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Re: Why can't FullSimplify give more uniform output?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg119742] Re: Why can't FullSimplify give more uniform output?
*From*: DrMajorBob <btreat1 at austin.rr.com>
*Date*: Mon, 20 Jun 2011 08:04:34 -0400 (EDT)
*References*: <201106192328.TAA01131@smc.vnet.net>
*Reply-to*: drmajorbob at yahoo.com
First of all, the line
Element[{x1, x2, t1, t2, u, c}, Reals]
does nothing whatsoever. Run the other code without it, and nothing will
change.
Other than that, I see nothing surprising. The result of FullSimplify for
s and dT need not look be the same, just because they are equal. If being
equal always made expressions LOOK the same, there'd be no need for
FullSimplify in the first place.
Bobby
On Sun, 19 Jun 2011 18:28:53 -0500, Jacare Omoplata
<walkeystalkey at gmail.com> wrote:
> 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
>
--
DrMajorBob at yahoo.com
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