Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1999
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1999

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: implcit plot with undefined expression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18863] Re: implcit plot with undefined expression
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Sun, 25 Jul 1999 03:30:04 -0400
  • Organization: University of Western Australia
  • References: <7n13kb$bf2@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

zoominzero at hotmail.com wrote:

> Hi,
> I've spent 4 days to try to use ImplicitPlot on an equation, without
> success:
> The Equation I try to plot has 2 nested square roots, ans 2 variables :
> something like Sqrt[2*Sqrt[2X^2 -Y^2] - 2*Y +X^2]==0
> (it's not exactly this one: it's  just to give you an idea )
>
> Of course this equation is not defined everywhere, and the domain where
> it's defined is complex. When i try to "ImplicitPlot" this equation,
> i've an answer :
> "The contour is attempting to traverse a cell in which some of the
> points have not evaluated to numbers, and it will be dropped"
> followed by
> "Further output of ContourGraphics::"ctpnt" will be suppressed during
> this calculation."
>
> So i don't have any answers ( and there are answers of course :)
>
> Is there some options or another solution to draw this implicit equation?

The following Notebook highlights the problem and indicates one approach to
solving it.

Notebook[{
Cell["\<\
Modify the function so that if the result is complex, a specific \
numerical value (here 1) is returned.\
\>", "Text"],

Cell[BoxData[
    \(TraditionalForm\`f[x_?NumericQ, y_?NumericQ] :=
      With[{t = N[\ at \(x\^2 - 2\ y + 2\ \ at \(2\ x\^2 - y\^2\)\)]},
        If[Head[t] === Complex, 1, t]]\)], "Input"],

Cell[TextData[{
  "To get an idea of the behavior, we make a plot for fixed ",
  Cell[BoxData[
      \(TraditionalForm\`y\)]],
  "."
}], "Text"],

Cell[BoxData[
    \(TraditionalForm\`\(Plot[f[x, 1.5], {x, \(-2\), 2},
        PlotPoints -> 100];\)\)], "Input"],

Cell[TextData[{
  "We see that the zero contour will be exceedingly sharp\[LongDash]and \
difficult for a non-adaptive plotting routine such as ",
  Cell[BoxData[
      FormBox[
        StyleBox[\(\(ContourPlot\)\(\ \)\),
          "Input"], TraditionalForm]]],
  " to find. Here we plot the 0.3 contour."
}], "Text"],

Cell[BoxData[
    \(TraditionalForm\`\(cp =
        ContourPlot[f[x, y], \ {x, \(-2\), 2}, {y, \(-1\), 3},
          PlotPoints -> 140, Contours -> {0.3}];\)\)], "Input"],

Cell["In this example, we can attempt direct solution", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`Solve[\ at \(x\^2 - 2\ y + 2\ \ at \(2\ x\^2 - y\^2\)\) ==

        0, y]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`{{y ->
          1\/4\ \((x\^2 - \ at \(16\ x\^2 - x\^4\))\)}, {y ->
          1\/4\ \((x\^2 + \ at \(16\ x\^2 - x\^4\))\)}}\)], "Output"]
}, Open  ]],

Cell[BoxData[
    FormBox[
      RowBox[{
        RowBox[{"pl", "=",
          RowBox[{"Plot", "[",
            RowBox[{
              RowBox[{"Evaluate", "[",
                FormBox[\(y /. %\),
                  "TraditionalForm"], "]"}], ",", \({x, \(-2\), 2}\),
              ",", \(PlotStyle -> Hue[1]\)}], "]"}]}], ";"}],
      TraditionalForm]], "Input"],

Cell[BoxData[
    \(TraditionalForm\`\(Show[cp, pl];\)\)], "Input"],

Cell[TextData[{
  "The agreement is quite good and you can show that the curves with ",
  Cell[BoxData[
      \(TraditionalForm\`y < 0\)]],
  " are spurious solutions."
}], "Text"]
}
]

Cheers,
    Paul
____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________




  • Prev by Date: Re: Compile problem: Mathematica 4
  • Next by Date: Re: Menu Control
  • Previous by thread: Re: implcit plot with undefined expression
  • Next by thread: Arbitrary Precision Arithmetic