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MathGroup Archive 2004

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Re: RE: Formal Definition of the Term "Form"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46183] Re: [mg46158] RE: [mg46150] Formal Definition of the Term "Form"
  • From: Richard Palmer <mapsinc at bellatlantic.net>
  • Date: Tue, 10 Feb 2004 00:05:54 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

A formal definition of the idea of FORM certainly exists.  The way you know
that is that Mathematica will evaluate the expression correctly for FORMs
and not evaluate for things that aren't forms.  I suspect that the
definition is quite messy.

On 2/9/04 5:54 AM, "David Park" <djmp at earthlink.net> wrote:

> Harold,
> 
> I don't think there is a precise definition or usage of the term "form" in
> the Mathematica book. I think it depends on the context of the command. For
> example, in the Coefficient command in Section 1.4.7 it definitely does not
> work if form is a pattern. But in Section 2.3.2 with the Cases statement
> form usually is a pattern. And in the actual Help for Cases the word
> "pattern" instead of "form" is used.
> 
> There are many places where The Book could probably be sharpened up. But it
> might threaten to make the book even longer! Help is probably a better guide
> in specific cases than the book. One place that the book could be improved
> is in discussing piecewise functions. UnitStep was only added to the main
> Mathematica with later versions. The book still tends to teach new users the
> conditional definition, If or Which constructions. I can't find an example
> in the main book where UnitStep is used to define a piecewise function. And
> the example in Help is slightly quixotic. As a result there are many
> questions about piecewise functions and calculus on MathGroup.
> 
> The way you are going at Mathematica you are quickly becoming an expert!
> 
> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/
> 
> From: Harold Noffke [mailto:Harold.Noffke at wpafb.af.mil]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> 
> MathGroup:
> 
> In methodically reviewing everything I've read in the Mathematica
> Book, I realized an important undefined term first makes its
> appearance in "1.4.7 Picking Out Pieces of Algebraic Expressions".
> Definitions are there for Coefficient[expr,form] and
> Exponent[expr,form].  The term "expr" has been previously discussed,
> but the term "form" starts to be used at this point without any prior
> definition I can find.
> 
> Does Mathematica have a formal definition for "form"?  Where may I
> find it?
> 
> Thanks.
> Harold
> 
> 


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