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MathGroup Archive 2005

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Re: Types in Mathematica, a practical example

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62948] Re: [mg62800] Types in Mathematica, a practical example
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Fri, 9 Dec 2005 05:10:30 -0500 (EST)
  • References: <000f01c5fbf8$e3979330$996f1081@fy.chalmers.se> <48AE76E3-6285-471E-A239-2FE0582CC233@mimuw.edu.pl>
  • Sender: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski wrote:

>
> On 8 Dec 2005, at 22:11, Ingolf Dahl wrote:
>
>> I feel it as a round-about way to solve the problem.
>> Andrzej Kozlowski, who suggests such a solution, thinks that I am 
>> looking at
>> Mathematica from the wrong view point. It is my strong belief that one
>> should be able, especially when mathematics is involved, to observe 
>> from as
>> many different view points as possible. An item is not really 
>> beautiful, or
>> properly designed, if it is not beautiful from all view points.
>
Hi Ingolf,

Then again beauty, as they say, is in the eye of the beholder. I mean an 
artist can put a bucket and pail of water and call it installation art, 
but that does not really take away from what it is and what it is used 
for. I concur with Andrzej, Mathematica (lets leave mathematics aside 
for now) allows one to solve problems using different approaches, but 
what is the best way is a matter of taste and experience, and to some 
degree competence in the sciences (the latter quality I am begining to 
appreciate after using Mathematica for about a year now) . And to your 
problem of using the lawsofcosines and sines essentially is a algebraic 
problem which can be solved using Solve, Reduce, but as to how you do it 
is IMHO irrelevant. That is, how you input the variables and such (I 
think thats where this type business comes in). Again reitereate my 
impression of Mathematica as a R&D tool, which probably does not lend it 
self well to making some applications user friendly or interactive.

As to your proposal of using undefined, if I am not mistaken, undefined 
is already taken :-) .I think it means expressions such as 0/0 or 
inf/inf (that is in mathematics ofcourse not in CS)

In response to Ssezi's post, I remember there was a post asking about 
clearing subscripted variables last june, here is the thread anyway, 
might be useful for your application
http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_frm/thread/c0dba6e4ca2d7700/759cf4eee37247ab?q=Clear+Subscripted+Variables&rnum=1#759cf4eee37247ab

Best Regards,

Pratik

>> The same
>> should apply to Mathematica, and I have also understood that 
>> Mathematica was
>> intentionally designed to be well-behaved when seen from different view
>> points. Or?
>
>
>
> About mathematics: it seems to me that almost all beautiful solutions 
> of difficult problems involve finding the right "point of view". Often 
> once the right point of view is found the problem is almost solved, 
> while from the other "wrong" points of view the problem looks 
> extremely hard and often uninteresting - (usually because it appears 
> that the only way to solve it is by a tedious computation or, in the 
> case o finite problems, by an exhaustive examination of all possible 
> cases).
>
> About Mathematica: it is true that Mathematica allows many styles of 
> programming and that this has many practical advantages, but it 
> certainly is not true that all these styles are equally efficient, 
> elegant and equally suitable to all types of problems. So if you mean 
> that for any problem that one wants to tackle with Mathematica it 
> should not matter whether you choose a functional approach, a 
> procedural approach, a re-write rule based approach, a recursive 
> approach etc, well this definitely is not true and I do not think it 
> is reasonable to expect otherwise. In a similar vein in mathematics 
> certain problems are more suited to be tackled with algebraic 
> techniques, certain with topological, others with analytic etc.
>
> About your concrete proposal : I personally do not think it would fit 
> in well with the functional style of programming that is usually the 
> most natural way to tackle problems involving lists, matrices etc in 
> Mathematica and also I do not feel any need for what you are proposing 
> and hence do not see any benefit if something of this kind were to be 
> implemented in Mathematica. But I am sure that this is just a matter 
> of taste, exactly as my preferring certain areas of mathematics to 
> others is only a matter of taste.
>
> Andrzej Kozlowski



-- 
Pratik Desai 

...Moderation, as well as Regularity of Thinking, so much to be wished for in the Heads of those who imagine they come into the World only to watch and govern it?s Motion
Gulliver's Travels
by Jonathan Swift




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