lin_algebra 0.3.1

A linear algebra package to compute image, kernel and rank of linear applications.
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# lin_algebra
A Rust library for linear algebra.

## Features
All operations are currently implemented for matrices over GF(2):

- Compute the echelon form of a matrix along with the history of all the row operations applied.
- Compute the rank of the linear application represented by a matrix.
- Compute the kernel of the linear application represented by a matrix.
- Compute the image of the linear application represented by a matrix.
- Solve system of equations in GF(2).

## Installation

Add the dependency to your `Cargo.toml`:

```toml
[dependencies]
lin_algebra = "0.3.1"
```

## Usage
```Rust
use lin_algebra::gf2_matrix::GF2Matrix;
use lin_algebra::matrix::MatrixTrait;

fn main() {
    // Reduces echelon form

    let gf2_mat = gf2_matrix::GF2Matrix::new(
        vec![vec![1,0,0,0], vec![0,1,0,1], vec![0,1,0,1]]
    )
    let (educed_echelon_form, row_operations) = gf2_mat.echelon_form();

    println!("Reduces echelon form {:?}", educed_echelon_form);
    println!(
        "Row operation applied to reach the reduces echelon form {:?}", row_operations
    );

    // Kernel
    println!("Kenel {:?}", gf2_mat.kernel());

    // Image
    println!("Image {:?}", gf2_mat.image());

    // Rank
    println!("Rank {}", gf2_mat.rank());

    // Solve M x = b
    let b = vec![1,0,0,1]
    println!("x: {:?}", gf2_mat.solve(&b));

    // Solve A X = Y
    let y_matrix = gf2_matrix::GF2Matrix::new(
        vec![vec![1,0,0,1], vec![1,1,0,1], vec![0,1,0,1]]
    )
    println!("x: {:?}", gf2_mat.solve_matrix_system(&y_matrix));

}
```

## License
MIT

## Python bindings

Python bindings are provided in the separate project
[`gf2_lin_algebra`](https://github.com/LucaBonamino/gf2_lin_algebra).

They are intentionally limited to GF(2) and focus on performance and simplicity. The Rust crate `lin_algebra` is designed to be more general.

## Roadmap

This project is under active development, with a focus on both research and practical use.

Current and planned directions include:
- improving the internal design of GF(2) matrices
- adding optimized representations (e.g. bit-packed storage)
- generalizing the Rust core to support linear algebra over arbitrary fields

The Python bindings (`gf2_lin_algebra`) are intentionally limited to GF(2), while the Rust crate (`lin_algebra`) aims to be more general.

For a detailed list of planned improvements and areas where help is welcome, see [ROADMAP.md](ROADMAP.md).

## Contributing

Contributions are welcome!

Please see [CONTRIBUTING.md](CONTRIBUTING.md) for guidelines.