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Re: The audience for Mathematica

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  • Subject: [mg102170] Re: The audience for Mathematica
  • From: AES <siegman at>
  • Date: Fri, 31 Jul 2009 05:56:17 -0400 (EDT)
  • Organization: Stanford University
  • References: <h4rq53$m3b$>

In article <h4rq53$m3b$1 at>,
 Alexei Boulbitch <Alexei.Boulbitch at> wrote:

(much stuff snipped)

> What I badly need are instruments that would enable one to easily bring an 
> expression to a desired form when making analytical transformations. 
> Such transformations may result in a further simplification that is not most 
> simple according to the Mathematica
> criterion, but is most simple from the user point of view. It may also help 
> in understanding of relative contributions of
> terms and may enable one to neglect some and thus, to further simplify the 
> whole expression and so on.
> That is how we worked during the pre-Mathematica era, and it often brought a 
> success. I know people (and many of them)
> who made important contributions just because they zealously rewrote and 
> rewrote long expressions 
> many times in many different forms until they have found advantageous ones.

I agree absolutely with the desire to have what's asked for above; but 
this is a function I've largely given up on obtaining from Mathematica, 
at least in an automated or automatically generated fashion.

The reason for this is mostly because what's wanted (that is, the 
restructuring of often lengthy analytical expressions into 
"advantageous" or user-understandable or user-meaningful forms) seems to 
me so widely varying, idiosyncratic, individual user-dependent, and 
difficult to specify, that trying to do it in Mathematica doesn't seem 
to me an effective or efficient way to use Mathematica or my time.

Given a lengthy multi-dimensional series expansion, for example, I may 
take the Series[] expansion generated by Mathematica; convert it to text 
form; re-shuffle the terms in the expression "by hand," using cut and 
paste, to get one of the "zealously rewritten" forms referred to above; 
use a new Mathematica cell to test that my rewritten form is equivalent 
to the original Mathematica generated form; and then use my rewritten 
form as input to TeX, while letting Mathematica do calculating and 
plotting using the form it likes.

It's also part of why I view Mathematica as great for generating 
graphical output for use in TeX-generated or PDF documents or 
presentations -- but not, by itself, as a tool for generating and 
presenting those documents or presentations, except in fairly simple 

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