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MathGroup Archive 2000

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Re: ? D[f,{x,n}]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25561] Re: [mg25495] ? D[f,{x,n}]
  • From: Carl Woll <carlw at u.washington.edu>
  • Date: Sat, 7 Oct 2000 03:36:09 -0400 (EDT)
  • References: <200010060350.XAA24795@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Jack,

It seems to me that your definition for D[f_,x_] should work for both D[f,x] and
D[f,{x,n}], since the pattern matcher can match x to {x,n}. So why do you need an
additional definition for D[f_,{x_,n_}]?
For example, I ran the following test:

In[1]:=
flag=True;

In[2]:=
Unprotect[D];
D[f_,x_]/;flag:=Block[{flag=False},D[mySimplification[f],x]]
Protect[D];

In[5]:=
mySimplification[f_]:=(Print[f];f)

In[6]:=
D[Cos[x],x]

Cos[x]

Out[6]=
-Sin[x]

In[7]:=
D[Cos[x],{x,2}]

Cos[x]

Out[7]=
-Cos[x]

The From In[6] and From In[7] lines correspond to the print statements in the
mySimplification command. So, a single definition of D[f_,x_] is all you need.

You don't mention what your package does, but I don't think I would have chosen
to overload D with additional definitions as you have chosen to do. What exactly
are you trying to do in this package?

Carl


Jack Goldberg wrote:

> Hi folks,
>
> I am touching up a package I have worked on for a number of years.
> Rather than send it off as is, I keep tweeking it to improve its
> usefulness.  I should know better...  My latest tweek leads me to
> a problem with  D[f,{x,n}].  Here's the story:
>
> In my package I define a constant "flag" which I set true: flag = True.
>
> Then I Unprotect D:  Unprotect[D]:  I want to modify f before the built-in
> D fires so I write a little program:
>
>         D[f_,x_]/;flag := Block[ {flag=False},
>           D[ mySimplification[f],x]
>                 ]
>
> So, what I think happens is this. Since flag = True and since Mathematica uses
> my definition of D before its own, this little snippet fires.  Block sets
> flag = False, mySimplification[f] fires, and my definition of D does not
> fire again (or I would be caught in a loop) so Mathematica's definition of D
> now works and I have accomplished my aim which is to simplify f before
> taking the derivative.  This seems to work.  However, this idea fails to
> work for  D[f,{x,n}]!  Here's my code:
>
>         D[f_,{x_,n_}]/;flag := Block[ {flag=False},
>           D[ mySimplification[f],{x,n} ]
>                 ]
>
> (Of course, the nature of mySimplification should be irrelevant.)
>
> While trying to work out this problem, I discovered that I don't
> understand the difference between  D[f,x] and D[f,{x,1}].  If I
> alter the definition of D[f,x] have I also altered the definition
> of  D[f,{x,1}]?  How about the other way around?  If I alter the
> definiton of  D[f,{x,1}] does this alter the definition of D[f,x]?
> It seems as though they should be linked internally but if so,
> I can find no reference to this linkage. This not a mute point since
> I found that in trying to use mySimplification in both  D[f,x] and
> D[f,{x,n}] it is necessary to know what happens if a user chooses to
> write D[f,x] in the form  D[f,{x,n}].
>
> Help is needed.  Thanks.
>



  • References:
    • ? D[f,{x,n}]
      • From: Jack Goldberg <jackgold@math.lsa.umich.edu>
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