On May 29, 2007, at 11:02 AM, William Stein wrote:

> In fact, the Mathematica documentation has something to say about this
> (see  
> http://reference.wolfram.com/mathematica/tutorial/ 
> WhyYouDoNotUsuallyNeedToKnowAboutInternals.html):
>
> "Particularly in more advanced applications of Mathematica, it may
> sometimes seem worthwhile to try to analyze internal algorithms in
> order to predict which way of doing a given computation will be the
> most efficient. And there are indeed occasionally major improvements
> that you will be able to make in specific computations as a result of
> such analyses.
>
> But most often the analyses will not be worthwhile. For the internals
> of Mathematica are quite complicated, and even given a basic
> description of the algorithm used for a particular purpose, it is
> usually extremely difficult to reach a reliable conclusion about how
> the detailed implementation of this algorithm will actually behave in
> particular circumstances."

Wow. I can't believe they actually said that. What incredible  
arrogance. I think this in itself demonstrates pretty clearly why open  
source alternatives are necessary.

david


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