• To: mathgroup at smc.vnet.net
• Subject: [mg124502] Re: Derivatives Output as TraditionalForm
• From: A Retey <awnl at gmx-topmail.de>
• Date: Sun, 22 Jan 2012 07:19:48 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jfb2rl\$hls\$1@smc.vnet.net>

```Hi,

> I have 2 Questions....
>
> (1)  Why isnt this code standard within Mathematica rather then
> having to be  Coded by the user?....I used to do all this with Format
> which was a Royal Nightmare by comparison.........I have never seen
> what purpose  this output   f^(0,1)[x,y]   served.......or does
> it???

I don't want to start a discussion about whether it was a good decision
to use that notation as the standard, but I think it probably is
interesting to mention what the rational behind it might be:

A derivative can be seen as something that acts on a function rather
than an expression, and that includes functions in a programming
language sense. It then is natural to think about argument slots rather
than named variables, and the StandardForm of Derivative reflects that.

When writing programs I find it very convenient to work with "function"
objects compared to expressions since it avoids all kinds of
complications with localizations and name spaces of those "artifical"
symbols which actually implicitly are just used as named arguments for
functions. If you wonder what I'm talking about, look at how this will
work without ever defining names for the arguments:

f = #1^2*#2^3 &

Derivative[0,1][f]

It probably needs a programmers viewpoint more than a mathematicians to
appreciate the "beauty" and usefulness of such a notation, but I think
with some good will you might see it...

hth,

albert

```

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