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Re: Algorithm Analysis Course: Should I use Mathematica for projects?

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  • Subject: [mg127313] Re: Algorithm Analysis Course: Should I use Mathematica for projects?
  • From: Andrzej Kozlowski <akozlowski at gmail.com>
  • Date: Sun, 15 Jul 2012 04:30:07 -0400 (EDT)
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I don't intend to get involved in more pompous and futile rhetorics so beloved by Richard, but so I will restrict myself to matters of substance.
 The stuff about "how it all works" is mere hypothesis - quite interesting in some ways but no more (and actually perhaps less) than similar hypothesis I have heard from my students. It's all rather unimportant.

>> Another thing, all your examples of length dependent retrieval involve changing the list in w way that could alter it's length.
> This is false. I set the several arrays in fixed size and then changed the contents, not the length.
> Your statement is also ungrammatical.   ... " it's"  is a contraction for "it is" ... not a possessive. :)

I will address only the first part of the above (the second is just too childish, even with the smiley, to bother with).

You used the construction:


B = Table[i, {i, 0, 1000}];
B[[5]] = j; Timing[Do[B[[50]]++, {i, 0, 100000}]]

This sort of thing can certainly change the length of a list. A simple example:

Clear[B]

 j /: {a___, j, b__} := {a, 1, 1, b}

B = Table[i, {i, 0, 5}];
Length[B]
6

B[[5]] = j;
Length[B]
7

It would seem to me that this alone should force re-evaluation of the =
list.
  
>>
>> Finally, I would like to mention that I have taken no position at all =
on the question in the subject of this thread. Clearly using a tool =
which was designed for a purpose other than the one you have in mind is =
rarely the optimal approach unless there are some benefits that =
compensate for the almost inevitable deficiencies. Mathematica was not =
designed primarily as an all purpose programming language so it is not =
the best tool for the study of the workings of such languages.
> That was not the issue.  Studying algorithms is not the same as =
studying the workings of programming languages.
> Mathematica would not be my first choice for either.

Studying algorithms is not the same as studying the working of =
programming languages and I never said it was. But algorithms have =
various aspects some of which can be studied without any mention of any =
programming language at all (as happens for example with algorithms in =
commutative algebra) and others (such as time and space complexity) =
require the introduction of a specific model of a computer and a =
suitable language - (as was done, for example, in volume 1 of Knuth's =
"The Art of Computer Programming"). Choosing such a model and a language =
is always to some extent arbitrary. One could probably create a computer =
especially designed to run Mathematica (as was once done with LISP at =
MIT) and if this computer became the "accepted standard" "the study of =
algorithms" for such a computer would not be exactly the same as the =
study of algorithms for th standard computers in use today.

Andrzej=



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