cova_algebra/
lib.rs

1//! A Rust library for abstract algebra.
2//!
3//! This crate provides implementations of various algebraic structures and operations,
4//! with a focus on modular arithmetic and abstract algebra concepts.
5//!
6//! # Features
7//!
8//! - **Modular Arithmetic**: Create custom modular number types with the `modular!` macro
9//! - **Abstract Algebra**: Implementations of fundamental algebraic structures:
10//!   - Groups (both Abelian and Non-Abelian)
11//!   - Rings
12//!   - Fields
13//!   - Modules
14//!   - Vector Spaces
15//!
16//! # Examples
17//!
18//! ## Modular Arithmetic
19//!
20//! ```
21//! use cova_algebra::{algebras::boolean::Boolean, modular, rings::Field};
22//!
23//! // Create a type for numbers modulo 7
24//! modular!(Mod7, u32, 7);
25//!
26//! let a = Mod7::new(3);
27//! let b = Mod7::new(5);
28//! let sum = a + b; // 8 ≡ 1 (mod 7)
29//! ```
30//!
31//! ## Vector Spaces
32//!
33//! ```
34//! use cova_algebra::{algebras::boolean::Boolean, rings::Field, tensors::fixed::FixedVector};
35//!
36//! let v1 = FixedVector::<3, f64>([1.0, 2.0, 3.0]);
37//! let v2 = FixedVector::<3, f64>([4.0, 5.0, 6.0]);
38//! let sum = v1 + v2;
39//! ```
40
41#![warn(missing_docs)]
42#![allow(incomplete_features)]
43#![feature(generic_const_exprs)]
44
45pub mod algebras;
46pub mod arithmetic;
47pub mod category;
48pub mod groups;
49pub mod modules;
50pub mod rings;
51pub mod tensors;
52
53pub use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
54
55pub use num_traits::{One, Zero};
56
57pub use crate::arithmetic::{Additive, Multiplicative};
58
59pub mod prelude {
60  //! # Prelude Module
61  //!
62  //! This module re-exports the most commonly used types, traits, and operations from the
63  //! algebra crate for convenient importing.
64  //!
65  //! ## Purpose
66  //!
67  //! The prelude pattern allows users to import multiple commonly used items with a single
68  //! import statement, reducing boilerplate and improving code readability.
69  //!
70  //! ## Contents
71  //!
72  //! The prelude includes:
73  //!
74  //! - Core algebraic structures: [`Algebra`], [`Group`], [`Ring`], [`Field`], [`VectorSpace`]
75  //! - Behavioral traits: [`Additive`], [`Multiplicative`]
76  //! - Group variants: [`AbelianGroup`], [`NonAbelianGroup`]
77  //! - Module types: [`LeftModule`], [`RightModule`], [`TwoSidedModule`]
78  //! - Semimodule types: [`LeftSemimodule`], [`RightSemimodule`], [`TwoSidedSemimodule`]
79  //! - Fundamental operators: [`Add`], [`Mul`], [`Sub`], [`Div`] and their assignment variants
80  //! - Identity concepts: [`Zero`], [`One`], [`Neg`]
81  //!
82  //! ## Usage
83  //!
84  //! ```
85  //! // Import everything from the prelude
86  //! use cova_algebra::prelude::*;
87  //! ```
88
89  pub use crate::{
90    algebras::Algebra,
91    arithmetic::{Additive, Multiplicative},
92    category::Category,
93    groups::{AbelianGroup, Group, NonAbelianGroup},
94    modules::{
95      LeftModule, LeftSemimodule, RightModule, RightSemimodule, TwoSidedModule, TwoSidedSemimodule,
96      VectorSpace,
97    },
98    rings::{Field, Ring},
99    Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, One, Sub, SubAssign, Zero,
100  };
101}
102
103#[cfg(test)]
104mod fixtures {
105  use crate::{modular, prime_field};
106
107  modular!(Mod7, u32, 7);
108  prime_field!(Mod7);
109}
cova_algebra/lib.rs

cova_algebra/
lib.rs
