Origins of the PyZEAL Project

This is the documentation of the PyZEAL numerics project. It deals with the calculation of zeros of holomorphic functions. Within this project we aspire to port much of the functionality of the original ZEAL (ZEros of AnaLytic functions [KVanBarelR+00]) Fortran90 package (and namesake for this project) to Python while both adding some convenience features as well as leveraging more recent algorithms and technologies.

PyZEAL originated as part of the PyZeta project which provides facilities for the calculation of dynamical zeta functions. These in turn allow one to determine dynamical invariants called Ruelle resonances as their zeros (see the image below). Dynamical determinants being examples for rather complicated holomorphic functions therefore set the context for the independent investigation and implementation of root finding algorithms for this class of functions in the form of the present project.

The following is an example of resonances for a dynamical system called a Schottky surface. Plots such as this (and significantly more complex numerical experiments) are straightforward to calculating by combining basic features of PyZEAL and PyZeta:

If you want to get off the ground with using PyZEAL in your own project as fast as possible then Getting Started is a good place to get started. For a softer introduction and additional information on the philosophy and aims of this project check out Welcome to PyZEAL!. For details on the theoretical background and a list of references relevant to PyZEAL visit Theoretical Background.