From: Richard Fateman <fateman@cs.berkeley.edu>
Subject: Re: Strange plotting behaviour of Maple V.5 - possibly a bug? (Re: 
Date: Tue, 24 Oct 2000 14:55:55 -0700
Newsgroups: sci.math.symbolic,comp.soft-sys.math.maple

I just tried

Plot[(1+1/n)^n,{n,C}]
in Mathematica 3.0 and got a nice sawtooth curve. This is not
a consequence of plotting point up, point down etc.
The plot actually includes intermediate points going up
and down. 

Macsyma 2.2 defaults to plotting (1+1/n)^n in single floats,
which leads it astray at even smaller values.  However
plotting (1+1.0D0/n)^n does somewhat better. Yet it has problems
with this example too, ending up with a blank plot. Seems something
is throwing a fit, perhaps overflowing.

RJF



Robert Israel wrote:
> 
> In article <39F48563.9C5F5C01@fmi.uni-konstanz.de>,
> Gottfried Barthel  <Gottfried.Barthel@uni-konstanz.de> wrote:
> 
> >motivated by the above posting, I wanted to have a look at the graph of
> >the (linearly interpolated) sequence, so for some positive integers a,
> >b,  a < b, I run the following command in Maple V.5 (on a SUN Ultra 10):
> 
> >> plot([seq([n, (1-1/n)^n],n=a..b);
> 
> >That works nicely for small ranges, but for [a,b]=[101,200], the
> >horizontal (n)-axis surprisingly ends somewhere near 143, and the range
> >[a,b]=[151,200] yields an empty plot. More precisely, for
> >[a,b]=[141,200] the displayed n-range is [141,142], and the plot is a
> >line joining [141, .366571...] and [142, .366580...], so that's fine;
> >for [a,b]=[142,200] the displayed n-range is [142,143], and the plot
> >shows just that part of the horizontal axis, and the interval -0.62..1.4
> >on the vertical axis, but no curve; for [a,b]=[143,200] I get an empty
> >plot.
> 
> >Is there any reasonable explanation for that strange behaviour?
> 
> The problem is that if n >= 143, (1-1/n)^n is a fraction whose
> numerator and denominator are integers that are too big to be represented
> as hardware floats (the largest possible hardware float being
> approximately 10^308).  The result is that evalhf (which is called
> by plot) returns Float(undefined).
> 
> It works if you use evalf on your list, or if you use plots[pointplot]
> instead of plot.  BTW, plots[pointplot] is also much faster for plotting
> long lists of points.
> 
> Robert Israel                                israel@math.ubc.ca
> Department of Mathematics        http://www.math.ubc.ca/~israel
> University of British Columbia
> Vancouver, BC, Canada V6T 1Z2