Struct PrimaryDecomposition 

pub struct PrimaryDecomposition<R: Field> { /* private fields */ }

Complete verified primary decomposition of an admitted polynomial ideal.

Components have distinct associated primes, are in canonical prime order, and intersect exactly to source. Embedded associated primes are retained.

Implementations

impl<R: Field> PrimaryDecomposition<R>

pub fn source(&self) -> &Ideal<PolynomialRing<R>>

Original ideal reconstructed by the primary components.

pub fn components(&self) -> &[Ideal<PolynomialRing<R>>]

Canonically ordered primary component ideals.

pub fn certificates(&self) -> &[PolynomialPrimaryCertificate<R>]

Complete primary evidence in component order.

pub fn associated_primes(&self) -> Vec<&PolynomialPrimeCertificate<R>>

Associated primes, including embedded primes, in component order.

pub const fn theorem(&self) -> &'static str

Exact completeness theorem for the retained component list.

impl PrimaryDecomposition<RationalField>

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

Independently recheck every primary claim and the exact intersection.

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

Deserialize and exactly reverify a complete primary decomposition.

impl PrimaryDecomposition<FiniteField>

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

Independently recheck every primary claim and the exact intersection.

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

Deserialize and exactly reverify a complete primary decomposition.

impl<R> PrimaryDecomposition<R>

where R: Field + Serialize, R::Element: Serialize, Ideal<PolynomialRing<R>>: Serialize,

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

Serialize the source and complete primary evidence.

Trait Implementations

impl<R: Clone + Field> Clone for PrimaryDecomposition<R>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<R: Field> Debug for PrimaryDecomposition<R>

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for PrimaryDecomposition<FiniteField>

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<'de> Deserialize<'de> for PrimaryDecomposition<RationalField>

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<R: Field> Display for PrimaryDecomposition<R>

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

Formats the value using the given formatter.

impl<R: PartialEq + Field> PartialEq for PrimaryDecomposition<R>

fn eq(&self, other: &PrimaryDecomposition<R>) -> 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<R> SemanticType for PrimaryDecomposition<R>

where R: Field + Serialize, R::Element: Serialize, Ideal<PolynomialRing<R>>: Serialize,

const TYPE_ID: &'static str = "noether/commalg/PrimaryDecomposition@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<R> Serialize for PrimaryDecomposition<R>

where R: Field + Serialize, R::Element: Serialize, Ideal<PolynomialRing<R>>: Serialize,

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

where S: Serializer,

Serialize this value into the given Serde serializer.

impl<R: Eq + Field> Eq for PrimaryDecomposition<R>

impl<R: Field> StructuralPartialEq for PrimaryDecomposition<R>