feanor_math::pid

Trait EuclideanRing

Source 
pub trait EuclideanRing: PrincipalIdealRing {
    // Required methods
    fn euclidean_div_rem(
        &self,
        lhs: Self::Element,
        rhs: &Self::Element,
    ) -> (Self::Element, Self::Element);
    fn euclidean_deg(&self, val: &Self::Element) -> Option<usize>;

    // Provided methods
    fn euclidean_div(
        &self,
        lhs: Self::Element,
        rhs: &Self::Element,
    ) -> Self::Element { ... }
    fn euclidean_rem(
        &self,
        lhs: Self::Element,
        rhs: &Self::Element,
    ) -> Self::Element { ... }
}
Expand description

Trait for rings that support euclidean division.

In other words, there is a degree function d(.) returning nonnegative integers such that for every x, y with y != 0 there are q, r with x = qy + r and d(r) < d(y). Note that q, r do not have to be unique, and implementations are free to use any choice.

§Example

let ring = StaticRing::<i64>::RING;
let (q, r) = ring.euclidean_div_rem(14, &6);
assert_el_eq!(ring, 14, ring.add(ring.mul(q, 6), r));
assert!(ring.euclidean_deg(&r) < ring.euclidean_deg(&6));

Required Methods§

Source

fn euclidean_div_rem( &self, lhs: Self::Element, rhs: &Self::Element, ) -> (Self::Element, Self::Element)

Computes euclidean division with remainder.

In general, the euclidean division of lhs by rhs is a tuple (q, r) such that lhs = q * rhs + r, and r is “smaller” than “rhs”. The notion of smallness is given by the smallness of the euclidean degree function EuclideanRing::euclidean_deg().

Source

fn euclidean_deg(&self, val: &Self::Element) -> Option<usize>

Defines how “small” an element is. For details, see EuclideanRing.

Provided Methods§

Source

fn euclidean_div( &self, lhs: Self::Element, rhs: &Self::Element, ) -> Self::Element

Computes euclidean division without remainder.

In general, the euclidean division of lhs by rhs is a tuple (q, r) such that lhs = q * rhs + r, and r is “smaller” than “rhs”. The notion of smallness is given by the smallness of the euclidean degree function EuclideanRing::euclidean_deg().

Source

fn euclidean_rem( &self, lhs: Self::Element, rhs: &Self::Element, ) -> Self::Element

Computes only the remainder of euclidean division.

In general, the euclidean division of lhs by rhs is a tuple (q, r) such that lhs = q * rhs + r, and r is “smaller” than “rhs”. The notion of smallness is given by the smallness of the euclidean degree function EuclideanRing::euclidean_deg().

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.

Implementors§

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