Just looking at more of my notes, in
http://www.cs.berkeley.edu/~fateman/generic/interval.tex, (which is the raw
source tex and has lots of notes not in the pdf, notes-intervals.txt, and
ninterval.lisp,
I thought I might add some simple observations. e.g.
evaluating a*x^2+b*x+c for numbers a,b,c and interval x, should not be done
either by the "obvious" way, nor by Horner's rule: we use completing the
square to make the evaluation use x a SINGLE time. transform
a*x^2+b*x+c => a* (x^2+(b/a)*x* +c/a)
(x^2+r*x +s) => (x + r/2)^2 -(r/2)^2 +s.
why? you get a smaller interval for almost no extra work.
This is much more interesting that implementing, for the hundredth time,
interval versions of +,*, ... and trying to merge them in to maxima. What
is infinity * interval? what if the interval is empty, e.g. the
intersection of two distinct ranges? What are the rules for multiplying it
by "und"?
RJF