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use crate::{Domain, EuclideanDomain, UnitaryRing};
#[derive(Clone, Debug, Default)]
pub struct QuotientRing<R: EuclideanDomain> {
base: R,
modulo: R::Elem,
one: R::Elem,
}
impl<R: EuclideanDomain> QuotientRing<R> {
pub fn new(base: R, modulo: R::Elem) -> Self {
assert!(base.contains(&modulo));
let one = base.quo(&base.one(), &modulo);
QuotientRing { base, modulo, one }
}
pub fn base(&self) -> &R {
&self.base
}
pub fn modulo(&self) -> &R::Elem {
&self.modulo
}
}
impl<R: EuclideanDomain> Domain for QuotientRing<R> {
type Elem = R::Elem;
fn contains(&self, elem: &Self::Elem) -> bool {
self.base.is_reduced(elem, &self.modulo)
}
}
impl<R: EuclideanDomain> UnitaryRing for QuotientRing<R> {
fn zero(&self) -> Self::Elem {
self.base.zero()
}
fn neg(&self, elem: &Self::Elem) -> Self::Elem {
self.base.rem(&self.base.neg(elem), &self.modulo)
}
fn add(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem {
self.base.rem(&self.base.add(elem1, elem2), &self.modulo)
}
fn one(&self) -> Self::Elem {
self.one.clone()
}
fn mul(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem {
self.base.rem(&self.base.mul(elem1, elem2), &self.modulo)
}
}