Re: Re: Problems with ImplicitPlot

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1272] Re: [mg1250] Re: Problems with ImplicitPlot*From*: Allan Hayes <hay at haystack.demon.co.uk>*Date*: Wed, 31 May 1995 03:05:39 -0400

In <3q14jp$725 at news0.cybernetics.net>, Mats Jirstrand <matsj at isy.liu.se> writes ->I have a problem with the function ImplicitPlot in the ->Graphics package! -> ->Why does Mathematica generate a plot of the unit circle ->for the first of the below commands but not for the second? -> ->ImplicitPlot[x^2+y^2-1==0, {x, -2, 2}] -> ->ImplicitPlot[(x^2+y^2-1)^2==0, {x, -2, 2}] -> -> -> ->I have also tried the ContourPlot function with the same result: -> ->ContourPlot[x^2+y^2-1, {x, -2, 2},{y, -2, 2}, -> Contours -> {0}, -> ContourShading -> False] -> ->Plots the unitcircle! -> -> ->ContourPlot[(x^2+y^2-1)^2, {x, -2, 2},{y, -2, 2}, -> Contours -> {0}, -> ContourShading -> False] -> ->An empty plot! -> -> ->~~Mats -> I don't see why ImplicitPlot is failing since it uses Solve and yx = Solve[(x^2+y^2-1)^2==0,y] Plot[Evaluate[y/.yx], {x,-2,2}] works OK (with some warnings). The main reason for ContourPlot[(x^2+y^2-1)^2, {x, -2, 2},{y, -2, 2}, Contours -> {0}, ContourShading -> False] failing is I think that ContourPlot[f[x,y],.., Contours -> {0}..] looks for distinct points {x1,y1},{x2,y2} where f[x1,y1] <= 0 <= f[x2,y2]. But there is also seems to be a numerical aspect since ContourPlot[(x^2+y^2-1)^2, {x, -2, 2},{y, -2, 2}, Contours -> {0}, ContourShading -> False, PlotPoints -> 3] gives the line x=0, whilst ContourPlot[(x^2+y^2-1)^2, {x, -2, 2},{y, -2, 2}, Contours -> {0}, ContourShading -> False, PlotPoints -> 7] does not. Allan Hayes hay at haystack.demon.co.uk