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Re: Simplifying and Rearranging Expressions

  • To: mathgroup at
  • Subject: [mg96009] Re: Simplifying and Rearranging Expressions
  • From: AES <siegman at>
  • Date: Sun, 1 Feb 2009 04:40:33 -0500 (EST)
  • Organization: Stanford University
  • References: <gls1u8$hjl$> <> <gm0q8p$rrr$>

In article <gm0q8p$rrr$1 at>,
 Andrzej Kozlowski <akoz at> wrote:

> To my amazement I have found something that I agree here. I do agree  
> that it is largely a pointless waste of time to use computer algebra,  
> which relies on pretty complex algorithms (like Groebner basis) to  
> make this **look** the way you want them to look, for reasons that  
> have no particular relation to these algorithms. Its a waste of  
> computing resources, the effort of mathematicians and programmers and  
> most of all the user, who could much more easily achieve this effect  
> in other ways, one of which is TeX (even better was, in my opinion,  
> was David Bailey's clever idea to use color to manipulate Mathematica  
> expressions almost as one does by hand - unfortunately this appears to  
> have been abandoned due to lack of interest).

Thank you -- always glad to have positive feedback (or negative 
feedback, for that matter).

> I don't think however there is any chance whatever of WRI  
> incorporating TeX into Mathematica, for two reasons. One is that it  
> would be going against their principal idea of having all Mathematica  
> expressions fully controllable by means of the Mathematica programming  
> language. Clearly this would not be true of TeX strings, if they were  
> meant to be interpreted for display.

Well, suppose you want to load an externally generated logo, in some 
format like jpeg or PDF, into a Mathematica notebook, just to be 
displayed as part of the exposition.  You _can_ modify this object using 
the Mathematica programming language if you want to; but you have no 
desire to do so, you just want to display it.

Isn't this a close analog?  Mathematica could modify or control those 
TeX input strings, e.g., via options in the TeX[--TeX strings---] 
command, as well as displaying them -- it just wouldn't be necessary or 
desirable to do so, in most cases.

> Secondly, because other CAS  
> systems have essentially tried to do this sort of thing with very  
> little to show for it in terms of market success. You seem to be  
> completely unaware of how tiny the TeX users community is compared  
> with the community of users of programs like Mathematica.

No, I'm aware of how massively _important_ TeX has been and continues to 
be to several equally important communities in this world -- which is to 
say, I have an understanding of what a limited (and even sometimes 
damaging) measure of importance "market success" can be, in a broader 
view of the world.

> This reminds me also that a lot of suggestions which you have made  
> about the way Mathematica ought to be (simple, cheap, computation  
> engine, no fancy staff) has already been tried by WRI and clearly  
> failed. It was called something like The Computation Center, and  
> limited version of Mathematica, that Wolfram once sold for a fraction  
> of the price of the full thing. The only problem was that hardly  
> anyone bought it (I suspect you did not either).

Not really my view.  I do believe that, if all positive and negative 
factors were taken into account, Wolfram could make a _much_ greater 
beneficial contribution to the world, _and_ make a lot of money, if the 
undeniably massive skills and talents of its employees were brought to 
the world in the form of some _modular_ collection of applications, 
utilities, and plug-ins of different levels of sophistication and 
complexity, separately purchasable, aimed at different users or market 
segments having different levels of sophistication and economic 
capability, each module well documented for its audience, all 
interoperable through some common set of formats.  

[And please give a broad and flexible interpretation to the term 
"modular" in the preceding sentence.]

> Not surprisingly WRI is likely to be pretty skeptical of bright ideas  
> that remind them of things that they or others have already tired and  
> have been shown not to work.

In addition to Mathematica, I've purchased, successfully used, but most 
often not particularly loved various components of MS Office, the Apple 
iLife and iWork packages, and the Adobe suite of of interrelated 
programs -- and a number of free-standing third-party apps for parts of 
the same tasks, which I've often liked much better.  

None of these four packages of course come close to Mathematica for 
overall capability; but they do illustrate many of the usability 
benefits -- not to mention the market success! -- of providing wide 
subsets of integrated capabilities through a "modular" approach to a 
related subset of tasks and objectives.

In other words, they worked just fine -- and were and are market 
successes as well.


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