Re: Placeholders in matrix notation

• To: mathgroup at smc.vnet.net
• Subject: [mg29956] Re: Placeholders in matrix notation
• From: dooglefish at aol.communicate (D.F.)
• Date: Thu, 19 Jul 2001 03:57:27 -0400 (EDT)
• References: <9j39rr\$ikv\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```>Subject: [mg29956] Re:  Placeholders in matrix notation
>From: "Hugh Philipp" hph at com.dtu.dk
To: mathgroup at smc.vnet.net
>Date: 7/18/01 2:20 AM Eastern Daylight Time
>Message-id: <9j39rr\$ikv\$1 at smc.vnet.net>
>
>I've had this problem before and I have used at least a dozen clumsy work
>arounds for it.
>
>Here is one:
>
>ff ={D[#[[1]],x],0}&;
>
>ff@{f[x],g[x]}
>
>Of course, I don't really like this method because you have to do the matrix
>operations explicitly in the function - designating the elements.
>
>
>The other way of doing it goes something like this:
>
>Unprotect[Times]
>
>d1 f_:=D[f,x]
>
>Protect[Times]
>
>{d1,0,d1}.{f[x],g[x],h[x]}
>
>I don't know if the gurus here think this is O.K. - I'm sure there will be
>
>Notice to that:
>
>d1 d1 f[x]
>
>evaluates to f''[x]
>
>...a nice 'feature'. - but BE CAREFUL becaue d1 d1 evaluates to 0.  So -
>there might be some other hidden 'features' with this approach.
>
>For example, the vector:  {d1 d1,d1} evaluates to {0,d1}
>
>Hope this helps,
>
>Hugh.

Yes, it works very well. Thank you.

\!\(\*
RowBox[{\(Unprotect[Times]\), "\n", \(d1\ f_ := D[f, x]\),
"\n", \(d2\ f_ := D[f, y]\), "\n", \(d3\ f_ := D[f, x, y]\),
"\n", \(Protect[Times]\), "\n",
RowBox[{"MatrixForm", "[",
RowBox[{
RowBox[{"(", GridBox[{
{"d1", "0"},
{"0", "d2"},
{"0", "d3"}
}], ")"}], ".",
RowBox[{"(", GridBox[{
{\(f1[x, y]\), \(f2[x, y]\), \(f3[x, y]\)},
{\(g1[x, y]\), \(g2[x, y]\), \(g3[x, y]\)}
}], ")"}]}], "]"}]}]\)

-Doug

```

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