Subject: Maxima gives incorrect results with ceiling
From: Richard Fateman
Date: Tue, 11 Dec 2007 06:15:25 -0800
No method can be guaranteed to converge, in general. How much precision do
you need to tell if a value is bounded away from zero, if it is actually
zero?
For certain classes of input, Bill Gosper has an algorithm in commercial
Macsyma.
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Robert Dodier
> Sent: Monday, December 10, 2007 11:19 PM
> To: Stavros Macrakis
> Cc: Maxima at math.utexas.edu
> Subject: Re: [Maxima] Maxima gives incorrect results with ceiling
>
> On 12/7/07, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
>
> > As I said, Maxima uses bigfloats *internally* to calculate
> > ceiling/floor. Unfortunately, the current method of using
> bigfloats is
> > not conservative enough to avoid error in some cases. The
> right way to
> > handle this would be interval arithmetic, but no one has
> coded that up
> > yet.
>
> Can you summarize the approach using interval arithmetic?
> I will take a look at it.
>
> Robert
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