floor, ceiling, and friends



-----Richard Fateman  wrote: -----

> I believe the commercial Macsyma has a sophisticated program
> involved in this, courtesy of Bill Gosper, which allows the system
> to decide how much precision is required to determine the
> sign of (or,especially, the zeroness of ..) an expression.

Too bad we don't have the source -- with Macysma 2.2, it's
easy to break 'floor':

(c1) p : sqrt(5) * (sqrt(5) - 1/sqrt(5))$  /* p = 4 */

(c2) floor(p);
(d2) 3       <--- bogus


(c3) floor(expand(p));
(d3) 4      <--- OK

Maybe this was fixed in later versions.

Barton