Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Re: V6 evaluation inside Table and plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76747] Re: [mg76669] Re: V6 evaluation inside Table and plot
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 26 May 2007 04:50:28 -0400 (EDT)
  • References: <f33onq$l4v$1@smc.vnet.net> <200705251043.GAA08270@smc.vnet.net>

On 25 May 2007, at 19:43, Szabolcs wrote:

>
> P.S. It is also interesting to note that while the documentation  
> says that
> "Whenever Derivative[n][f] is generated, Mathematica rewrites it as
> D[f[#],{#,n}]&",
> Derivative[] doesn't seem to work this way.


This statement (in the documentation) is badly misleading. I am  
pretty sure that "rewrites" is not meant to suggest that Derivative  
actually uses D since one can easily show that it does not. I think  
all that statment is trying to convey is the "form" of the output  
that Derivative tries to produce. Even this is strictly speaking  
wrong, for, if anything it should say

Evaluate[D[f[#],{#, n}]] &

We can see this just by taking f=Sin. Then:

Derivative[3][Sin]

-Cos[#1] &

while


D[Sin[#1], {#1, 3}] &

D[Sin[#1], {#1, 3}] &

which takes a lot of imagination to see as "the same". On the other  
hand:


Evaluate[D[Sin[#1],{#1, 3}]] &


-Cos[#1] &

which does have the same form. But, as I wrote above, one can easily  
show that this is not what Derivative actually does:

Unprotect[D];
D[f_, n_] := Null /; (Print[d[f, n]]; False)


Derivative[3][Sin]


-Cos[#1] &

while


Evaluate[D[Sin[#1],{#1, 3}]] &


d[Sin[#1], {#1, 3}]

-Cos[#1] &

So that piece of documentation was a kind of "figurative"  
description, and since it is misleading it would be better not to  
have it at all.

As for the original problem: I think it is safest to define functions  
with named variables like this:

f = Function[x, x^2] /. x -> Unique[x]

This, I beleive, should never run into any problems (except, of  
course, deliberately contrived ones).

Andrzej Kozlowski








  • Prev by Date: Re: Re: Re: Weird result in Mathematica 6
  • Next by Date: Re: Stopping Automatic Animation in v6
  • Previous by thread: Re: V6 evaluation inside Table and plot
  • Next by thread: Re: V6 evaluation inside Table and plot