Trait EuclideanDomain 

pub trait EuclideanDomain:
    Ring
    + Div<Output = Self>
    + Rem<Output = Self> {
    // Required methods
    fn div_rem(&self, other: &Self) -> (Self, Self);
    fn abs(&self) -> Self;

    // Provided method
    fn gcd(&self, other: &Self) -> Self { ... }
}

Euclidean domain: ring with division algorithm

A Euclidean domain is a ring where division with remainder is defined. Examples: integers Z, polynomials K[x] over field K, Gaussian integers Z[i]

Key property: For any a, b ≠ 0, exists q, r such that a = q*b + r where either r = 0 or deg(r) < deg(b)

Required Methods

fn div_rem(&self, other: &Self) -> (Self, Self)

Division with remainder: returns (quotient, remainder)

Example

let (q, r) = a.div_rem(&b);
assert_eq!(a, &(&q * &b) + &r);

fn abs(&self) -> Self

Absolute value (for content extraction and normalization)

Provided Methods

fn gcd(&self, other: &Self) -> Self

Greatest common divisor using Euclidean algorithm

Example

assert_eq!(gcd(12, 18), 6);

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl EuclideanDomain for i64

fn div_rem(&self, other: &Self) -> (Self, Self)

fn abs(&self) -> Self

impl EuclideanDomain for Ratio<i64>

fn div_rem(&self, other: &Self) -> (Self, Self)

fn abs(&self) -> Self

Implementors