       Re: Pattern in immediate definition

• To: mathgroup at smc.vnet.net
• Subject: [mg120754] Re: Pattern in immediate definition
• From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
• Date: Tue, 9 Aug 2011 07:18:38 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j1o6dl\$4i4\$1@smc.vnet.net>

```On Mon, 08 Aug 2011 09:23:17 +0100, eLVa <elvadrias at gmail.com> wrote:

> Hi,
>
> I want to write more clearly the following definition :
> TestFunction[{{a_, b_, c_}, {d_, e_, f_}, {g_, h_, k_}}] =
> (* immediate definition with = *)
>  Module[{F, det},
>   F = {{a, b, c}, {d, e, f}, {g, h, k}};
>   det = Det[F];
>   Flatten[Table[D[det, F[[i, j]]], {i, 1, 3}, {j, 1, 3}]]
>   ]
>
> After that, I can pass any 3x3 matrix to the function and get the
> result directly replaced, without having to evaluate the derivatives
> again , i.e I don't want it to be written :
>
> TestFunction[F_] :=
> (* delayed definition with := *)
>  Module[{det},
>   det = Det[F];
>   Flatten[Table[D[det, F[[i, j]]], {i, 1, 3}, {j, 1, 3}]]
>   ]
>
> for it will compute everything every time I get to call the function
> (which will be inefficient since I will call it often).
>
> However, I find the trick with the temporary F that gets to be
> assigned the matrix of {{a,b,c},{d,e,f},{g,h,i}} ugly and potentially
> dangerous since it uses the value of the variables (a,b,...,k) if they
> are defined.
>
> I would like something close to :
> TestFunction[F_<....>] = Module[<...>] where in the first <..> I get
> to specify that the argument is a 3x3 matrix and so I can have access
> obviously just a symbol and not a matrix). This way I just have to
> worry about F not being defined elsewhere. It will also be a cleaner
> definition in my opinion.
>
> Is that possible in any way ??
> Thanks
>

Generally it will be better to evaluate the definition explicitly if that
is what is required rather than leaving it implicit and depending on the
values of various globally defined symbols. Here is a straightforward and
safe way to accomplish this while still having the benefit of using a
delayed definition:

Block[{a, b, c, d, e, f, g, h, k, F, det},
F = {{a, b, c}, {d, e, f}, {g, h, k}};
det = Det[F];
TestFunction[{{a_, b_, c_}, {d_, e_, f_}, {g_, h_, k_}}] :=
Evaluate@Flatten[Table[D[det, F[[i, j]]], {i, 1, 3}, {j, 1, 3}]]
]

As you can see, this is nothing more than a re-ordering of your code with
Module also being replaced by Block.

```

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