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Re: Why can't FullSimplify give more uniform output?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg119751] Re: Why can't FullSimplify give more uniform output?
*From*: Jacare Omoplata <walkeystalkey at gmail.com>
*Date*: Mon, 20 Jun 2011 19:37:11 -0400 (EDT)
*References*: <itnd2c$7hj$1@smc.vnet.net>
Thanks for the answer.
On Jun 20, 8:05 am, Bob Hanlon <hanl... at cox.net> wrote:
> Simplify and FullSimplify provide the simplest form that they find within
their time constraints. Given different starting forms for an expression,
there is no guarantee that they will arrive at identical forms.
>
> $Assumptions = {u > 0, c > u};
>
> T1 = (t1 - ((u x1)/c^2))/Sqrt[1 - (u^2/c^2)];
>
> T2 = (t2 - ((u x2)/c^2))/Sqrt[1 - (u^2/c^2)];
>
> dT = T2 - T1;
>
> expr1 = FullSimplify[dT]
>
> (c^2*(-t1 + t2) + u*(x1 - x2))/
> (c*Sqrt[(c - u)*(c + u)])
>
> s = (t2 - t1 - ((u/c^2)*(x2 - x1)))/Sqrt[1 - ((u^2)/(c^2))];
>
> s == dT // Simplify
>
> True
>
> expr2 = FullSimplify[s]
>
> (c*(-t1 + t2 + (u*(x1 - x2))/c^2))/
> Sqrt[(c - u)*(c + u)]
>
> expr3 = FullSimplify[Expand[s]]
>
> (c^2*(-t1 + t2) + u*(x1 - x2))/
> (c*Sqrt[(c - u)*(c + u)])
>
> expr3 is identical to expr1
>
> expr1 === expr3
>
> True
>
> Bob Hanlon
>
> ---- Jacare Omoplata <walkeystal... 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
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