       Re: Help !! plot roots of an expression

• To: mathgroup at smc.vnet.net
• Subject: [mg72428] Re: [mg72349] Help !! plot roots of an expression
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 27 Dec 2006 06:11:18 -0500 (EST)

```poly=(w-w1) (w + 2  q +en^2 +  s w^3) + r;

Collect[poly,w]

s*w^4 - s*w1*w^3 + w^2 + (en^2 + 2*q - w1)*w + r - en^2*w1 - 2*q*w1

soln=Transpose[{Re[w],Im[w]}/.
{Reduce[poly==0/.{s->2,w1->1,en->5,r->3/2},w]//ToRules}];

Plot[#,{q,-22.5,0},
PlotStyle->{
{AbsoluteThickness,AbsoluteDashing[{3,10}],Red},
{AbsoluteDashing[{10,10}],Blue},
{AbsoluteThickness,AbsoluteDashing[{3,10}],Green},
{AbsoluteDashing[{10,10}],Orange}},
Frame->True,Axes->False,
PlotRange->{{-22.6,0.1},Automatic},
ImageSize->400]&/@
soln;

List@@(First/@Reduce[poly==0/.
{s->2,w1->1,en->5,r->3/2},w,Reals])//N

{q<-17.778,q==-17.778,q==-11.7695,q>-11.7695}

Bob Hanlon

---- mintoo <varun.tangri at gmail.com> wrote:
> I have a polynomial. A simple example is like this
>
> (w-w1) (w + 2  q +en^2 +  s w^3) + r
> The actual example is more complicated.  It is a function of several
> variables e.g. q, en, s, r etc..
> I also need to Collect & FullSimplify this expression.
> Finally, from that result, I want to plot the roots of this polynomial
> (imaginary & real part) vs. q (say) or vs en etc.. other variables can
> be given fixed values.
>
> I'll the thankful if you give me hints how to do this!!
>

```

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