Zeros

This repository contains code for computing images and animations of zeros of polynomials that were shown in my public talks:

• Ničle, TEDxUL, October 2014, see also the related blog post.
• Zeros, Sydney Mathematical Research Institute, August 13, 2024

Prerequisites

The code works on MacOS, but should also run on Linux. It relies on the following software:

• Python 3
• XCode C compiler, although gcc ought to work
• ImageMagick
• ffmpeg

XCode is part of Apple's ecosystem. There are many ways to obtain Python 3, just visit the web site. You can get the rest with the Homebrew package manager:

brew install imagemagick ffmpeg

You will additionally need the following Python libraries:

• pycairo
• pillow
• numpy

They can be install with the Python pip3 package manager:

pip3 install pycairo pillow numpy

To compile the C code, you need these libraries:

• libtiff
• GNU Scientific Library

They can be installed with Homebrew by running

brew install libtiff gsl

Programs

There are two programs:

1. zeros is a C program that computes zeros of polynomials with given coefficients and degrees, and generates grayscale TIFF, see the folder C
2. algebraic.py is a Python program that computes zeros of polynommials with given complexity (sum of absolute values of coefficients) and degrees, and generates PNG images, see the folder algebraic.