Subject: Maxima gives incorrect results with ceiling
From: Richard Fateman
Date: Fri, 7 Dec 2007 17:23:11 -0800
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Daniel Lakeland
> Sent: Friday, December 07, 2007 1:36 PM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] Maxima
>
....
> I don't have a proof, but it seems as if it should be the case that
> for SOME bf precision, numerical cancellation should cease to be a
> problem for calculating the integer part of a bf. The doubling
> strategy should find that bf precision in log(n) time, and the "jump
> to it" strategy should work in constant time for any case where
> cancellation is not a major issue.
Unfortunately, this is not the case. ceiling(expression) requires, for
example,
that you be able to determine if expression is <=0 or >0. How many digits
do you need to prove this, in general?
Answer: no limit.
Proof -- Richardson's undecidability results c. 1968.
For expression in some subclass of what is allowed in Maxima, there are
possibilities.
>
RJF