I see Mathematica has announced a new release
I went through a period, pre release 1.0, when I used Mathematica's precursor rather heavily, in conjuntion with Maple (basically if the two produced the same results I used it, after sanity checks, if they didn't I sent in a bug report to Mathematica...)
I was also taken by their early graphics capabilities, which for the time were rather good.
Then I stopped using symbolic manipulators on a regular basis - and I never really used Mathematica's numerical capabilities except for occasional need for arbitary precision arithmetic.
So... what is the verdict?
Anyone used the new version? Should I go back to the fold and be subsumed?
I am tempted, but not convinced the marginal effort is worth the results.
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I can't say anything about the new mathematica; our site-licensed version has not been updated yet.
But out of curiosity, what other math packages do people use? My favorites are GP/Pari for random calculations (hooray arbitrary precision!) and Matlab for any sort of numerical work. It never really seemed like the functional programming style of mathematica made any sense for numerical work, unless you really wanted to rework all your algorithms. It is great for tedious integrals, though.
I'm still on version 4.2, but I find it indispensable. I do quite a bit of quantum theory, and doing integrals by hand is for the birds. But I also use it for 1D and 2D NMR data processing; it's great to be able to compare theory and experiment on the same platform.
The learning curve is, however, very steep.
For the odd matrix inversion or integral, I find maxima works very well. It is the open-sourced descendant of Macsyma. It continues to be updated and maintained, and it is free. Plotting via gnuplot in 2D and 3D is also supported.
First off, I don't work for Wolfram Research! Like you I have used Mathematica since before version 1.0 (i.e. SMP), and I have used it ever since then. It has become an extension to my brain to such an extent that all aspects of my research into information processing would be tedious or impossible without it. Since version 3 it has replaced my paper-based lab notebook; nowadays I rarely use pen and paper. It has a fundamental appeal to the mathematician/physicist in me, because it has an internal logical coherence that is designed in at a very low level. Its numerical speed is right up there with hand crafted compiled C code (I have checked this for myself). Really, the only off-putting thing is its price, but if you see how much time it saves you then it makes sense to buy it. If I didn't get it courtesy of the place that I work, then I would dip into my own pocket to buy it. Yes, really!
I was a beta tester for Mathematica version 6 (see here) so I have used V6 for a while now. The most obvious difference compared to earlier versions is that its graphics are now much higher quality and fully interactive. Also, there is now the capability of producing shrink-wrapped applications that others can run using the so-called Mathematica Player; the unrestricted Pro version of Player is soon to be released, and I sincerely hope it will cost very little otherwise it's a waste of time. There's lots more information on what's new in V6 at the URL linked above.
I'm now waiting for my release version of V6 to arrive any day, to replace the soon-to-expire beta version that I am currently using.