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f(x)=x: why Plot continues to add new levels of recursion?

  • To: mathgroup at
  • Subject: [mg121261] f(x)=x: why Plot continues to add new levels of recursion?
  • From: Alexey Popkov <lehin.p at>
  • Date: Tue, 6 Sep 2011 03:58:51 -0400 (EDT)
  • Delivered-to:


Please consider the following example (plotting function f(x)=x):

NumberOfEvals[r_] :=
    Plot[x, {x, -Pi, Pi}, MaxRecursion -> r,
     EvaluationMonitor :> Sow[x]]][[2, 1]]]
data = Table[{r, NumberOfEvals[r]}, {r, 0, 15}];
f = Fit[data, {1, r, r^2}, r] // Factor
Show[ListPlot[data, Axes -> False, Frame -> True,
  FrameLabel -> {"MaxRecursion", "Number  of evaluation  points "},
  PlotLabel -> StandardForm@"Plot[x,{x,-\[Pi],\[Pi]}]"],
 Plot[f, {r, 0, 15}, PlotRange -> All]]

=> (100 + 3 r + r^2)/2
=> <Graphics>

One can see that the number of evaluation points for function f(x)=x
grows as (100 + 3 r + r^2)/2 where 'r' is the value of option

It is clear that in the case of f(x)=x it is not necessary to go
deeper in recursion because the bend angle between successive segments
of the
approximating polyline in this case is always approximately equal to
zero. In Mathematica 5.2 Plot does no recursion in this case:



Why in Mathematica 7 Plot makes these superfluous evaluations? Is it
possible to force it to behave like Plot in version 5.2?

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