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/