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Re: Grad in VectorAnalysis`

  • To: mathgroup at smc.vnet.net
  • Subject: [mg103853] Re: Grad in VectorAnalysis`
  • From: Erik Max Francis <max at alcyone.com>
  • Date: Fri, 9 Oct 2009 07:17:08 -0400 (EDT)
  • References: <hakjlm$d72$1@smc.vnet.net>

Murray Eisenberg wrote:
> After...
> 
>    Needs["VectorAnalysis`"]
>    SetCoordinates[Cartesian[x, y, z]]
> 
>    f[x_, y_] = x/(1 - x^2 - y^2)
> 
> ... why does the following not actually return the formula for gradient...
> 
>    Grad[f[x, y, z]]  (* or even Grad[Evaluate[f[x,y,z]]]
> 
> ... whereas the following does return it:
> 
>    Grad[x/(1 - x^2 - y^2)]

Because you defined a function with two arguments (f[x, y]).  A function 
f with three arguments (f[x, y, z]) is not defined and so Mathematica 
leaves it in symbolic form.  Try instead:

In[6]:= Grad[f[x, y]]

Out[6]= {(2 x^2)/(1 - x^2 - y^2)^2 + 1/(1 - x^2 - y^2), (
  2 x y)/(1 - x^2 - y^2)^2, 0}

or defining f as taking those three arguments (and just don't use the 
third):

In[7]:= f[x_, y_, z_] := x/(1 - x^2 - y^2)

In[8]:= Grad[f[x, y, z]]

Out[8]= {(2 x^2)/(1 - x^2 - y^2)^2 + 1/(1 - x^2 - y^2), (
  2 x y)/(1 - x^2 - y^2)^2, 0}

In[9]:= %6 == %8

Out[9]= True

-- 
Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/
  San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
   All generalizations are dangerous, even this one.
    -- Dumas Fils


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