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RE: Plot, Cursor and Spelling Errors questions

  • To: mathgroup at
  • Subject: [mg14438] RE: [mg14393] Plot, Cursor and Spelling Errors questions
  • From: "Ersek, Ted R" <ErsekTR at>
  • Date: Wed, 21 Oct 1998 03:32:34 -0400
  • Sender: owner-wri-mathgroup at

Ranko Bojanic wrote:
>I am having problems when trying to plot the graph of an error curve
>when the magnitude of the error curve is close to the $MachineEpsilon
>number. The following example is typical:
>n = 15;
>f[x_] := Exp[x];
>xLst = Table[Cos[((2*k - 1)*Pi)/(2*n)], {k, 1, n}]//Reverse; yLst =
>N[Map[f,xLst], 30];
>fLst = Transpose[{xLst, yLst}];
>p[x_] := InterpolatingPolynomial[fLst, x]; Plot[Evaluate[f[x]-P[x]], {x,
>-1, 1}, PlotPoints -> 50];
>Why the Plot function cannot draw the graph of the difference? I can
>still get a graph by computing 1000 points on the error curve and using
>ListPlot with PlotJoined->True, but the graph is not very smooth.
>The problem here is not in the accuracy of computations, as the ListPlot
>function shows, but in the way Plot processes data. 
That is true.  For efficiency Plot uses machine precision arithmetic.  In
the example you give you have to force the use of arbitrary precision
numbers and this isn't straight forward.

>Is there a way to force Plot to draw the error curve correctly?

I have sent Wolfram Research a suggestion indicating that Plot and
similar commands should have an option 'MachineArithmetic->True' (or
False).  Until they give use such an option the code below will solve
the problem.

      Plot[h[x],{x,xmin,xmax}, opts]

PrecisionPlot[Evaluate[f[x]-p[x]], {x,-1, 1}, PlotPoints -> 50];

(* Graphic not shown. *)

Actually I figured a way I can add such an Option to the Plot command in
version 3.0, but the necessary program is messy.

>An unrelated programming question:While  Mathematica is doing a lengthy
>computation, I would like to change the cursor into a watch cursor. I
>could not find any information on how to do it. Is there a simple
>command to change the current cursor into a watch cursor - something
>like SetCursor and InitCursor in Pascal.
I doubt this is possible if the feature is not built into the front end, and
I have not herd that it is.
>Last question: If you run the program listed here, you will probably get
>the messages :
>General::spell:Possible spelling error: new symbol "yLst" is similar
>to existing symbol {xLst} General::spell:Possible
>spelling error: new symbol "fLst" is similar
>to existing symbol {xLst,yLst}
>Is there a way to turn off these spelling errors messages?

There are two spelling messages.
They can be turned off using:


To turn them back on use:


Ted Ersek

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