Struct FractionalIdeal 

pub struct FractionalIdeal { /* private fields */ }

A nonzero fractional ideal of an exact number-field order.

The ideal is stored as a canonical row-Hermite rational lattice in the ambient field’s distinguished power basis. Construction from generators forms their NumberFieldOrder-span; equality therefore compares ideals, not the supplied generator list.

Implementations

impl FractionalIdeal

pub fn new( order: NumberFieldOrder, generators: &[NumberFieldElement], ) -> Result<Self, FractionalIdealError>

Construct the fractional ideal generated over order by exact field elements.

pub fn order(&self) -> &NumberFieldOrder

The coefficient order of this ideal.

pub fn basis(&self) -> Vec<NumberFieldElement>

Canonical Z-basis of this fractional ideal.

pub fn contains(&self, element: &NumberFieldElement) -> bool

Whether an exact field element lies in this fractional ideal.

pub fn is_integral(&self) -> bool

Whether this fractional ideal is contained in its coefficient order.

pub fn as_ideal(&self) -> Result<Ideal<NumberFieldOrder>, FractionalIdealError>

View this value as a generic integral ideal when it lies in its order.

pub fn add(&self, other: &Self) -> Result<Self, FractionalIdealError>

Sum of two fractional ideals of the same order.

pub fn mul(&self, other: &Self) -> Result<Self, FractionalIdealError>

Product of two fractional ideals of the same order.

pub fn norm(&self) -> Rational

Exact absolute ideal norm, extended multiplicatively to fractional ideals.

pub fn valuation( &self, prime: &PrimeIdeal<NumberFieldOrder>, ) -> Result<i64, IdealFactorizationError>

The signed P-adic valuation of this fractional ideal.

pub fn factor( &self, ) -> Result<Vec<(PrimeIdeal<NumberFieldOrder>, i64)>, IdealFactorizationError>

Complete signed prime-ideal factorization in this maximal order.

The result is reconstructed exactly after moving negative powers to the left side, so no unchecked factor list can escape this method.

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

Serialize this exact ideal to canonical JSON.

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

Restore and validate an exact fractional ideal from canonical JSON.

Trait Implementations

impl Add<&FractionalIdeal> for &FractionalIdeal

type Output = Result<FractionalIdeal, FractionalIdealError>

The resulting type after applying the + operator.

fn add(self, rhs: &FractionalIdeal) -> Self::Output

Performs the + operation.

impl Clone for FractionalIdeal

fn clone(&self) -> FractionalIdeal

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FractionalIdeal

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for FractionalIdeal

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for FractionalIdeal

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

Formats the value using the given formatter.

impl Mul<&FractionalIdeal> for &FractionalIdeal

type Output = Result<FractionalIdeal, FractionalIdealError>

The resulting type after applying the * operator.

fn mul(self, rhs: &FractionalIdeal) -> Self::Output

Performs the * operation.

impl PartialEq for FractionalIdeal

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 SemanticType for FractionalIdeal

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

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

where S: Serializer,

Serialize this value into the given Serde serializer.

impl Eq for FractionalIdeal