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

*To*: mathgroup at smc.vnet.net*Subject*: [mg121261] f(x)=x: why Plot continues to add new levels of recursion?*From*: Alexey Popkov <lehin.p at gmail.com>*Date*: Tue, 6 Sep 2011 03:58:51 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hello, Please consider the following example (plotting function f(x)=x): NumberOfEvals[r_] := Length[Reap[ 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 MaxRecursion. 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: In[1]:= l[div_]:=Length@Reap[Plot[Sow[x];x,{x,-Pi, Pi},PlotDivision\[Rule]div,DisplayFunction\[Rule](#&)]][[2,1]] Table[l[div],{div,1,10}] Out[2]= {25,25,25,25,25,25,25,25,25,25} Why in Mathematica 7 Plot makes these superfluous evaluations? Is it possible to force it to behave like Plot in version 5.2?