Struct PadicIntegralEmbedding 

pub struct PadicIntegralEmbedding { /* private fields */ }

Canonical fixed-cap embedding Z_p -> Q_p and checked integral retraction.

Implementations

impl PadicIntegralEmbedding

pub fn new(target: PadicField) -> Self

Construct the canonical embedding attached to a fixed-cap field.

pub fn source(&self) -> &PadicRing

Integral source context.

pub fn target(&self) -> &PadicField

Fraction-field target context.

pub fn apply( &self, value: &PadicElement, ) -> Result<PadicElement, PadicEmbeddingError>

Embed an integral value after checking its exact source context.

pub fn retract( &self, value: &PadicElement, ) -> Result<PadicElement, PadicEmbeddingError>

Retract a field value after certifying nonnegative valuation.

pub fn retract_polynomial( &self, value: &Polynomial<PadicField>, ) -> Result<Polynomial<PadicRing>, CoefficientMappingError>

Retract every coefficient of a polynomial after certifying integrality.

pub fn retract_power_series( &self, value: &PowerSeries<PadicField>, ) -> Result<PowerSeries<PadicRing>, CoefficientMappingError>

Retract every retained series coefficient after certifying integrality.

pub fn retract_vector( &self, value: &Vector<PadicField>, ) -> Result<Vector<PadicRing>, CoefficientMappingError>

Retract every vector coefficient after certifying integrality.

pub fn retract_matrix( &self, value: &Matrix<PadicField>, ) -> Result<Matrix<PadicRing>, CoefficientMappingError>

Retract every matrix coefficient after certifying integrality.

pub fn verify(&self) -> Result<(), VerificationError>

Recheck that source and target have identical prime and precision identity.

pub fn to_json(&self) -> Result<String, NoetherError>

Canonical JSON containing both endpoint contexts.

pub fn from_json(value: &str) -> Result<Self, NoetherError>

Deserialize and revalidate the embedding endpoints.

Trait Implementations

impl Clone for PadicIntegralEmbedding

fn clone(&self) -> PadicIntegralEmbedding

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CoefficientMap for PadicIntegralEmbedding

type Source = PadicRing

Source coefficient context.

type Target = PadicField

Target coefficient context.

type Error = PadicEmbeddingError

Scalar application failure.

fn source(&self) -> &Self::Source

Exact source context accepted by this map.

fn target(&self) -> &Self::Target

Exact target context produced by this map.

fn apply(&self, value: &PadicElement) -> Result<PadicElement, Self::Error>

Apply the map after checking that value belongs to the exact source.

impl Debug for PadicIntegralEmbedding

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

Formats the value using the given formatter.

impl Display for PadicIntegralEmbedding

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

Formats the value using the given formatter.

impl PartialEq for PadicIntegralEmbedding

fn eq(&self, other: &PadicIntegralEmbedding) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl SemanticType for PadicIntegralEmbedding

const TYPE_ID: &'static str = "noether/numthy/PadicIntegralEmbedding@1"

Versioned, language-neutral semantic identity.

fn canonical_bytes(&self) -> Result<Vec<u8>, NoetherError>

Serialize without backend- or language-specific identity.

fn describe() -> &'static TypeDescription

Return static discovery metadata for the type.

impl Eq for PadicIntegralEmbedding

impl StructuralPartialEq for PadicIntegralEmbedding