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MathGroup Archive 2004

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plotting groups of polynomial roots

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51247] plotting groups of polynomial roots
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Sun, 10 Oct 2004 01:57:18 -0400 (EDT)
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

If you take the first and last term away from a binomial polynomial and 
set the result equal to zero,
you get a number of strange roots.
This method allows you to plot such roots.
I didn't know it would work when I wrote it up,
but I plan to use it in the future
on some other polynomial root structures.

(* root group where x^q+1=(x+1)^q: binomial expansion without x^q and 1*)
digits=21
s[q_]=Sum[(q!/((q-k)!*k!))*x^(q-k),{k,1,q-1}]
ExpandAll[s[2]]
ExpandAll[s[3]]
a=Flatten[Table[x/. NSolve[s[n]==0,x],{n,2,digits}]];
a0=Floor[Abs[a]]
Dimensions[a][[1]]
b=Table[{Re[a[[n]]],Im[a[[n]]]},{n,1,Dimensions[a][[1]]}];
ListPlot[b,PlotRange->All]
Respectfully, Roger L. Bagula

tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
URL :  http://home.earthlink.net/~tftn
URL :  http://victorian.fortunecity.com/carmelita/435/ 


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