> Being smart about plotting is only useful if we are
> smart enough about it. I am not yet convinced that we are.
> What happens if you plot sin(1/x) near x=0?
The only really robust and accurate way to plot arbitrary functions is
interval arithmetic. We should eventually be able to do as well as the
very nice commercial GrafEq system
http://www.peda.com/grafeq/gallery/rogue.html (though one of their
examples, http://www.peda.com/grafeq/gallery/rogue/xx_exponential.html,
must be using some other technique).
Unfortunately, we do not yet have an interval arithmetic system for
Maxima. Anyway, that assumes that all your computations return
intervals and not precise results, which won't immediately be true for
built-in functions let alone user-defined functions.
In the meantime, I do think there are some useful approximations.
-s