gf2_lin_algebra

Python package for linear algebra operations in GF(2)

gf2_lin_algebra is a high-performance Python library for doing linear algebra over the finite field GF(2) (binary matrices and vectors).
The implementation is written in Rust for speed and safety, and exposed to Python using PyO3.

This package is useful for:

• cryptography research
• boolean matrix algebra
• solving linear system of equations over over GF(2)
• teaching and exploration of finite fields

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Features

• Native Rust backend (fast, safe, no dependencies)
• Matrix and vector representation over GF(2)
• Rank, image, kernel, row-reduction, solving linear system of equations
• Pythonic API (GF2Matrix)
• Designed to be simple and educational
• Actively developed and open source

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Installation

pip install gf2-lin-algebra

or clone the repo and install locally:

git clone https://github.com/LucaBonamino/gf2_lin_algebra.git
cd lin_algebra_py
pip install .

Quick Example

from gf2_lin_algebra import GF2Matrix

# Create matrix
mat = GF2Matrixx([
    [1,0,1],
    [0,1,1],
    [1,1,0]
    ])

# Check shape
print(mat.shape())     # -> (3, 3)

# Compute rank
print(mat.rank())      # -> 3

# Compute kernel
print(mat.kernel())

# Compute image
print(mat.image())

# Solve system of equations
print(mat.solve([1,1,0]))

# Solve matrix sytem of equation
mat_y = GF2Matrixx([
    [0,1,1],
    [1,1,0],
    [0,0,1]
    ])
print(mat.solve_matrix_system(mat_y))

Roadmap

This package focuses on providing a clean, user-friendly Python API for linear algebra over GF(2).

While performance is important, gf2_lin_algebra intentionally keeps a clear and debuggable implementation, suitable for learning, research, and experimentation.

Planned directions include:

• improving performance while preserving a readable, educational code path
• exposing optimized operations implemented in the Rust crate lin_algebra
• refining the Python API for clarity and consistency
• adding examples, documentation, and tests

Most low-level optimizations and algorithmic improvements are developed in the Rust backend. This package focuses primarily on usability and ergonomics for Python users.

For a more detailed list of ideas and areas where help is welcome, see ROADMAP.md.

Contributing

Contributions are welcome! Please see CONTRIBUTING.md for guidelines.