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MathGroup Archive 2003

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Re: Complex root finding

  • To: mathgroup at
  • Subject: [mg39238] Re: [mg39233] Complex root finding
  • From: Daniel Lichtblau <danl at>
  • Date: Wed, 5 Feb 2003 00:11:13 -0500 (EST)
  • References: <>
  • Sender: owner-wri-mathgroup at

Alan Lewis wrote:
> I have a complex-valued function f(z).
> If z = x + I y, suppose f(z) has a finite number of simple zeros
> in the rectangle   a < x < b,  c < y < d. (and no poles).
> I can start FindRoot somewhere and it will likely find a root.
> But, my question is:
> is there a (best?) systematic way to use Mathematica to find
> all the roots in the region?

A method using the Cauchy integral formula for finding roots on a
segment may be found at

It is not hard to modify this technique to work with a rectangle.

Daniel Lichtblau
Wolfram Research

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