Solve more cases.

expreduce/resources/arithmetic.m

@@ -125,8 +125,8 @@
 Verbatim[Times][beg___, a_Integer^m_Rational, a_Integer^n_Rational, end___] := beg*a^(m+n)*end;
 Times[c : (Rational[_Integer, d_Integer] | 
      Complex[_Integer, Rational[_Integer, d_Integer]]), 
-  Power[a_Integer, Rational[1, r_Integer]]] :=
- Times[c*a, a^(1/r - 1)] /; (Mod[d, a] === 0 && a > 1)
+  Power[a_Integer, Rational[1, r_Integer]], rest___] :=
+ Times[c*a, a^(1/r - 1), rest] /; (Mod[d, a] === 0 && a > 1)
 Sin[x_]*Cos[x_]^(-1)*rest___ := Tan[x]*rest;
 Cos[x_]*Sin[x_]^(-1)*rest___ := Cot[x]*rest;
 Attributes[Times] = {Flat, Listable, NumericFunction, OneIdentity, Orderless, Protected};
@@ -207,6 +207,7 @@
         ESameTest[-(I/(2 Sqrt[3])), Times[-2/12 I,Sqrt[3]]],
         ESameTest[-(I/(2 Sqrt[3])), Times[2/-12 I,Sqrt[3]]],
         ESameTest[(3+(5 I)/4)/Sqrt[3], Times[1+5/12 I,Sqrt[3]]],
+        ESameTest[I/(2 Sqrt[3] a^2), (0+1/6*I)*3^(1/2)*a^(-2)],
     ], EKnownFailures[
         ESameTest[-2^(1/3), (-2)*2^(-2/3)],
         ESameTest[-2^(1+a), (-2)*2^(a)],

expreduce/resources/simplify.m

@@ -45,8 +45,11 @@
       tryVal = FixedPoint[Replace[#, expandRules]&, e];
       If[LeafCount[tryVal] < LeafCount[e], e = tryVal];
     ];
-    tryVal = ComplexExpand[e];
-    If[LeafCount[tryVal] < LeafCount[e], e = tryVal];
+    (*Avoid expressions containing expensive expressions to expand.*)
+    If[FreeQ[e, a_Plus^(b_Integer?((# >= 5) &))],
+      tryVal = ComplexExpand[e];
+      If[LeafCount[tryVal] < LeafCount[e], e = tryVal];
+    ];
     (* also need to try complexexpand to simplify cases like (-1)^(1/3) (1 + I Sqrt[3]) *)
     e = Replace[e, Sqrt[inner_] :> Sqrt[FactorTerms[inner]]];
     e

expreduce/resources/solve.m

@@ -280,7 +280,7 @@
    fullSimplified = eqn // FullSimplify;
    If[fullSimplified =!= eqn, Return[Solve[fullSimplified, var]]];
 
-   Print["Solve found no solutions"];
+   Print["Solve found no solutions for ", eqn, " for ", var];
    SolveFailed
    ];
 solveMultOrdered[eqns_List, vars_List] := 

expreduce/resources/trig.m

@@ -16,6 +16,7 @@
 Sin[(5/2)*Pi] := 1;
 Sin[Indeterminate] := Indeterminate;
 Sin[ArcSin[a_]] := a;
+Sin[ArcTan[1/2]] := 1/Sqrt[5];
 Attributes[Sin] = {Listable, NumericFunction, Protected};
 
 Cos::usage = "`Cos[x]` is the cosine of `x`.";
@@ -37,6 +38,7 @@
 Cos[inner : Verbatim[Plus][Repeated[_*I]]] := Cosh[-I*inner // Distribute]
 Cos[Indeterminate] := Indeterminate;
 Cos[ArcCos[a_]] := a;
+Cos[ArcTan[1/2]] := 2/Sqrt[5];
 Attributes[Cos] = {Listable, NumericFunction, Protected};
 
 Tan::usage = "`Tan[x]` is the tangent of `x`.";