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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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