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MathGroup Archive 1996

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Re: Re: A simple question? Correction

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3655] Re: [mg3654] Re: A simple question? Correction
  • From: Allan Hayes <hay at haystack.demon.co.uk>
  • Date: Tue, 2 Apr 1996 21:54:47 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Count Dracula points out that the last definition in my previous  
posting on this topic should be

   G[F_, vars__][args__] :=
       G[F, vars][Sequence@@Sort[{args}]] = D[F[vars], args]

 not

   G[F_, vars__][args__] :=
       G[F, vars][Sequence@@Sort[args]] = D[F[vars], args]

The corrected form is attached.

Allan Hayes
hay at haystack.demon.co.uk



A generally applicable technique will shorten to Count Dracula's  
solution to the problem posed by nader at math.chalmers.se (Nader  
Tajvidi) in [mg3627]. The problem is

> For a function f[x,y] I want to create a 2x2x2x2 matrix called
> fourthDs. The elements of fourthDs will be the fourth  
derivatives> of f with respect to x and y in the following form:
>      fourthDs[[1,1,1,1]]=D[f[x,y],{x,4}]
>      fourthDs[[2,2,2,2]]=D[f[x,y],{y,4}]
>      fourthDs[[1,2,1,1]]=D[f[x,y],{x,3},{y,1}]

Count Dracula's solution is

>>For a function f with arguments vars, and maxord = maximum order
>>of derivative needed in the matrix, the function dmatrix will
>>create such a matrix.
>>   G[F_, vars__][args__] /; OrderedQ[{args}] :=
>>       G[F, vars][args] = D[F[vars], args]
>>
>>   G[z__][args__] := G[z] @@ Sort[{args}]
>>
>>   dmatrix[f_Symbol, vars__Symbol, maxord_Integer] :=
>>       Outer[ G[f, vars], Sequence @@ Table[{vars}, {maxord}] ]


We can replace the first two definitions with

   G[F_, vars__][args__] :=
       G[F, vars][Sequence@@Sort[{args}]] = D[F[vars], args]


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