Struct FiniteSchemeClosedPoint 

pub struct FiniteSchemeClosedPoint { /* private fields */ }

One geometric closed point of an affine finite-field scheme.

Coordinates live in an explicit residue-field presentation. The point is represented by the lexicographically least conjugate in its relative Frobenius orbit, so conjugate geometric coordinates define one canonical value.

Implementations

impl FiniteSchemeClosedPoint

pub fn scheme(&self) -> &Scheme<FiniteField>

Scheme containing this closed point.

pub fn base_embedding(&self) -> &FiniteFieldEmbedding

Checked embedding of the base field into the residue field.

pub fn residue_field(&self) -> &FiniteField

Explicit finite residue-field presentation.

pub fn coordinates(&self) -> &[FiniteFieldElement]

Canonical geometric coordinates in the residue field.

pub fn degree(&self) -> usize

Degree of the closed point over the scheme’s base field.

pub fn frobenius_orbit(&self) -> &[Vec<FiniteFieldElement>]

Complete relative-Frobenius orbit, starting at the canonical conjugate.

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

Recheck the residue presentation, orbit, minimal degree, and equations.

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

Serialize the complete residue-field and orbit evidence.

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

Deserialize and exactly reverify a closed point.

Trait Implementations

impl Clone for FiniteSchemeClosedPoint

fn clone(&self) -> FiniteSchemeClosedPoint

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FiniteSchemeClosedPoint

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for FiniteSchemeClosedPoint

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for FiniteSchemeClosedPoint

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

Formats the value using the given formatter.

impl PartialEq for FiniteSchemeClosedPoint

fn eq(&self, other: &FiniteSchemeClosedPoint) -> 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 FiniteSchemeClosedPoint

const TYPE_ID: &'static str = "noether/commalg/FiniteSchemeClosedPoint@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 FiniteSchemeClosedPoint

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 FiniteSchemeClosedPoint

impl StructuralPartialEq for FiniteSchemeClosedPoint