Struct ProjectiveSpace 

pub struct ProjectiveSpace<R: CommutativeRing> { /* private fields */ }

Projective space with one explicit base and homogeneous coordinate ring.

Implementations

impl<R: CommutativeRing + Display> ProjectiveSpace<R>

pub fn base_change<M>( &self, map: &M, ) -> Result<ProjectiveSpace<M::Target>, BaseChangeError>

where M: CoefficientMap<Source = R>,

Extend the base while preserving the exact homogeneous coordinate-ring presentation.

impl<R: CommutativeRing> ProjectiveSpace<R>

pub fn new(base: R, dimension: usize) -> Result<Self, SchemeError>

Construct standard projective dimension-space with coordinates x0, ....

pub fn with_names<I, S>( base: R, dimension: usize, names: I, ) -> Result<Self, SchemeError>

where I: IntoIterator<Item = S>, S: Into<String>,

Construct projective space with explicit ordered homogeneous coordinates.

pub fn base(&self) -> &R

Base coefficient context.

pub fn dimension(&self) -> usize

Projective dimension.

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

Ordered homogeneous coordinate names.

pub fn coordinate_ring(&self) -> &PolynomialRing<R>

Exact homogeneous coordinate ring.

impl ProjectiveSpace<RationalField>

pub fn closed_subscheme( &self, ideal: Ideal<PolynomialRing<RationalField>>, ) -> Result<Scheme<RationalField>, SchemeError>

Construct a homogeneous closed subscheme in this projective space.

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

Serialize this ambient context.

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

Restore and validate this ambient context.

impl ProjectiveSpace<FiniteField>

pub fn closed_subscheme( &self, ideal: Ideal<PolynomialRing<FiniteField>>, ) -> Result<Scheme<FiniteField>, SchemeError>

Construct a homogeneous closed subscheme in this projective space.

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

Serialize this ambient context.

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

Restore and validate this ambient context.

Trait Implementations

impl<R: Clone + CommutativeRing> Clone for ProjectiveSpace<R>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<R> Debug for ProjectiveSpace<R>

where R: CommutativeRing,

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

Formats the value using the given formatter.

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

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<R> Display for ProjectiveSpace<R>

where R: CommutativeRing,

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

Formats the value using the given formatter.

impl<R: PartialEq + CommutativeRing> PartialEq for ProjectiveSpace<R>

fn eq(&self, other: &ProjectiveSpace<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 SemanticType for ProjectiveSpace<FiniteField>

const TYPE_ID: &'static str = "noether/commalg/ProjectiveSpace@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 SemanticType for ProjectiveSpace<RationalField>

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

where R: CommutativeRing + 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 + CommutativeRing> Eq for ProjectiveSpace<R>

impl<R: CommutativeRing> StructuralPartialEq for ProjectiveSpace<R>