Why can't FullSimplify give more uniform output?

*To*: mathgroup at smc.vnet.net*Subject*: [mg119734] Why can't FullSimplify give more uniform output?*From*: Jacare Omoplata <walkeystalkey at gmail.com>*Date*: Sun, 19 Jun 2011 19:28:53 -0400 (EDT)

Hello, I ask this question just out of curiosity. Below is my input and output. The expressions "s" and "dT" are equal, as can be seen by Out[17]. But the output from FullSimplify is different for those two as can be seen by Out[12] and Out[15]. Why can't they be simplified to expressions that look alike? Thanks. (PS. Also please tell me if my code is inefficient. I'm still learning Mathematica) In[1]:= Element[{x1, x2, t1, t2, u, c}, Reals] Out[1]= (x1 | x2 | t1 | t2 | u | c) \[Element] Reals In[7]:= $Assumptions = {u > 0, c > u} Out[7]= {u > 0, c > u} In[9]:= T1 = (t1 - ((u x1)/c^2))/Sqrt[1 - (u^2/c^2)] Out[9]= (t1 - (u x1)/c^2)/Sqrt[1 - u^2/c^2] In[10]:= T2 = (t2 - ((u x2)/c^2))/Sqrt[1 - (u^2/c^2)] Out[10]= (t2 - (u x2)/c^2)/Sqrt[1 - u^2/c^2] In[11]:= dT = T2 - T1 Out[11]= -((t1 - (u x1)/c^2)/Sqrt[1 - u^2/c^2]) + ( t2 - (u x2)/c^2)/Sqrt[1 - u^2/c^2] In[12]:= FullSimplify[dT] Out[12]= (c^2 (-t1 + t2) + u (x1 - x2))/(c Sqrt[(c - u) (c + u)]) In[14]:= s = (t2 - t1 - ((u/c^2)*(x2 - x1)))/Sqrt[1 - ((u^2)/(c^2))] Out[14]= (-t1 + t2 - (u (-x1 + x2))/c^2)/Sqrt[1 - u^2/c^2] In[15]:= FullSimplify[s] Out[15]= (c (-t1 + t2 + (u (x1 - x2))/c^2))/Sqrt[(c - u) (c + u)] In[16]:= s - dT Out[16]= (t1 - (u x1)/c^2)/Sqrt[1 - u^2/c^2] - (t2 - (u x2)/c^2)/Sqrt[ 1 - u^2/c^2] + (-t1 + t2 - (u (-x1 + x2))/c^2)/Sqrt[1 - u^2/c^2] In[17]:= FullSimplify[s - dT] Out[17]= 0

**Follow-Ups**:**Re: Why can't FullSimplify give more uniform output?***From:*DrMajorBob <btreat1@austin.rr.com>