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Q: Symbolic manipulation with Mathematica

 Hi fellows,

 I would like to know whether is possible to do the 
following with Mathematica:

In[15]:= test = f[x] + x*D[f[x],x]

Out[15]= f[x] + x f'[x]

In[16]:= test /. f[x]->f[x,y]

Out[16]= f[x, y] + x f'[x]

However, I would like to get something like:

        f[x,y] + x*D[f[x,y],x]

which then Mathematica can write in the form:

Out[17]= f[x, y] + x f     [x, y]

     Other manipulation I am trying to do is as follows:

In[18]:= y = x/e

Out[18]= -

In[19]:= test = f[x,y] + x*D[f[x,y],x]

                       (0,1)    x
                      f     [x, -]
              x                 e     (1,0)    x
Out[19]= f[x, -] + x (------------ + f     [x, -])
              e            e                   e

      If there any way to get this ecuation in the form:

                      f     [x, y]    (1,0)
          f[x, y] + x (------------ + f     [x, y])

     					             d f[x,y]
      Finally, is there any way to use the notation: --         

      instead of    f     [x,y]

      One more thing, is there any special symbol for the Laplacian
and Gradient operators in Mathematica.?

  I'll apreciate any suggestion.


E-mail: sergio at


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