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

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