Struct Inclusion 

pub struct Inclusion<R>
where
    R: RingStore,
    R::Type: RingExtension,
{ /* private fields */ }

The ring homomorphism induced by a RingExtension.

Example

let base = StaticRing::<i32>::RING;
let extension = dense_poly::DensePolyRing::new(base, "X");
let hom = extension.inclusion();
let f = extension.add(hom.map(8), extension.indeterminate());
assert_el_eq!(extension, extension.from_terms([(8, 0), (1, 1)].into_iter()), &f);

Implementations

impl<R> Inclusion<R>

where R: RingStore, R::Type: RingExtension,

pub fn new(ring: R) -> Self

Returns the Inclusion from the base ring of the given ring to itself.

Trait Implementations

impl<R> Clone for Inclusion<R>

where R: RingStore + Clone, R::Type: RingExtension,

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<R> Debug for Inclusion<R>

where R: RingStore + Debug, R::Type: RingExtension,

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

Formats the value using the given formatter.

impl<R> Homomorphism<<<<R as RingStore>::Type as RingExtension>::BaseRing as RingStore>::Type, <R as RingStore>::Type> for Inclusion<R>

where R: RingStore, R::Type: RingExtension,

type CodomainStore = R

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

type DomainStore = <<R as RingStore>::Type as RingExtension>::BaseRing

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

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

Returns a reference to the domain ring.

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

Returns a reference to the codomain ring.

fn map(&self, x: El<<R::Type as RingExtension>::BaseRing>) -> El<R>

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

fn map_ref(&self, x: &El<<R::Type as RingExtension>::BaseRing>) -> El<R>

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

fn mul_assign_ref_map( &self, lhs: &mut El<R>, rhs: &El<<R::Type as RingExtension>::BaseRing>, )

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_map( &self, lhs: &mut El<R>, rhs: El<<R::Type as RingExtension>::BaseRing>, )

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_map_through_hom<First: ?Sized + RingBase, H: Homomorphism<First, <<R::Type as RingExtension>::BaseRing as RingStore>::Type>>( &self, lhs: &mut El<R>, 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_ref_map_through_hom<First: ?Sized + RingBase, H: Homomorphism<First, <<R::Type as RingExtension>::BaseRing as RingStore>::Type>>( &self, lhs: &mut El<R>, 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 fma_map( &self, lhs: &El<R>, rhs: &El<<R::Type as RingExtension>::BaseRing>, summand: El<R>, ) -> El<R>

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

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 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)).

impl<R> Copy for Inclusion<R>

where R: Copy + RingStore, El<R>: Copy, R::Type: RingExtension,