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MathGroup Archive 2005

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Re: Re: Language vs. Library

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61236] Re: Re: Language vs. Library
  • From: "Steven T. Hatton" <hattons at globalsymmetry.com>
  • Date: Thu, 13 Oct 2005 01:39:44 -0400 (EDT)
  • References: <dii8o0$9cc$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

David Annetts wrote:

> Hi Steve,
> 
>> Very much so.  Mathematica provides a huge number of symbols,
>> options, commands, end etc.  Distinguishing the essential
>> from the incidental is necessary in order to effectively use
>> a tool as complex as this.
> 
> That is quite a different question, as it depends on what you want to use
> the program for.

What I'm trying to identify is which parts of Mathematica are logically more
primitive than the others.  One think I'm confident of is that the core
language is expressed in FullForm, and involves neither boxes nor cells,
nor does it require any special characters such as \[Del]. 

> I'd regard as anything in Chapter of the Book entitled "A Practical
> Introduction to Mathematica" as essential, core Mathematica.  To that
> core, I would add commands in any context that you need to use the program
> effectively, for example, if you use Mathematica for statistical analysis,
> then anything in the Statistics` context would have to be regarded as core
> too.

I'm thinking in terms of logical precedence.  IOW, what are the axioms? 
Which "theorem" depends on others...

This is a good example of the kind of understanding I am seeking - and
finally gaining:

http://documents.wolfram.com/mathematica/Demos/Notebooks/Step-by-StepDifferentiation.html

> Anything else is surely non-core, at least to _your_ needs.  As your use
> of the program changes, so too will your "core" knowledge need to change.

Try this:

A = Array[a (10#1 + #2) &, {3, 3}]
v = {x, y, z}
A.v // MatrixForm
Clear[A,v];
A = Array[a (10#1 + #2) &, {3, 3}] // MatrixForm
v = {x, y, z} // MatrixForm
A.v

Why are the results different?

Explain this:

Clear[a, i]
a[i] = eye;
i = 3;
a[3] = three;
Print["a[i]=", a[i]]
Clear[i];
Print["a[i]=", a[i]]

-- 
"Philosophy is written in this grand book, The Universe. ... But the book
cannot be understood unless one first learns to comprehend the language...
in which it is written. It is written in the language of mathematics, ...;
without which wanders about in a dark labyrinth."   The Lion of Gaul


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