There are quite a few examples of interval number
systems implemented, including RealInterval in
Mathematica and Range arithmetic in Maple. There
are probably a large number of interval packages
in Lisp and in C. To do this right requires some
control over the direction of rounding.
I've written papers on interval arithmetic and
"honest" plotting. Some ISSAC conference;
http://www.cs.berkeley.edu/~fateman/papers/intervalplot.ps
I think.
Stavros Macrakis wrote:
>>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
>
> _______________________________________________
> Maxima mailing list
> Maxima@www.math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima