Re: Finding many complex roots
- To: mathgroup at smc.vnet.net
- Subject: [mg37797] Re: Finding many complex roots
- From: bghiggins at ucdavis.edu (Brian Higgins)
- Date: Wed, 13 Nov 2002 01:11:23 -0500 (EST)
- References: <aqo0mp$fql$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Marco, I would suggest you look at Stan Wagon's book "Mathematica in Action" . On page 289 he shows how to use ContourPlot to find roots of two functions f(x,y)=0, and g(x,y)=0. In case you do not have the book here is the essence of his approach: Suppose I want to find the complex roots of Sin[x]+x=0. eqn = Sin[x] + x; s1 = ComplexExpand[TrigToExp[eqn /. x -> u + I v]] f[u_, v_] = First[Cases[s1, Times[Complex[0, 1], x__] -> x, \[Infinity]]]; g[u_, v_] = DeleteCases[s1, Times[Complex[0, 1], x__], \[Infinity]]; The complex roots are then the solutions to f[u,v]=0,g[u,v]=0. These roots can be visualized as the intersections when the two level curves are superimposed using ContourPlot Show[Map[ContourPlot[Evaluate[#[x, y]], {x, -10, 10}, {y, -10, 10}, Contours -> {0}, ContourShading -> False, PlotPoints -> 80] &, {f, g}]] In his book, Stan Wagon goes further to show how one can write a small code to extract the numerical data from the ContourPlot . Cheers, Brian "Marco" <caiazzo at ieee.org> wrote in message news:<aqo0mp$fql$1 at smc.vnet.net>... > Hi, > I have to find many complex roots of complex function like > f[z]=0 where z is complex. > I try first the graphical approch: > ImplicitPlot[{Re[f[a+ Ib]]==0,Im[f[a+I b]]==0},{a,amin,amax},{b,bmin,bmax}] > or somethink else, and it works good and I visualize the solution in the > specificated region. > Now I'd like to compute the finding automaticaly. > I' seen other posts which illustrates how find many roots of real function > of real varible but I'm unable to genaralize in 2D case. > Some one can help me? > > P.S. sorry for my english > > Thanks x1000