Tests for Together pass.

expreduce/resources/manip.m

@@ -1,20 +1,15 @@
-DistributeMultiply[e_, multiplicand_] := 
+ExpreduceDistributeMultiply[e_, multiplicand_] := 
   If[Head[e] === Plus, (#*multiplicand) & /@ e, e*multiplicand];
 
 Together::usage = "`Together[e]` attempts to put the terms in `e` under the same denominator.";
-Together[(rest___ + a_*Rational[b_,c_])/d_] := (Print[5];Together[(a b+Expand[c Plus[rest]])/(c d)]);
-Together[a_+Rational[b_,c_]*d_] := (Print[7];Together[(a c+b d)/c]);
+Together[(rest___ + a_*Rational[b_,c_])/d_] := Together[(a b+Expand[c Plus[rest]])/(c d)];
+Together[a_+Rational[b_,c_]*d_] := Together[(a c+b d)/c];
 Together[(e_)^p_?((NumberQ[#] && # =!= -1)&)] := Together[Together[e]^p];
 
-Together[(a_/b_+rest___)/d_] := (Print[1];Together[(a+Expand[DistributeMultiply[Plus[rest], b]])/(b d)]);
-(*Together[(a_/b_+rest___)/(c_*d_)] := (Print[4];Together[(a+Expand[b Plus[rest]])/(b c d)]);*)
-Together[a_/b_+c_+rest___] := (Print[2];Together[(a+b c)/b+rest]);
-Together[1/(a__Plus) + b__] := (Print[3];Together[(1+Expand[a*Plus[b]])/(a)]);
-Together[1/(a__Plus)+1/(b__Plus) + c___] := (Print[6];Together[(a+b+Expand[a*b*Plus[c]])/(a*b)]);
-Together[1/(a_Symbol)+ rest___] := (Print[8];Together[(1+Expand[a*Plus[rest]])/(a)]);
-
-(*Together[(b_/c_+rest__)*d_^(-1)*e_^(-1)] := (Print[9];Together[(b+Expand[c Plus[rest]])/(c d e)]);*)
-(*Together[(b_/c_+rest__)*d_^(-1)*e_^(-2)] := (Print[9];Together[(b+Expand[c Plus[rest]])/(c d e^2)]);*)
+Together[(a_/b_ + rest___)/d_] := Together[(a+Expand[ExpreduceDistributeMultiply[Plus[rest], b]])/(b d)];
+Together[b_/a_ + rest___] := Together[(b+Expand[a*Plus[rest]])/(a)];
+(* Needed because 1/a is actually a^-1 *)
+Together[1/a_ + rest___] := Together[(1+Expand[a*Plus[rest]])/(a)];
 
 Together[e_] := e;
 Attributes[Together] = {Listable, Protected};
@@ -26,7 +21,7 @@
     ], ETests[
         ESameTest[(c+a d+b d)/d, a+b+c/d//Together],
         ESameTest[(a+b+c+d)/((a+b) (c+d)), 1/(a+b)+1/(c+d)//Together],
-        ESameTest[(a+b+c-a^2 c-a b c+d-a^2 d-a b d)/((a+b) (c+d)), 1/(a+b)+1/(c+d)-a//Together],
+        ESameTest[(a+b+c-a^2*c-a b c+d-a^2*d-a b d)/((a+b) (c+d)), 1/(a+b)+1/(c+d)-a//Together],
         (*Only for when we have Cancel:*)
         (*ESameTest[-(a/(2+a)), Together[a/(-2+a+a^2)-a^2/(-2+a+a^2)]],*)
         ESameTest[(a+b c)/b, a/b+c//Together],
@@ -36,7 +31,7 @@
         ESameTest[(6+a+2 b)/(2 a), (3+a/2+b)/a//Together],
         ESameTest[a/(b e), (a/b)/e//Together],
         ESameTest[(12+a)/(4 a), (3 + a*1/4)/a//Together],
-        ESameTest[1/2 (6+foo[a]), 3 + foo[a]*2/4//Together],
+        ESameTest[(1/2) (6+foo[a]), 3 + foo[a]*2/4//Together],
         ESameTest[(6+a)/(2 a), 1/2 + 3/a//Together],
         ESameTest[(a+b c)/(a b), (c+ a/b)/a//Together],
         ESameTest[(a+b c+b e)/(b d), (c+e+ a/b)/d//Together],
@@ -46,12 +41,12 @@
         ESameTest[(c+a d+b d)/d, Together[(c + a*d + b*d)/d]],
         ESameTest[(6+a+2 b)/(2 a), (3+a/2+b)/a//Together],
         ESameTest[a/(b e), (a/b)/e//Together],
-        ESameTest[(a+a^2 c+a b c+a d+b d)/(a (a+b)), Together[1/(a + b) + c+d/a]],
+        ESameTest[(a+a^2*c+a b c+a d+b d)/(a (a+b)), Together[1/(a + b) + c+d/a]],
         ESameTest[(a+b) (c+d), (a+b)(c+d)//Together],
         ESameTest[(a+b+c+d)/((a+b) (c+d)), 1/(a + b)+1/(c+d)//Together],
         ESameTest[1/(a+b), 1/(a + b)//Together],
         ESameTest[(a+b c e f)/(b c), a/(b*c)+(e*f)//Together],
-        ESameTest[(a+b+c-a^2 c-a b c+d-a^2 d-a b d)/((a+b) (c+d)), Together[1/(a + b) + 1/(c + d) - a]],
+        ESameTest[(a+b+c-a^2*c-a b c+d-a^2*d-a b d)/((a+b) (c+d)), Together[1/(a + b) + 1/(c + d) - a]],
         ESameTest[(a+b)/(a b), 1/a+1/b//Together],
         ESameTest[(a+b+a b c)/(a b), 1/a+1/b+c//Together],
         ESameTest[(1+c d)/c, 1/c+d//Together],