Find complex zeros of a function

This package uses a discretised version of the argument principle to find regions containing zeros of a function.

Installing the package

using Pkg
Pkg.add("FindComplexZeros")

Using the package

using FindComplexZeros

findZerosWithSubdivision

Find zeros of a function within a given rectangular domain.

Each line of result contains the upper left, lower right corner of the rectangular box that contains the zero

An example:

function an_exp_sum(x)
    return (2+im)*exp((1+im)*x) + (3.5+im)*exp(x) + -im + (2 + 3im)*exp(-x) + (5 - im)*exp((-1+im)*x)
end

findZerosWithSubdivision(-10.2 + 10.22im, 10.1 - 10.1im, an_exp_sum)

countZeros

Count zeros of a function in a given rectangular domain

An example:

countZeros(-5 + 5im, 5 - 5im, x -> (x - 2)^3*(x-1))

Documentation

Further documentation can be accessed at the REPL or in IJulia by typing ? followed by the name of the function.

?findZerosWithSubdivision
?countZeros

ComplexPortraits.jl Phase portraits for complex functions (helpful for visualising where the zeros are)

This project is part of Wang Yanhua's final year capstone project at Yale-NUS College, Asymptotic Locus of Zeros of Exponential Sums. If you have any questions, drop a message to yanhua [at] u.yale-nus.edu.sg.