RE: Plotting problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg35349] RE: Plotting problem*From*: "David Park" <djmp at earthlink.net>*Date*: Tue, 9 Jul 2002 06:48:16 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Steven, The Mathematica Plot routine is not quite as sophisticated as you were hoping for. For 2D plots Mathematica uses an adaptive algorithm that samples the points and tries to pick points to minimize the bending of the curve between adjacent pairs of points. So, chances are that it will never even hit the singular points in your function. So you just get a straight line because that is what your curve is except for the singular point. If, by chance, Mathematica does hit a singular point it will issue a warning message. You have to find the singular points yourself and add them to the plot. You could do this using Epilog. f[x_] := (3 x^2 - 5 x + 2)/(x - 1) Plot[f[x], {x, -2, 3}, Epilog -> {AbsolutePointSize[4], Point[{1, Limit[f[x], x -> 1]}]}]; In more complicated cases, you could write a routine to find the zeros in the denominator. (Just to keep things short I am restricting to cases where they also occur in the Numerator. We should really add code to check for this.) f[x_] := (24*x - 50*x^2 + 35*x^3 - 10*x^4 + x^5)/ (3 - 4*x + x^2) Solve[Denominator[f[x]] == 0] // Flatten pointlist = Limit[{x, f[x]}, #] & /@ % {x -> 1, x -> 3} {{1, 3}, {3, -3}} Plot[f[x], {x, -2, 4}, Epilog -> {AbsolutePointSize[5], Point /@ pointlist}]; In my answers I have used the Limit routine, pure functions (Function) and the Map command, which you should look up in Help. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > From: Steven Hodgen [mailto:shodgen at mindspring.com] To: mathgroup at smc.vnet.net > > Hello, > > I'm a total Mathematica newbie, and I'm trying to get it to plot a simple > rational eq. in such a way that it indicates where missing points are. > Since I'm not sure how you'd prefer the eq. expressed, I've typed > in in the > parents so there can be no question of where the denominator is, > as well as > a cell expression. > > (3 x^2 - 5 x + 2)/(x - 1) > > Cell[BoxData[ > FractionBox[ > RowBox[{ > RowBox[{"3", > SuperscriptBox["x", "2"]}], "-", > RowBox[{"5", "x"}], "+", "2"}], > RowBox[{"x", "-", "1"}]]], "Input"] > > When I Plot[], this is just draws a straight line. There is no indication > where the hole is. How can I get this "fully correct" graph? > > Thanks > --Steven > > >