&&FreeQ({a,b,n},x))
     ISetDelayed(Limit(Power(x_,Plus(b_DEFAULT,Times(a_DEFAULT,Power(x_,n_DEFAULT)))),Rule(x_Symbol,C0)),
-      With(list(Set(r,ConditionalExpression(C1,And(Element(a,Reals),Greater(b,C0),Greater(n,C0))))),Condition(r,UnsameQ(r,Undefined)))),
-    // Limit(x_^(b_.+a_.*x_^n_.),x_Symbol->0):=With({r=ConditionalExpression(0,b∈Reals&&a>0&&n<0&&Cos(-n*Pi)>0&&Sin(-n*Pi)>0)},r/;r=!=Undefined)
+      With(list(Set(r,ConditionalExpression(C1,And(Element(a,Reals),Greater(b,C0),Greater(n,C0))))),Condition(r,And(UnsameQ(r,Undefined),FreeQ(list(a,b,n),x))))),
+    // Limit(x_^(b_.+a_.*x_^n_.),x_Symbol->0):=With({r=ConditionalExpression(0,b∈Reals&&a>0&&n<0&&Cos(-n*Pi)>0&&Sin(-n*Pi)>0)},r/;r=!=Undefined&&FreeQ({a,b,n},x))
     ISetDelayed(Limit(Power(x_,Plus(b_DEFAULT,Times(a_DEFAULT,Power(x_,n_DEFAULT)))),Rule(x_Symbol,C0)),
-      With(list(Set(r,ConditionalExpression(C0,And(Element(b,Reals),Greater(a,C0),Less(n,C0),Greater(Cos(Times(CN1,n,Pi)),C0),Greater(Sin(Times(CN1,n,Pi)),C0))))),Condition(r,UnsameQ(r,Undefined)))),
-    // Limit(x_^(b_.+a_.*x_^n_.),x_Symbol->Infinity):=With({r=ConditionalExpression(Infinity,b∈Reals&&a>0&&n>0)},r/;r=!=Undefined)
+      With(list(Set(r,ConditionalExpression(C0,And(Element(b,Reals),Greater(a,C0),Less(n,C0),Greater(Cos(Times(CN1,n,Pi)),C0),Greater(Sin(Times(CN1,n,Pi)),C0))))),Condition(r,And(UnsameQ(r,Undefined),FreeQ(list(a,b,n),x))))),
+    // Limit(x_^(b_.+a_.*x_^n_.),x_Symbol->Infinity):=With({r=ConditionalExpression(Infinity,b∈Reals&&a>0&&n>0)},r/;r=!=Undefined&&FreeQ({a,b,n},x))
     ISetDelayed(Limit(Power(x_,Plus(b_DEFAULT,Times(a_DEFAULT,Power(x_,n_DEFAULT)))),Rule(x_Symbol,oo)),
-      With(list(Set(r,ConditionalExpression(oo,And(Element(b,Reals),Greater(a,C0),Greater(n,C0))))),Condition(r,UnsameQ(r,Undefined)))),
-    // Limit(x_^(a_.*x_^n_.),x_Symbol->Infinity):=With({r=ConditionalExpression(1,a∈Reals&&n<0)},r/;r=!=Undefined)
+      With(list(Set(r,ConditionalExpression(oo,And(Element(b,Reals),Greater(a,C0),Greater(n,C0))))),Condition(r,And(UnsameQ(r,Undefined),FreeQ(list(a,b,n),x))))),
+    // Limit(x_^(a_.*x_^n_.),x_Symbol->Infinity):=With({r=ConditionalExpression(1,a∈Reals&&n<0)},r/;r=!=Undefined&&FreeQ({a,n},x))
     ISetDelayed(Limit(Power(x_,Times(a_DEFAULT,Power(x_,n_DEFAULT))),Rule(x_Symbol,oo)),
-      With(list(Set(r,ConditionalExpression(C1,And(Element(a,Reals),Less(n,C0))))),Condition(r,UnsameQ(r,Undefined)))),
+      With(list(Set(r,ConditionalExpression(C1,And(Element(a,Reals),Less(n,C0))))),Condition(r,And(UnsameQ(r,Undefined),FreeQ(list(a,n),x))))),
     // Limit(x_^p_,x_Symbol->Infinity):=If(p<0,0,Infinity,ConditionalExpression(Infinity,p>0))
     ISetDelayed(Limit(Power(x_,p_),Rule(x_Symbol,oo)),
       If(Less(p,C0),C0,oo,ConditionalExpression(oo,Greater(p,C0)))),

diff --git a/symja_android_library/rules/LimitRules.m b/symja_android_library/rules/LimitRules.m
@@ -1,10 +1,10 @@
 {
  Limit(x_*Sqrt(2*Pi)^(x_^(-1))*(Sin(x_)/(x_!))^(x_^(-1)), x_Symbol->Infinity):= E,
  Limit(x_*((x_!)^(-1*x_^(-1))), x_Symbol->Infinity):= E,
- Limit(x_^(a_.*(x_^n_.) + b_.), x_Symbol->0):= With({r=ConditionalExpression( 1, Element(a,Reals)&&b>0&&n>0 )}, r /; r=!= Undefined),
- Limit(x_^(a_.*(x_^n_.) + b_.), x_Symbol->0):= With({r=ConditionalExpression( 0, Element(b,Reals)&&a>0&&n<0&&Cos(-n*Pi)>0&&Sin(-n*Pi)>0 )}, r /; r=!= Undefined),
- Limit(x_^(a_.*(x_^n_.) + b_.), x_Symbol->Infinity):= With({r=ConditionalExpression( Infinity, Element(b,Reals)&&a>0&&n>0 )}, r /; r=!= Undefined),
- Limit(x_^(a_.*(x_^n_.)), x_Symbol->Infinity):= With({r=ConditionalExpression( 1, Element(a,Reals)&&n<0 )}, r /; r=!= Undefined),
+ Limit(x_^(a_.*(x_^n_.) + b_.), x_Symbol->0):= With({r=ConditionalExpression( 1, Element(a,Reals)&&b>0&&n>0 )}, r /; r=!= Undefined&& FreeQ({a,b,n},x)),
+ Limit(x_^(a_.*(x_^n_.) + b_.), x_Symbol->0):= With({r=ConditionalExpression( 0, Element(b,Reals)&&a>0&&n<0&&Cos(-n*Pi)>0&&Sin(-n*Pi)>0 )}, r /; r=!= Undefined && FreeQ({a,b,n},x)),
+ Limit(x_^(a_.*(x_^n_.) + b_.), x_Symbol->Infinity):= With({r=ConditionalExpression( Infinity, Element(b,Reals)&&a>0&&n>0 )}, r /; r=!= Undefined && FreeQ({a,b,n},x)),
+ Limit(x_^(a_.*(x_^n_.)), x_Symbol->Infinity):= With({r=ConditionalExpression( 1, Element(a,Reals)&&n<0 )}, r /; r=!= Undefined && FreeQ({a,n},x)),
  Limit(x_^p_, x_Symbol->Infinity):= If(p<0, 0, Infinity, ConditionalExpression(Infinity, p>0)),
  Limit(m_?NumberQ^x_, x_Symbol->Infinity):= If(m>1, Infinity, If(m==1, 1, 0)) /; Positive(m),
  Limit(m_?NumberQ^(-x_), x_Symbol->Infinity):= 0 /; m>1,