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Re: V6 evaluation inside Table and plot
*To*: mathgroup at smc.vnet.net
*Subject*: [mg76649] Re: V6 evaluation inside Table and plot
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Fri, 25 May 2007 06:33:35 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <f33onq$l4v$1@smc.vnet.net>
Gerry Flanagan wrote:
> Define a simple function
>
> In[7]:= f = Function[{x}, x^3]
>
> Out[7]= Function[{x}, x^3]
>
> Taking two derivatives works as it should
>
> In[2]:= f''[x]
>
> I was converting some packages to work with V6, and immediately ran into
> some evaluation issues I don't understand. It looks like forms like
> f''[x] (derivative) are evaluated differently inside of Table and Plot
> than outside.
>
> Out[2]= 6 x
>
> But this does not?
>
> In[20]:= Table[f''[x], {x, 0, 1, .2}]
>
> Out[20]= {0, 0, 0, 0, 0, 0}
>
> Strangely, this works
>
> In[4]:= Table[f'[x], {x, 0, 1, .2}]
>
> Out[4]= {0., 0.12, 0.48, 1.08, 1.92, 3.}
>
> Determining the derivative outside the Table makes it work again.
>
> In[12]:= g = f'';
>
> In[21]:= tmp = Table[g[x], {x, 0, 1, .2}]
>
> Out[21]= {0., 1.2, 2.4, 3.6, 4.8, 6.}
>
> Gerry Flanagan
>
Hi Gerry,
Just two comments. First, since you name the function and manipulate it,
it might be more judicious to use a body definition without pure
function (in this case, f behave as expected within Table). Second, the
behavior you notice in version 6 is also present in earlier version of
Mathematica (at least 5.2).
(* Version 6.0 *)
In[1]:=
Clear[f]
f[x_] := x^3
{f'[x], f''[x]}
Table[{x, f[x], f'[x], f''[x]}, {x, 0, 1, .2}] // TableForm
Out[3]= {3*x^2, 6*x}
Out[4]//TableForm= 0. 0. 0. 0.
0.2 0.008 0.12 1.2
0.4 0.064 0.48 2.4
0.6 0.216 1.08 3.6
0.8 0.512 1.92 4.8
1. 1. 3. 6.
In[5]:=
Clear[f]
f = Function[{x}, x^3]
{f'[x], f''[x]}
Table[{x, f[x], f'[x], f''[x]}, {x, 0, 1, .2}] // TableForm
Out[6]= Function[{x}, x^3]
Out[7]= {3*x^2, 6*x}
Out[8]//TableForm= 0. 0. 0. 0
0.2 0.008 0.12 0
0.4 0.064 0.48 0
0.6 0.216 1.08 0
0.8 0.512 1.92 0
1. 1. 3. 0
(* Version 5.2 *)
Clear[f]
f[x_]:= x^3
{ f'[x], f''[x]}
Table[ { x, f[x], f'[x], f''[x]}, { x,0,1,.2}]//TableForm
==>
{3*x^2, 6*x}
0 0 0 0
0.2 0.008 0.12 1.2
0.4 0.064 0.48 2.4
0.6 0.216 1.08 3.6
0.8 0.512 1.92 4.8
1. 1. 3. 6.
Clear[f]
f= Function[ {x}, x^3]
{ f'[x], f''[x]}
Table[ { x, f[x], f'[x], f''[x]}, { x,0,1,.2}]//TableForm
==>
Function[{x}, x^3]
{3*x^2, 6*x}
0 0 0 0
0.2 0.008 0.12 0
0.4 0.064 0.48 0
0.6 0.216 1.08 0
0.8 0.512 1.92 0
1. 1. 3. 0
Regards,
Jean-Marc
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