I can't answer for the others, but Maple 9 (which I'm stuck with for various technical reasons) not infrequently finds itself with a square root, which it correctly deduces might have either sign --- and subsequently becomes incapable of squaring that again to lose the sign! WFL On 3/15/11, Henry Baker <hbaker1@pipeline.com> wrote:
Over the years, I've had occasion to use Macsyma/Maxima to produce formulae that were then utilized in my computer code (Lisp/C/...). While these symbolic algebra tools are extremely useful, there is one area where symbolic algebra systems could be improved quite a lot -- the handling of signs (e.g., +/-).
While Maxima does a pretty good job of understanding the absolute value function ('abs'), it doesn't seem to know very much about the intimately related "sign" ('signmum') function. For example, although 'asinh' is a perfectly good odd function, Maxima doesn't know how to move 'signum' in and out of the 'asinh' function.
Dealing with 'signum' in a high quality way should be considerably easier than attempting to handle 'if-then-else' expressions (aka "()?:" expressions in C/C++, etc.). But there are occasions where symbolic algebra systems would be extremely helpful if they could handle such if-then-else expressions. The alternative is pretty ugly: it may be necessary to create a software "harness" and then evaluate the alternative expressions with every conceivable boolean combination -- a strategy that quickly blows up exponentially, but it is still better if this strategy is implemented mechanically, to make sure that all combinations are checked.
I haven't had a lot of experience with other symbolic algebra systems. Do Maple & Mathematica (or any others) do a better job of handling these signum and/or if-then-else expressions?
Alternatively, has anyone here had any experience in teaching the Macsyma/Maxima simplifier about such expressions, so that I could expand its capabilities ?
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