Since I, probably, one of the most experienced Maple users on this list, and I haven't used Matlab, Mathematica and SAGE for a long enough time, I may be biased. Anyway, my opinion is that Maple is user friendly and easy to learn, but it is very slow comparing with others and has a lot of problems related to both programming bugs and mathematical inconsistencies. Mathematica is much faster, produces better quality graphics and has much less bugs. However, it uses an akward language, also has some mathematical inconsistencies and its licensing policy is very bad. For example, when I tried to install it in Linux running in the Microsoft VirtualPC (in Windows) on the same computer and the same Windows where I had it installed, I was told that I can do that only if I sign a form that I delete Mathematica installed in Windows. The most ridiculous thing in this story was that my Windows Mathematica version was sent to me complimentary from Wolfram Research. Matlab is a very good product for numerical computations and its graphics beats even Mathematica, not talking about Maple. However, it has a lot of free clones, such as Octave, scilab, and NumPy with SciPy etc., and it is not clear why a person (I am not talking about firms or companies - they might have their reasons) would buy it for fun when the same fun can be obtained for free. SAGE is free, fast, mathematically consistent, and includes a lot of mathematical capabilities unavailable in anything else (in particular, it includes PARI, Maxima, GAP, Singular, and NumPy with SciPy). Also, it is under active development. I have a lot of fun with it as well as with Python - the programming language on which SAGE is based. A negative side of it is that it doesn't run on Windows (except VirtualPC, vmware, or other virtualization.) - that may be changed in the future though. Alec