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Controlling StepLeftButton and StepRightButton in Animator

If one sets DisplayAllSteps -> True in an Animator, then why doesn't this 
also apply to the StepLeftButton and StepRightButton?

Here is an example. This is a stripped down case from a display that 
actually has a plot. What I want to do is illustrate that the following 
complex function maps the unit circle into the real axis.

w[z_] := (\[ImaginaryI] (1 - z))/(1 + z)

  {Row[{HoldForm[w[\[ExponentialE]^(\[ImaginaryI] "\[Theta]")]] ==
      w[\[ExponentialE]^(\[ImaginaryI] "\[Theta]")],
     " maps to the real line"}],
   Row[{"Abs[Numerator] = ",
       N@Abs[1 - \[ExponentialE]^(\[ImaginaryI] \[Theta])]}],
   Row[{"Abs[Denominator] = ",
       N@Abs[1 + \[ExponentialE]^(\[ImaginaryI] \[Theta])], {10, 9},
       ExponentFunction -> (Null &)]}],
   Row[{"w = ",
       Chop@N@w[\[ExponentialE]^(\[ImaginaryI] SetPrecision[\[Theta],
            22])], {10, 2}, ExponentFunction -> (Null &)]}],
   Row[{"\[Theta] = ",
     Dynamic[NumberForm[N[\[Theta]] // Chop, {10, 9}]]}]}],
  Join[{-\[Pi] + 10^-8, -\[Pi] + 10^-5, -\[Pi] + 10^-3},
   Range[-\[Pi] + .01, \[Pi] - .01, (2 \[Pi] - .02)/
     50], -Reverse@{-\[Pi] + 10^-8, -\[Pi] + 10^-5, -\[Pi] + 10^-3}],
  DisplayAllSteps -> True,
  AnimationDirection -> ForwardBackward}]

I have a series of discrete steps on theta and I add extra specific points 
at each end to get very close to -Pi and Pi. If one moves the slider with 
the mouse, or runs the animation, one can see each of these steps. However, 
if one uses the StepLeft and StepRight buttons many steps are skipped. Is 
there a way to use every step? If not, this seems like a design flaw.

David Park
djmpark at

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