       Re: How to find one expression in terms of another

• To: mathgroup at smc.vnet.net
• Subject: [mg119746] Re: How to find one expression in terms of another
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 20 Jun 2011 08:05:17 -0400 (EDT)

```Element is not used the way that you think. See documentation.

\$Assumptions = True;

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;

FullSimplify[dT /. t2 -> dt + t1]

(c^2*dt + u*(x1 - x2))/(c^2*Sqrt[1 - u^2/c^2])

FullSimplify[dT /. t2 -> dt + t1, Element[c, Reals]]

(c^2*dt + u*(x1 - x2))/(Sqrt[(c - u)*(c + u)]*Abs[c])

\$Assumptions = Element[c, Reals];

FullSimplify[dT /. t2 -> dt + t1]

(c^2*dt + u*(x1 - x2))/(Sqrt[(c - u)*(c + u)]*Abs[c])

Bob Hanlon

---- Jacare Omoplata <walkeystalkey at gmail.com> wrote:

=============
I want to find dT in terms of dt. They are given below.

In:= Element[{x1, x2, t1, t2, u, c}, Reals]

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

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:= dt = t2 - t1

Out= -t1 + t2

If I knew that dT can be written in terms of dt in the form,
dT = a dt + b,
Can I use Mathematica to find a and b?

I tried using  Solve[dT == a dt + b, dt], but that gives an error.

If I didn't know that dT can be expressed this way, can I still
express it in terms of dt ?

```

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