From 0707f826aa723466ba7643be0221cdf57d88cafa Mon Sep 17 00:00:00 2001
From: cmwslw <cwalker32@gmail.com>
Date: Tue, 18 Jul 2017 00:28:42 -0700
Subject: [PATCH] More cases for Together.

---
 expreduce/resources/manip.m | 22 +++++++++++++++++++---
 1 file changed, 19 insertions(+), 3 deletions(-)

diff --git a/expreduce/resources/manip.m b/expreduce/resources/manip.m
index 981a260..1473225 100644
--- a/expreduce/resources/manip.m
+++ b/expreduce/resources/manip.m
@@ -1,5 +1,6 @@
 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+c rest)/(c d)]);
+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[(e_)^p_?((NumberQ[#] && # =!= -1)&)] := Together[Together[e]^p];
 
 Together[(a_/b_+rest___)/d_] := (Print[1];Together[(a+Expand[b Plus[rest]])/(b d)]);
@@ -7,6 +8,7 @@
 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[e_] := e;
 Attributes[Together] = {Listable, Protected};
@@ -18,7 +20,8 @@
         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/(2+a)), Together[a/(-2+a+a^2)-a^2/(-2+a+a^2)]],
+        (*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],
         ESameTest[(b c+a d)/(b d), (a+(b c)/d)/b//Together],
         ESameTest[(b c+a d)/d, a+(b c)/d//Together],
@@ -32,6 +35,19 @@
         ESameTest[(a+b c+b e)/(b d), (c+e+ a/b)/d//Together],
         ESameTest[(6+a)/(2 a), (3 + a/2)/a//Together],
         ESameTest[(a b+c rest)/(c d), (rest + a*b/c)/d//Together],
-        ESameTest[(1+a c+b c)/(a+b), 1/(a+b)+c//Together]
+        ESameTest[(1+a c+b c)/(a+b), 1/(a+b)+c//Together],
+        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+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)/(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],
+        ESameTest[(a+b+a b c+a b d)/(a b), 1/a+1/b+c+d//Together]
     ]
 };