NetNews Usenet Archive 1992 #16/NN_1992_16.iso/spool/sci/math/9483

Internet Message Format | 1992-07-23 | 1.7 KB

From: [e-mail] (Jeff Patterson)
Date: Thu, 23 Jul 1992 19:45:06 GMT
Subject: Re: Mathematica Help
Message-ID: <[e-mail]>
Organization: HP Signal Analysis Division - Rohnert Park, CA
Path: sparky!uunet!zaphod.mps.ohio-state.edu!mips!sdd.hp.com!hpscdc!hplextra!hpl-opus!hpnmdla!hpsad!jpat
Newsgroups: sci.math
References: <[e-mail]>
Lines: 35

Mathematica will not let you make assignments to an element of a list
directly. You can build up lists using Prepend, Append, Insert etc.
However here's a one liner to do what you want:

  v=Thread[DD[f[x1,x2,x3],{x1,x2,x3}]] /. DD->D

Thread[f[arg1,{arg2,arg3}] forms {f[arg1,arg2],f[arg1,arg3]}. So the
in the above line Thread[DD[f[x1,x2,x3],{x1,x2,x3}]] forms:

 {DD[f[x1,x2,x3],x1],DD[f[x1,x2,x3],x2],DD[f[x1,x2,x3],x3]}.

The /. DD->D replaces all the DD heads with D heads which results in the
partial derivatives being taken. The last bit of subterfuge is necessary
because the derivitive operator D allows a list in the second position
as in D[f[x1,x2],{x1,5}] which yields the 5th partial of f wrt x1, so we
first get the final list in the form we want (no list in second position)
using the dummy head DD and then change the head to the desired D.

Another way is to use the Outer function as in:

 v=Outer[D,{f[x1,x2,x3]},{x1,x2,x3}]

Outer applies the fuction in arg 1 to a list formed by the outer product
of lists in arg2 and arg3. Thus

In[211]:= Outer[Plus,{a,b},{c,d}]
Out[211]= {{a + c, a + d}, {b + c, b + d}}

Note that using the above you can build a matrix of partials directly

 Outer[D,{f1[x1,x2,x3],f2[x1,x2,x3]},{x1,x2,x3}] produces a list of two lists.
The first list contains all the partials of f1 and the second all the partials
of f2.

Hope this helps-Jeff