These are the calculations made using Mathematica 3.0 The results of these calculations are used in problem 3 on the second midterm.

 

Solve[{w-b^3*x-y==b^3*t,2*w+u*b^3*x-2*u*y==-1*b^3*t,a^3*x+y-a^3*z==0,
    u*a^3*x-2*u*y-a^3*z==0},{w,x,y,z}]
      
     -a^3 b^3 t + b^6 t - a^3 b^3 t u + b^6 t u + 2 a^3 b^3 t u^2 - 2 b^6 t u^2
w= - --------------------------------------------------------------------------
            -2 a^3 + 2 b^3 + 4 a^3 u + 5 b^3 u-2 a^3 u^2 + 2 b^3 u^2

                      -3 (b^3 t + 2 b^3 t u)
x= - ----------------------------------------------------------
     -2 a^3 + 2 b^3 + 4 a^3 u + 5 b^3 u - 2 a^3 u^2 + 2 b^3 u^2

                       3 a^3 b^3 t (-1 + u)
y= ---------------------------------------------------------
     2 a^3 - 2 b^3 - 4 a^3 u - 5 b^3 u + 2 a^3 u^2 - 2 b^3 u^2


                   9 b^3 t u
z= --------------------------------------------------------------------------
   2 a^3 - 2 b^3 - 4 a^3 u - 5 b^3 u + 2 a^3 u^2 - 2 b^3 u^2

Simplify[%]


      b^3 (-a^3 + b^3) t (-1 - u + 2 u^2)
w= ----------------------------------------
   -2 a^3 (-1 + u)^2 + b^3(2 + 5 u + 2 u^2)   

           -3 b^3 t (1 + 2 u)
x= ----------------------------------------
   -2 a^3 (-1 + u)^2 + b^3(2 + 5 u + 2 u^2)

          3 a^3 b^3 t (-1 + u)
y= ----------------------------------------
   -2 a^3 (-1 + u)^2 + b^3(2 + 5 u + 2 u^2)
 
                 9 b^3 t u
z= ----------------------------------------
   -2 a^3 (-1 + u)^2 + b^3(2 + 5 u + 2 u^2)


FullSimplify[%]


      b^3 (-a^3 + b^3) t (-1 + u) (1 + 2 u) 
w= -----------------------------------------
   -2 a^3 (-1 + u)^2 + b^3 (2 + u) (1 + 2 u)

           -3 b^3 t (1 + 2 u) 
x= -----------------------------------------
   -2 a^3 (-1 + u)^2 + b^3 (2 + u) (1 + 2 u)

          3 a^3 b^3 t (-1 + u) 
y= -----------------------------------------
   -2 a^3 (-1 + u)^2 + b^3 (2 + u) (1 + 2 u)

                 9 b^3 t u 
z= -----------------------------------------
   -2 a^3 (-1 + u)^2 + b^3 (2 + u) (1 + 2 u)

For other mathematica calculation, the programs are called: ~thamlin/phy703/

		2ndmid3.nb
		2ndmid4.nb
		2ndmid5.nb