//! Abstraction of ring structure\

use core::ops::{Mul, Add};

use crate::group::AbelianGroup;

pub mod modring;

/// (R, add, mul) is a ring if
/// 
/// 1. (R, add) is an abelian group
/// 2. R is closed under multiplication
/// 3. multiplication in R is associative
/// 4. multiplication is distributed over addition
pub trait Ring: 
    Sized +
    AbelianGroup +        // 1
    Mul<Output = Self> +  // 2
    AssociativeMul +      // 3
    DistributiveMul       // 4 
{ }

/// # Safety
/// 
/// this trait is safe only when for all a, b, c: a * (b * c) = (a * b) * c
pub trait AssociativeMul: Sized + Mul<Output = Self> {}

/// # Safety
/// 
/// this trait is safe only when for all a, b, c: a * (b + c) = a * b + a * c
pub trait DistributiveMul: Sized + Mul<Output = Self> + Add<Output = Self> {}