skzeros is a Python package for finding the all the roots of a holomorphic function in a given region of the complex plane. It is based on subdivision using the argument principle combined with AAA rational approximation of the logarithm derivative.

You can install skzeros using pip:

pip install skzeros

import numpy as np
import skzeros

A = -0.19435
B = 1000.41
C = 522463
T = 0.005


def f(z):
    return z**2 + A * z + B * np.exp(-T * z) + C


def f_z(z):
    return 2 * z + A - T * B * np.exp(-T * z)


r = skzeros.Rectangle(complex(-2500, -15000), complex(10, 15000))
res = skzeros.find_zeros(r, f, f_z, max_arg_principle=7)

For a description of the algorithm please see https://arxiv.org/pdf/2509.15936. For code to reproduce all results in the paper please see the paper directory.

• cxroots
• POLZE