supertropicalpy 0.1.2

A Python package for supertropical algebra with tangible and ghost elements

SupertropicalPy

A comprehensive Python package for supertropical algebra, featuring tangible and ghost elements, matrix operations, and linear system solving using Cramer's rule.

🚀 Try it now! Click the "Open in Colab" badge above to run the interactive tutorial instantly in your browser - fast and free! No installation needed.

✨ Features

• 🎯 Tangible & Ghost Elements: Full support for both element types with automatic conversion

• 🧮 Supertropical Operations: Addition $\oplus$ defined by $a\oplus b=\max{a,b}$ (with ghost rules), and multiplication $\odot$ defined by $a\odot b=a+b$.

• 📐 Matrix Operations: Matrix multiplication, permanent (supertropical determinant), adjoint.

• 🔧 Linear System Solver: Cramer's rule implementation for solving $Ax = b$

• 🚀 NumPy Integration: Efficient computations using NumPy arrays

• 📚 Comprehensive Documentation: Full API reference, theory guide, and interactive tutorials

• ✅ Type Safety: Automatic type coercion and validation

📦 Installation

pip install supertropicalpy

Or install from source:

git clone https://github.com/TetewHeroez/supertropicalpy.git

cd supertropicalpy

pip install -e .

📖 Documentation

• Full documentation is available at: GitHub Pages

• Theory Guide: Mathematical background on supertropical algebra

• Interactive Tutorial: Jupyter notebook with executable examples

• API Reference: Complete API documentation

🧪 Running Tests

# Install dev dependencies
pip install -e ".[dev]"

# Run tests
pytest

Run with coverage

pytest --cov=supertropical

📚 Building Documentation Locally

# Install docs dependencies
pip install -e ".[docs]"

# Build HTML docs
cd docs
sphinx-build -b html source build
pytest --cov=supertropical

📚 Building Documentation Locally

# Install docs dependencies

pip install -e ".[docs]"

# Build HTML docs

cd docs

sphinx-build -b html source build

# Or use make (on Unix/Mac/Windows with make installed)
cd docs

make html

🎓 Mathematical Background

Supertropical algebra extends tropical algebra with ghost elements:

Operations:

• Addition: $a \oplus b = \max(a, b)$ with special ghost rules

• Multiplication: $a \odot b = a + b$ (classical addition)

Elements:

• Tangible: Regular elements (e.g., $5.0$)

• Ghost: Elements marked with $\nu$ (e.g., $5.0\nu$)

• Zero: $-\infty$ (additive identity)

• One: $0$ (multiplicative identity)

Key Properties:

• Matrix permanent replaces determinant

• Cramer's rule works for nonsingular matrices (permanent is tangible)

• Applications in optimization, algebraic geometry, and phylogenetics

🤝 Contributing

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

1. Fork the repository
2. Create your feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

📄 License

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

👥 Authors

• Supertropical Team

🙏 Acknowledgments

• Based on research by Izhakian, Z., & Rowen, L. on supertropical algebra

📞 Contact

• GitHub: https://github.com/TetewHeroez/supertropicalpy

• Issues: https://github.com/TetewHeroez/supertropicalpy/issues

• Documentation: https://tetewhereoez.github.io/supertropicalpy