Re: Re: pure functions vs. functions

• To: mathgroup at smc.vnet.net
• Subject: [mg57629] Re: [mg57584] Re: [mg57415] pure functions vs. functions
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Thu, 2 Jun 2005 05:17:18 -0400 (EDT)
• Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

```What do you mean by procedurally?

On 6/1/05, Marcin Rak <umrakmm at cc.umanitoba.ca> wrote:
> Thanks for the thurough description of when one would go about using the
> pure function.
> I've never programmed in a language of this sort - I'm used to procedural
> and object orianted but Mathematica (which seems to simply be a whole bunch
> of statements nested one within the other is something completely
> different).
>
> Perhaps you could help me understand also the structure of programs in
> Mathematica, by answering whether the following is true:
> 1) Each line of input in Mathematica is simply at most a whole bunch of
> nested commands where the output of the inner is used as the input of the
> outer?
>
> 2) The only way to program proceduraly in Mathematica is to employ the
> entire notebook?
>
> Thanks again
> MR
> ----- Original Message -----
> From: "David Park" <djmp at earthlink.net>
To: mathgroup at smc.vnet.net
> Subject: [mg57629] [mg57584] Re: [mg57415] pure functions vs. functions
>
>
> > MR,
> >
> > First, pure functions are very useful in Mathematica and it's great that
> you
> > are looking at them.
> >
> > Pure functions are usually used where we want to carry out some operation
> on
> > expressions without actually going to the bother of defining a named
> > function. Maybe it is something you want to do on the fly and you are only
> > going to use it once.
> >
> > Here is a function that takes the square of an expression.
> >
> > f[x_]:=x^2
> >
> > We use it...
> >
> > f[2a]
> > 4*a^2
> >
> > But maybe we only wanted to do this once. So why bother defining f. (Of
> > course, in this case we could just use (2a)^2 but I'm trying to use a
> simple
> > example where f might actually be more complicated.) We could just use...
> >
> > #^2 &[2a]
> > 4*a^2
> >
> > The pure function is just a substitute for 'f'. Instead of using a name of
> a
> > function we simply describe the action we want from the function and don't
> > bother with assigning a name.
> >
> > Here is an example where we might want to use pure functions. We are going
> > to show how a simple linear equation is solved step-by-step for x. (Copy
> the
> > code and paste it into a Mathematica notebook to evaluate.)
> >
> > Print["Equation to solve for x"]
> > a x + b == c
> > Print["Subtract b from each side"]
> > # - b & /@ %%
> > Print["Divide each side by a"]
> > #/a & /@ %%
> >
> > We can do the entire derivation in one cell. The interspersed Print
> > statements annotate the steps. %% refers to the second previous output
> > (jumping over the Print statements). Each operation is defined by a pure
> > function, which is mapped to each side of the equation. It would be
> > cumbersome to define functions to subtract b from an expression, or to
> > divide an expression by a because we would never use them again.
> >
> > The Function statement is just a longer method of writing a pure function.
> > Sometimes I find Function useful because it is a little more explicit and
> it
> > is easier to follow if I'm trying to write nested pure functions.
> >
> > David Park
> >
> >
> >
> >
> >
> > From: Marcin Rak [mailto:umrakmm at cc.umanitoba.ca]
To: mathgroup at smc.vnet.net
> >
> >
> > Hey everyone, I had a beginner question:  what exactly is the difference
> > between a pure function and just a function?
> > ie. the difference between declaring functions using
> > f[arg1_,...,argn_] := "some expression making use of the arguments"
> >
> > and explicilty calling Function[{arg1_,...,argn_}, "same expression
> > making use of the arguments"]
> >
> > They have different heads!!
> >
> > Thanks
> > MR
> >
> >
> >
> >
> >
>
>

--
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161

```

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