
Re: How to find one expression in terms of another expression?
Posted:
Jun 20, 2011 6:51 PM


On Jun 19, 4:29 pm, Jacare Omoplata <walkeystal...@gmail.com> wrote: > I want to find dT in terms of dt. They are given below. > > In[1]:= Element[{x1, x2, t1, t2, u, c}, Reals] > > Out[1]= (x1  x2  t1  t2  u  c) \[Element] Reals > > In[3]:= T1 = (t1  ((u x1)/c^2))/Sqrt[1  (u^2/c^2)] > > Out[3]= (t1  (u x1)/c^2)/Sqrt[1  u^2/c^2] > > In[4]:= T2 = (t2  ((u x2)/c^2))/Sqrt[1  (u^2/c^2)] > > Out[4]= (t2  (u x2)/c^2)/Sqrt[1  u^2/c^2] > > In[5]:= dT = T2  T1 > > Out[5]= ((t1  (u x1)/c^2)/Sqrt[1  u^2/c^2]) + ( > t2  (u x2)/c^2)/Sqrt[1  u^2/c^2] > > In[6]:= dt = t2  t1 > > Out[6]= 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 ?
Omit 'dt = t2  t1'. Otherwise, every time you write 'dt' it will be replaced by 't2  t1'. Here is all you need:
In[1]:= 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 = Simplify[T2  T1] /. t2  t1 > dt {b,a} = CoefficientList[dT,dt]
Out[3]= (c^2*dt + u*(x1  x2))/(c^2*Sqrt[1  u^2/c^2])
Out[4]= {(u*(x1  x2))/(c^2*Sqrt[1  u^2/c^2]), 1/Sqrt[1  u^2/c^2]}

