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Re: Mathematica as a programming language.
Mark Evans wrote an excellent summary of the strengths of Mathematica. I concur with most of it. However Mathematica as a programming language or system has many weaknesses which Mark did not mention. First, Mathematica has, in any release, many bugs. Many of them are virtually inexplicable, given the description in one MathSource of the alleged test process. For example, one version for Windows could not print a cell that was more than a page. I found the bug the day I took release of the upgrade. Hmmm.. My current version does not properly export the aspect ratio of PostScript graphs. A note to Mathematica confirmed that this too was a bug, and would be fixed in the "next release" which I have paid for and have been waiting for over two years for. These rather obvious bugs are never admitted with a tone of apology, but rather a "who cares" attitude. I have never heard a Wolfram employee *apologize* for a bug that represents a fundamental failure of a major system function. I know (as a software developer) that major bugs will occasionally creep into the best of products, but Wolfram has placed itself on a pedestal. Just read the hype in the Mathematica book. As for the programming capabilities themselves, a major aspect of any programming *system* is the editing and debugging capabilities. Mathematica has debugging capabilities that are, well, Cro-Magnon. That is, they are virtually non-existent. Numerous people have asserted this, and I have never heard anyone debate it. When you are programming, it helps to have good debugging facilities. As for the packages, many of them simply do not represent careful, state of the art programming, and this is obvious to anyone who reads them. Often, the problems are left unfixed, and the user discovers them at the worst possible moment, like after having invested hours of thought and planning under the assumption that the function will work as advertised. For example, there is a statistics package for continuous distributions. It includes the PDF (probability density function) and the general function CDF(x), which is the integral of the probability density function from minus infinity to x. One distribution included in the package is the NonCentral Chi-square distribution. The CDF function (inexplicably) is "not implemented" for this rather smooth function. Neither is quantile calculation. No explanation is given. However, if you try to numerically integrate this function, you discover Mathematica does not appear to be able to do it. At the same time, you discover why the Mathematica book is best described as a user's guide and not a manual, as it is difficult to obtain any clue from documentation or error messages why this operation fails to work. If you plot the PDF of the NonCentral Chi-square, you see no obvious reason why Mathematica should have much difficulty numerically integrating it. Such is frequently the case with Mathematica. Slick appearance can give way to slipshod reality. Overall, it is a product well worth having, in my opinion. It has done wonderful things for me on occasion. But, for someone used to full debugging capabilities and well-checked system functions, it can offer some "interesting" surprises that, well, don't quite agree with the slick typesetting and marketing hype. ==== [MESSAGE SEPARATOR] ====