Algebra Crate

A Rust library providing algebraic structures and operations, with a focus on modular arithmetic and abstract algebra concepts.

Features

• Modular Arithmetic: Create custom modular number types with the modular! macro
• Abstract Algebra: Implementations of fundamental algebraic structures:
  • Groups (both Abelian and Non-Abelian)
  • Rings
  • Fields

Usage

Modular Arithmetic

Create a new modular number type using the modular! macro:

modular!(Mod7, u32, 7);  // Creates a type for numbers modulo 7

let a = Mod7::new(3);
let b = Mod7::new(5);
let sum = a + b;  // 8 ≡ 1 (mod 7)

Algebraic Structures

The crate provides traits for various algebraic structures:

• Group: Basic group operations with identity and inverse
• AbelianGroup: Commutative groups with addition operations
• NonAbelianGroup: Non-commutative groups with multiplication operations
• Ring: Structures with both addition and multiplication
• Field: Rings with multiplicative inverses

Dependencies

• num: For numeric traits and operations

Examples

use algebra::{Group, Ring};

modular!(Mod7, u32, 7);

// Group operations
let a = Mod7::new(3);
let inverse = a.inverse();  // 4 (mod 7)
let identity = Mod7::identity();  // 0 (mod 7)

// Ring operations
let one = Mod7::one();  // 1 (mod 7)
let zero = Mod7::zero();  // 0 (mod 7)