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ListPlot with multiple (related) series.

• To: mathgroup at smc.vnet.net
• Subject: [mg33420] ListPlot with multiple (related) series.
• From: crf3 at po.cwru.edu (Curt Fischer)
• Date: Thu, 21 Mar 2002 09:26:56 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Dear Group,

equations as a function of a parameter of the equations b.  Problem
is, there are multiple solution sets and my graph does not show which
x goes with which y at a given b.  How can I make such a graph?

Details:
In my problem, I have three equations in three unknowns x, y, and z. 
b is a parameter in these equations.  Using NSolve, I built a function
which takes b as a variable and returns the values of x, y, and z,
like this;

soln[b_]:=NSolve[{eqns},{x,y,z}]

This is all good.  My equations are rational, and NSolve returns at
most three solutions sets {x,y,z} for any given b.

Now, I want to plot x and y vs. b, on the same graph.  I want the
graph to show every solution set for each b.

I tried:

Show[{
      ListPlot[
        Flatten[
          Table[Table[{i, x/.soln[i][[n]]]}, {i,1,10,.2}],{n, 1, 3}],
1],
        PlotStyle -> {PointSize[ .02], RGBColor[1, 0, 0]}, 
        DisplayFunction -> Identity],
      ListPlot[
        Flatten[
          Table[Table[{i, y/.soln[i][[n]]]}, {i,1,10,.2}],{n, 1, 3}],
1],
        PlotStyle -> {PointSize[ .02], RGBColor[0, 1, 0]}, 
        DisplayFunction -> Identity]}, 
    DisplayFunction -> $DisplayFunction]

which worked and a output a graph. Problem is, since there are three
solutions, there are three distinct red (x) and three distinct green
(y) points for every b.  There is no way of knowing which x goes with
which y from this graph.

How can I make a graph which preserves this information?  It is not as
important to me to keep to color difference in x and y as it is to
distinguish solution 1 from solution 2 from solution 3...but is there
an easy way to do both in the same graph?

Thanks for your help.
--
Curt Fischer
crf3 at po.cwru.edu

• Follow-Ups:
  • Re: ListPlot with multiple (related) series.
    • From: Daniel Lichtblau <danl@wolfram.com>