Struct ZnReductionMap 

pub struct ZnReductionMap<R, S>
where
    R: RingStore,
    R::Type: ZnRing,
    S: RingStore,
    S::Type: ZnRing,
{ /* private fields */ }

The homomorphism Z/nZ -> Z/mZ that exists whenever m | n. In addition to the map, this also provides a function ZnReductionMap::smallest_lift() that computes the “smallest” preimage under the map, and a function ZnReductionMap::mul_quotient_fraction(), that computes the multiplication with n/m while also changing from Z/mZ to Z/nZ. This is very useful in many number theoretic applications, where one often has to switch between Z/nZ and Z/mZ.

Furthermore, many implementations of ZnRing currently do not support CanHomFrom-homomorphisms when the moduli are different (but divide each other).

Implementations

impl<R, S> ZnReductionMap<R, S>

where R: RingStore, R::Type: ZnRing, S: RingStore, S::Type: ZnRing,

pub fn new(from: R, to: S) -> Option<Self>

pub fn mul_quotient_fraction(&self, x: El<S>) -> El<R>

Computes the additive group homomorphism Z/mZ -> Z/nZ, x -> (n/m)x.

Example

let Z5 = Zn::new(5);
let Z25 = Zn::new(25);
let f = ZnReductionMap::new(&Z25, &Z5).unwrap();
assert_el_eq!(Z25, Z25.int_hom().map(15), f.mul_quotient_fraction(Z5.int_hom().map(3)));

pub fn smallest_lift(&self, x: El<S>) -> El<R>

Computes the smallest preimage under the reduction map Z/nZ -> Z/mZ, where “smallest” refers to the element that has the smallest lift to Z.

Example

let Z5 = Zn::new(5);
let Z25 = Zn::new(25);
let f = ZnReductionMap::new(&Z25, &Z5).unwrap();
assert_el_eq!(Z25, Z25.int_hom().map(-2), f.smallest_lift(Z5.int_hom().map(3)));

pub fn any_preimage(&self, x: El<S>) -> El<R>

pub fn smallest_lift_ref(&self, x: &El<S>) -> El<R>

Trait Implementations

impl<R, S> Homomorphism<<R as RingStore>::Type, <S as RingStore>::Type> for ZnReductionMap<R, S>

where R: RingStore, R::Type: ZnRing, S: RingStore, S::Type: ZnRing,

type CodomainStore = S

The type of the RingStore used by this object to store the codomain ring.

type DomainStore = R

The type of the RingStore used by this object to store the domain ring.

fn map(&self, x: El<R>) -> El<S>

Applies this homomorphism to the given element from the domain ring, resulting in an element in the codomain ring.

fn codomain<'a>(&'a self) -> &'a Self::CodomainStore

Returns a reference to the codomain ring.

fn domain<'a>(&'a self) -> &'a Self::DomainStore

Returns a reference to the domain ring.

fn map_ref(&self, x: &Domain::Element) -> Codomain::Element

Applies this homomorphism to the given element from the domain ring, resulting in an element in the codomain ring.

fn mul_assign_map(&self, lhs: &mut Codomain::Element, rhs: Domain::Element)

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring.

fn mul_assign_ref_map(&self, lhs: &mut Codomain::Element, rhs: &Domain::Element)

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring.

fn mul_map( &self, lhs: Codomain::Element, rhs: Domain::Element, ) -> Codomain::Element

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring.

fn fma_map( &self, lhs: &Codomain::Element, rhs: &Domain::Element, summand: Codomain::Element, ) -> Codomain::Element

Fused-multiply-add. This computes lhs * rhs + summand, where rhs is mapped into the ring via this homomorphism.

fn mul_ref_fst_map( &self, lhs: &Codomain::Element, rhs: Domain::Element, ) -> Codomain::Element

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring.

fn mul_ref_snd_map( &self, lhs: Codomain::Element, rhs: &Domain::Element, ) -> Codomain::Element

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring.

fn mul_ref_map( &self, lhs: &Codomain::Element, rhs: &Domain::Element, ) -> Codomain::Element

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring.

fn compose<F, PrevDomain: ?Sized + RingBase>( self, prev: F, ) -> ComposedHom<PrevDomain, Domain, Codomain, F, Self>

where Self: Sized, F: Homomorphism<PrevDomain, Domain>,

Constructs the homomorphism x -> self.map(prev.map(x)).

fn mul_assign_ref_map_through_hom<First: ?Sized + RingBase, H: Homomorphism<First, Domain>>( &self, lhs: &mut Codomain::Element, rhs: &First::Element, hom: H, )

Multiplies the given element in the codomain ring with an element obtained by applying this and another homomorphism to a given element from another ring.

fn mul_assign_map_through_hom<First: ?Sized + RingBase, H: Homomorphism<First, Domain>>( &self, lhs: &mut Codomain::Element, rhs: First::Element, hom: H, )

Multiplies the given element in the codomain ring with an element obtained by applying this and another homomorphism to a given element from another ring.