As far as I know, nobody has tried to compare CAS's since Michael Wester's attempts in the 1990's. And even then, his final test, which had over 500 problems purporting to be from "all areas of mathematics" was not in any way comprehensive: no topology, no abstract algebra, not much logic, nothing on graphics, and so on. And these tests only tested the "breadth" of a system - the number of different problems it could spit out a correct answer to. In these tests, and in some smaller ones developed by Barry Simon, Axiom performed very poorly.
Nobody that I know of has attempted a more modern comparison, looking a depth as much as breadth. It may well be that Axiom does not have the black-box problem solving abilities of some of its rivals (put a problem in, get an answer out), but it may be that in depth and in its fundamental design paradigms, it outweighs others. Does anybody know of any research in this area? I started a while back trying to get some material together to write a small article comparing CAS's for teaching and learning, but never got very far with it (something common to all my projects at the moment!) It seems to me that this would be a worthwhile effort. cheers, Alasdair
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