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Re: Derivatives Output as TraditionalForm

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124532] Re: Derivatives Output as TraditionalForm
  • From: "mathgroup " <fizzymath at knology.net>
  • Date: Mon, 23 Jan 2012 02:56:39 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jfb2rl$hls$1@smc.vnet.net> <201201221219.HAA25947@smc.vnet.net>

Thank You for Responding....

what you wrote was very Interesting....I'm quite mundane when it comes to 
Programming but I have enough background to appreciate what you 
said.....Your example  certainly gives  food for thought....

In fact, I went back to some old work I had done....lo and behold,  I had a 
reason to use the form  f^(0,1)[x,y]  for something and when I tried it with 
the new found Derivatives code, it didnâ??t work....I was able to fix it, etc. 
but then I realized that perhaps the 'Raw Form' for the end user gives him 
many more Options....it proved to be a much easier approach for what I was 
trying to do....and actually made more sense..

So, again Wolfram has shown itself to be much Smarter then me...but that's 
why I use Mathematica and like it so much...

Interesting how an answer can change your attitude.....I will never again 
feel upset by this as output form..... f^(0,1)[x,y]

jerry B

-----Original Message----- 
From: A Retey
Sent: Sunday, January 22, 2012 6:19 AM
To: mathgroup at smc.vnet.net
Subject: [mg124532] Re: Derivatives Output as TraditionalForm

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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