Math Software Packages for Windows & Linux: Updated List & Resources

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RJ Emery
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For the Windows and/or Linux platforms, I am trying to get a handle on what major math software packages exist today. At one time, I recall there being Maple, Mathematica and MatLab. No doubt the list of worthwhile packages has grown since then.

Anyone know of an authoritative list of what exists for what purposes?

What would be a good source, such as a monthly magazine or on-line resource, to read about software packages for math, physics and engineering?
 
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Maxima is a free alternative.