' III_Poly5A.txt 
' The following function shows the extreme range of values for a plot that may mislead the
'     user. We modified the plot function shown below where the curve  between 0<P{x} < 1
'     is not easily shown on the graph. (The zeros & one pole are accurate.) 

' Click on the Set 2D if not already set.
' Under Options: Display Menu,
'       click Show Discontinuous?
'          click  Yes, No Limit Markers.

N{x} = x^2 * (x - 1)^2 * 20                         ' mpy by 20 to increase zeros.

D{x} = (x + 1)^2

P{x} = (N{x} / D{x}) 

' ***************************** Note: Compression routine. *******************************
'  We need a "compress" routine to avoid overflow, yet still show the basic pattern.
'  If  | F{x} | >= 1, then compute 
'                               Co <-- Sign[F{x}] * Ln[Abs[F{x}]] + 1
' Otherwise,
'                                if -1 < F{x} < 1, then 
'                                   Co <-- F{x}    (unalterd) 
' *********************************************************************************************

Co{x} = Unit[Abs[P{x}]-1] * (Sign[P{x}]*Ln[Abs[P{x}]] + Sign[P{x}]) + Unit[1-Abs[P{x}]] * Sign[P{x}] * (Exp[Abs[P{x}]] - 1) / (Exp[1]-1)

F<x> = <x, Co,0>
Plot[F, {x, -4, 4, 400}]	


