Struct QadicRing 

pub struct QadicRing { /* private fields */ }

The fixed-cap Witt ring W(F_q) / p^N.

The complete residue-field presentation and the absolute precision cap are context identity. Elements use FLINT’s qadic_t backend but are restricted to nonnegative valuation, so every power-basis coefficient has a fixed N-digit p-adic storage bound.

Implementations

impl QadicRing

pub fn coefficient_frobenius(&self, exponent: u64) -> QadicRingFrobenius

Checked lift of residue-field Frobenius on this Witt-ring presentation.

impl QadicRing

pub fn precision_restriction( &self, target_absolute_precision: u64, ) -> Result<QadicRingRestriction, QadicRestrictionError>

Construct a first-class restriction to a coarser fixed-cap Witt ring.

pub fn divide_uniformizer_exact( &self, value: &QadicElement, exponent: u64, ) -> Result<QadicElement, QadicUniformizerDivisionError>

Divide by p^exponent, requiring the quotient to remain integral.

impl QadicRing

pub fn new( residue_field: FiniteField, absolute_precision: u64, ) -> Result<Self, QadicContextError>

Construct W(residue_field) / p^N from a verified finite-field presentation.

pub fn residue_field(&self) -> &FiniteField

Residue field F_q, including its normalized defining presentation.

pub fn prime(&self) -> &Integer

Residue characteristic p.

pub fn residue_degree(&self) -> usize

Residue degree [F_q : F_p].

pub fn coefficient_ring(&self) -> &PadicRing

Base p-adic integer ring supplying the power-basis coefficients.

pub fn absolute_precision(&self) -> u64

Immutable absolute precision cap N.

pub fn cardinality(&self) -> Integer

Exact cardinality q^N of the truncated Witt ring.

pub fn element<T: Into<Integer>>(&self, value: T) -> QadicElement

Embed an integer through Z_p -> W(F_q).

pub fn element_from_coefficients( &self, coefficients: &[PadicElement], ) -> Result<QadicElement, InvalidQadicCoordinatesError>

Construct an element from ascending Z_p coordinates in the declared q-adic power basis.

Missing high coordinates are zero, and at most residue_degree coordinates may be supplied. Every coordinate must belong to this context’s exact coefficient ring.

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

Serialize the residue-field presentation and absolute precision as typed JSON.

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

Deserialize and revalidate a fixed-precision Witt-ring context.

pub fn residue( &self, value: &QadicElement, ) -> Result<FiniteFieldElement, ContextMismatchError>

Reduce an integral q-adic value to F_q.

pub fn teichmuller( &self, value: &FiniteFieldElement, ) -> Result<QadicElement, ContextMismatchError>

Lift a residue-field value to its Teichmüller representative.

pub fn generator(&self) -> QadicElement

Distinguished Teichmüller lift of the residue-field power-basis generator.

pub fn restrict( &self, value: &QadicElement, absolute_precision: u64, ) -> Result<QadicElement, QadicRestrictionError>

Explicitly discard high p-adic digits.

Trait Implementations

impl Clone for QadicRing

fn clone(&self) -> QadicRing

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CoefficientFrobeniusContext for QadicRing

type Frobenius = QadicRingFrobenius

Concrete checked Frobenius-map value returned for this context.

fn coefficient_frobenius(&self, exponent: u64) -> Self::Frobenius

Construct the declared nonnegative Frobenius power.

fn residue_characteristic(&self) -> &Integer

Residue characteristic whose power scales monomial exponents.

impl Debug for QadicRing

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for QadicRing

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for QadicRing

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

Formats the value using the given formatter.

impl PartialEq for QadicRing

fn eq(&self, other: &Self) -> 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 PrecisionContext for QadicRing

type Precision = u64

Domain-specific precision shape.

fn precision(&self) -> &Self::Precision

The immutable precision specification of this context.

fn refines( &self, candidate: &Self::Precision, reference: &Self::Precision, ) -> bool

Whether candidate contains at least the information in reference.

impl Ring for QadicRing

type Element = QadicElement

Elements manufactured and validated by this context.

fn contains(&self, value: &Self::Element) -> bool

Test whether a value belongs to this exact context.

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

The additive identity in this context.

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

The multiplicative identity in this context.

fn add( &self, a: &Self::Element, b: &Self::Element, ) -> Result<Self::Element, ContextMismatchError>

Add two elements after checking their context.

fn sub( &self, a: &Self::Element, b: &Self::Element, ) -> Result<Self::Element, ContextMismatchError>

Subtract two elements after checking their context.

fn mul( &self, a: &Self::Element, b: &Self::Element, ) -> Result<Self::Element, ContextMismatchError>

Multiply two elements after checking their context.

fn neg( &self, value: &Self::Element, ) -> Result<Self::Element, ContextMismatchError>

Negate an element after checking its context.

fn is_zero(&self, value: &Self::Element) -> bool

Test whether a value is the additive identity.

fn sum_products( &self, products: &[(&Self::Element, &Self::Element)], ) -> Result<Self::Element, ContextMismatchError>

Compute a sum of pairwise products in this context.

impl SemanticType for QadicRing

const TYPE_ID: &'static str = "noether/numthy/QadicRing@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 Serialize for QadicRing

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl UnitInversion for QadicRing

fn inverse_unit( &self, value: &Self::Element, ) -> Result<Self::Element, UnitError>

Invert value when it belongs to this context and is a unit.

impl ValuedRing for QadicRing

fn uniformizer(&self) -> Self::Element

A chosen uniformizer.

fn valuation_lower_bound(&self, value: &Self::Element) -> Option<i64>

A proven lower bound for the valuation, or None for zero.

impl CommutativeRing for QadicRing

impl Eq for QadicRing