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Re: vs. f[a]. When are they equal?

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On 4/26/11 at 4:43 AM, fateman@cs.berkeley.edu (Richard Fateman) wrote:

>Here's a fun thing to do with our function f[x_]:=1/(1-Exp[I x])  .

>try Plot[Re[f[x]],{x,0.01,20}]
>On my system it look like a plot of y=0.  A bug (Mathematica 7)?

Look closely at a plot of y = 0 and you will see that it is
different from a plot of f[x] above. The difference is much more
obvious if you move the origin for the axes. That is

Plot[0 , {x, .01, 20}, AxesOrigin -> {0, .5}]

is clearly different from

Plot[f[x], {x, .01, 20}, AxesOrigin -> {0, .5}]

Nothing at all is being plotted when you attempt to plot f[x].

This is not a bug since Plot is designed to plot functions where
they have real values. Doing

Plot[Im[f[x]], {x, .01, 20}, AxesOrigin -> {0, .5}]

shows the function has real values at regularly spaced points.
The likelihood of Mathematica selecting these points when
evaluating f[x] is essentially zero. Consequently, Plot all plot
sees as values for f[x] are complex values which are not plotted.

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Re: vs. f[a]. When are they equal? Bill Rowe <readnews@sbcglobal.net> - 2011-04-27 09:38 +0000

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