# Solving Polynomial Systems with phcpy

## TL;DR

This paper discusses recent developments in phcpy, a Python interface for PHCpack, enhancing its online accessibility, GPU support, and suitability for interactive exploration of polynomial systems in scientific applications.

## Contribution

It introduces new features in phcpy, including online availability, GPU parallelization, and improved usability for solving polynomial systems in STEM fields.

## Key findings

- phcpy is now accessible via JupyterHub with multiple kernels
- GPU support significantly speeds up large polynomial system solutions
- phcpy is effective for interactive exploration of polynomial systems

## Abstract

The solutions of a system of polynomials in several variables are often needed, e.g.: in the design of mechanical systems, and in phase-space analyses of nonlinear biological dynamics. Reliable, accurate, and comprehensive numerical solutions are available through PHCpack, a FOSS package for solving polynomial systems with homotopy continuation. This paper explores new developments in phcpy, a scripting interface for PHCpack, over the past five years. For instance, phcpy is now available online through a JupyterHub server featuring Python2, Python3, and SageMath kernels. As small systems are solved in real-time by phcpy, they are suitable for interactive exploration through the notebook interface. Meanwhile, phcpy supports GPU parallelization, improving the speed and quality of solutions to much larger polynomial systems. From various model design and analysis problems in STEM, certain classes of polynomial system frequently arise, to which phcpy is well-suited.