Struct abstalg::QuotientRing

pub struct QuotientRing<R: EuclideanDomain> { /* fields omitted */ }

A quotient ring of an Euclidean domain by a principal ideal.

Implementations

impl<R: EuclideanDomain> QuotientRing<R>

pub fn new(base: R, modulo: R::Elem) -> Self

Creates a new quotient ring from the given Euclidean domain and one of its element.

pub fn base(&self) -> &R

Returns the base ring from which this ring was constructed.

pub fn modulo(&self) -> &R::Elem

Returns the modulo element from which this ring was constructed.

Trait Implementations

impl<R: Clone + EuclideanDomain> Clone for QuotientRing<R> where
    R::Elem: Clone,
    R::Elem: Clone, 

fn clone(&self) -> QuotientRing<R>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<R: Debug + EuclideanDomain> Debug for QuotientRing<R> where
    R::Elem: Debug,
    R::Elem: Debug, 

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<R: Default + EuclideanDomain> Default for QuotientRing<R> where
    R::Elem: Default,
    R::Elem: Default, 

fn default() -> QuotientRing<R>

Returns the "default value" for a type.

impl<R: EuclideanDomain> Domain for QuotientRing<R>

type Elem = R::Elem

The type of the elements of this domain.

fn contains(&self, elem: &Self::Elem) -> bool

Checks if the given element is a member of the domain. Not all possible objects need to be elements of the set.

impl<R: EuclideanDomain> UnitaryRing for QuotientRing<R>

fn zero(&self) -> Self::Elem

The additive identity element of the ring.

fn neg(&self, elem: &Self::Elem) -> Self::Elem

The additive inverse of the given element.

fn add(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem

The additive sum of the given elements

fn one(&self) -> Self::Elem

The multiplicative identity element of the ring.

fn mul(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem

The multiplicative product of the given elements.

fn is_zero(&self, elem: &Self::Elem) -> bool

Checks if the given element is the additive identity of the ring.

fn sub(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem

The difference of the given elements.

fn is_one(&self, elem: &Self::Elem) -> bool

Checks if the given element is the multiplicative identity of the ring.