pycontinuum 0.1.1

A pure Python library for polynomial homotopy continuation methods

PyContinuum

A pure Python library for polynomial homotopy continuation methods.

Overview

PyContinuum is a modern, pip-installable, user-friendly Python library for solving polynomial systems using numerical homotopy continuation methods. It provides a clean, Pythonic interface for computing all solutions to systems of polynomial equations without requiring external compiled binaries.

Key Features (planned):

• Clean Python API: Define polynomials and solve systems with an intuitive interface
• Core Homotopy Methods: Robust implementation of predictor-corrector path tracking
• Start System Generation: Automated total-degree homotopy and custom start systems
• Solution Processing: Classification, refinement, and filtering of solutions
• Visualization: Tools to visualize path tracking and solution sets
• No External Dependencies: Pure Python implementation with optional accelerators
• Educational: Clear documentation and examples for teaching and learning

Quick Example

from pycontinuum import polyvar, PolynomialSystem, solve

# Define variables
x, y = polyvar('x', 'y')

# Define polynomial system
f1 = x**2 + y**2 - 1      # circle
f2 = x**2 - y             # parabola
system = PolynomialSystem([f1, f2])

# Solve the system
solutions = solve(system)

# Display solutions
print(solutions)

Installation

pip install pycontinuum
pip install pycontinuum[viz]
pip install pycontinuum[monodromy]

Publishing (maintainers)

python -m pip install --upgrade pip build twine
python -m build
python -m twine check dist/*
# TestPyPI
setx TWINE_USERNAME __token__
setx TWINE_PASSWORD pypi-XXXXX
python -m twine upload --repository testpypi dist/*
# PyPI
python -m twine upload dist/*

Status

This project is under active development. Current focus is on implementing the core functionality for the v1.0 release.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

PyContinuum draws inspiration from existing software in numerical algebraic geometry, including:

• PHCpack and phcpy
• Bertini and PyBertini
• HomotopyContinuation.jl