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MathGroup Archive 2004

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RE: Formal Definition of the Term "Form"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46158] RE: [mg46150] Formal Definition of the Term "Form"
  • From: "David Park" <djmp at earthlink.net>
  • Date: Mon, 9 Feb 2004 05:54:06 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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

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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