Crate cova_algebra 

A Rust library for abstract algebra.

This crate provides implementations of various 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
  • Modules
  • Vector Spaces

Examples

Modular Arithmetic

use cova_algebra::{algebras::boolean::Boolean, modular, rings::Field};

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

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

Vector Spaces

use cova_algebra::{algebras::boolean::Boolean, rings::Field, tensors::fixed::FixedVector};

let v1 = FixedVector::<3, f64>([1.0, 2.0, 3.0]);
let v2 = FixedVector::<3, f64>([4.0, 5.0, 6.0]);
let sum = v1 + v2;

Re-exports

pub use crate::arithmetic::Additive;

pub use crate::arithmetic::Multiplicative;

Modules

algebras

Implementation of an Algebra interface and various algebras

arithmetic

Basic arithmetic traits and operations.

category

Category Theory Primitives

groups

Group theory abstractions and implementations.

modules

Module theory abstractions and implementations.

prelude

Prelude Module

rings

Ring theory abstractions and implementations.

tensors

Tensors Module

Macros

impl_mul_scalar_clifford

A macro that implements scalar multiplication for Clifford algebra elements.

modular

A macro for creating custom modular number types.

prime_field

A macro for creating prime field types.

Traits

Add

The addition operator +.

AddAssign

The addition assignment operator +=.

Div

The division operator /.

DivAssign

The division assignment operator /=.

Mul

The multiplication operator *.

MulAssign

The multiplication assignment operator *=.

Neg

The unary negation operator -.

One

Defines a multiplicative identity element for Self.

Sub

The subtraction operator -.

SubAssign

The subtraction assignment operator -=.

Zero

Defines an additive identity element for Self.