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Have you ever used Mathematica? I'm guessing that you haven't. It is a program that not only allows calculation in symbolic logic, it can do just about any problem you throw at it, well into the graduate level. None of the modules that you have provided do that.
The question becomes, how hairy is the optimization? If you are talking about something he can solve once on paper -- for instance the shapes that are being cut are the same each time, then he doesn't need the power of Mathematica, or another technical computing platform. If, on the other hand, you are talking about something which you can't solve once for -- for instance if all of the shapes that are being cut change, and they are irregular, there may be a need for Mathematica.
I don't work for Wolfram, and am in no way affliliated with them, but back when I was getting my degree in Mathematics, Mathematica impressed me more then any of its competitors -- Matlab, Maple, etc. If you need a lot of power, I would recommend trying it. I am pretty sure you can get it on a 30 day trial. If there is a real need, you will be more then able to justify the cost.
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Can't resist to give a quick answer to your question:
Being a physicist, I have indeed used Mathematica, though I generally prefer Maple for most stuff since I like the interface better. As you said, it is a question of the complexity of the optimization. I don't think you need the full power of Mathematica for this, though I haven't thought it through. If it's an If I recall correctly, the first reply in this thread pointed to a good, scientific discussion of the subject. The reason I pointed at those Math:: modules was because before engaging in hairy XS/Inline::C library wrapping, it's probably a better idea to try with what's availlable already. If that's not good enough by a small margin, it's probably a better idea to extend what's on CPAN than to roll one's own. That doesn't mean I consider Mathematica an inadequate tool for the job.
Steffen
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