       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. But the output from FullSimplify is
different for those two as can be seen by Out and Out. 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:= Element[{x1, x2, t1, t2, u, c}, Reals]

Out= (x1 | x2 | t1 | t2 | u | c) \[Element] Reals

In:= \$Assumptions = {u > 0, c > u}

Out= {u > 0, c > u}

In:= T1 = (t1 - ((u x1)/c^2))/Sqrt[1 - (u^2/c^2)]

Out= (t1 - (u x1)/c^2)/Sqrt[1 - u^2/c^2]

In:= T2 = (t2 - ((u x2)/c^2))/Sqrt[1 - (u^2/c^2)]

Out= (t2 - (u x2)/c^2)/Sqrt[1 - u^2/c^2]

In:= dT = T2 - T1

Out= -((t1 - (u x1)/c^2)/Sqrt[1 - u^2/c^2]) + (
t2 - (u x2)/c^2)/Sqrt[1 - u^2/c^2]

In:= FullSimplify[dT]

Out= (c^2 (-t1 + t2) + u (x1 - x2))/(c Sqrt[(c - u) (c + u)])

In:= s = (t2 - t1 - ((u/c^2)*(x2 - x1)))/Sqrt[1 - ((u^2)/(c^2))]

Out= (-t1 + t2 - (u (-x1 + x2))/c^2)/Sqrt[1 - u^2/c^2]

In:= FullSimplify[s]

Out= (c (-t1 + t2 + (u (x1 - x2))/c^2))/Sqrt[(c - u) (c + u)]

In:= s - dT

Out= (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:= FullSimplify[s - dT]

Out= 0

```

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