       Re: Eliminate Complex Roots

• To: mathgroup at smc.vnet.net
• Subject: [mg64407] Re: Eliminate Complex Roots
• From: bghiggins at ucdavis.edu
• Date: Thu, 16 Feb 2006 03:05:14 -0500 (EST)
• References: <200602130815.DAA12562@smc.vnet.net><dsru2d\$5bv\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Pratik and Bob

Thanks much for the suggestion of using FindInstance and Reduce.

Pratik, your code only finds 1 root but a simple modification allows
one to plot(usingListPlot) all three real roots:

data = ListPlot[Partition[Flatten[N[Table[Flatten[{
b, a /. FindInstance[a^3 + 10*a^2 - 15*a + b ==
0, a, Reals,3]}], {b, -20, 30, .5}]] /. {x_, y1_, y2_,  y3_} -> {{x,
y1}, {x, y2}, {x, y3}}], 2]]

Downside with the above approach is that you cannot use
PlotJoined->True. Of course, a work around is to separate out the
individual roots and use MultipleListPlot or Show with multiple
ListPlot

Still would like to be able to do this using Plot, and thereby make use
of Plots automatic gridding capabilities...

Looking at Bob's suggestion, it seems I am still stuck with knowing
which root to extract out for Plotting. I can in a pinch manipulate the
solution from Reduce and use ListPlot as done above.

Another approach that seems to work well is to use ImplicitPlot making
use of its built in ContourPlot routine. For systems of equations, I
also need to use Eliminate to get a single implicit equation with two
unknowns and it seems to work well, but may not be general enough for
the kinds of problems I am interested in, viz, plotting multiple steady
states of dynamical systems as a function of a parameter.

Brian

> Perhaps using FindInstance? Here is my attempt anyway
>
> Clear[a,b]
> ListPlot[Flatten[a/.Table[FindInstance[a^3 + 10*a^2 - 15*a + b ==
> 0,a,Reals],{b,-10,30}]//N],PlotJoined->True,PlotRange->All]

```

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