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Re: machine precision number plot fixed in V6?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83077] Re: [mg83043] machine precision number plot fixed in V6?
  • From: Carl Woll <carlw at wolfram.com>
  • Date: Fri, 9 Nov 2007 05:21:38 -0500 (EST)
  • References: <200711081113.GAA27782@smc.vnet.net>

congruentialuminaire at yahoo.com wrote:

>Hello Mathematica UG:
>
>I was doing some work with the PrecisionPlot package (http://
>library.wolfram.com/infocenter/MathSource/715/)
>
>When I ran it under V6, no output was emitted. So I looked again at
>the documentation provided by Ted Ersek. Even though it is 8 years
>old, it contains the following function and plot which does not work
>correctly as recently as V5.
>
>In V6, the invocation with SetPrecision works and emits a smooth plot
>(presumably eliminating the need for this package). Here are the lines
>of code.
>
>-----------------------------------------------------------
>(* a function that does not plot well with machine-precision numbers
>*)
>f2[x_] = ArcSec[x] - Normal[Series[TrigToExp[ArcSec[x]], {x, \
>[Infinity], 7}]]
>
>(* a jagged plot results under V5 and V6 *)
>Plot[f2[t], {t, 25, 40}]
>
>(* a smooth plot results only under V6 *)
>Plot[f2[SetPrecision[t, 17]], {t, 25, 40}]
>------------------------------------------------------------
>
>If there is a simple explanation for what was fixed in V6 to make this
>work, I am interested to know.
>
>TIA.
>
>Regards..Roger
>
>  
>
The key difference is that V6 Plot now accepts the WorkingPrecision 
option, and presumably the code to handle extended precision arithmetic 
is triggered because of the presence of SetPrecision. At any rate, in 
V6, the proper way to do a plot with precision 17 is:

Plot[f2[t], {t,25,40}, WorkingPrecision->17]

Carl Woll
Wolfram Research


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