Struct FrobeniusSemilinearMap 

pub struct FrobeniusSemilinearMap<R: CoefficientFrobeniusContext> { /* private fields */ }

A map v -> A sigma^r(v) between finite free modules over one context.

Vectors are columns, A has shape target_dimension x source_dimension, and sigma is the context’s checked coefficient Frobenius. Composition records the unreduced sum of Frobenius exponents and twists the inner matrix before multiplication.

Implementations

impl<R: CoefficientFrobeniusContext> FrobeniusSemilinearMap<R>

pub fn new(matrix: Matrix<R>, frobenius_exponent: u64) -> Self

Construct the map v -> A sigma^r(v) represented by matrix and r.

pub fn identity(context: R, dimension: usize) -> Self

Construct the identity map on a free module of the requested dimension.

pub fn context(&self) -> &R

Exact coefficient context of the source and target modules.

pub fn matrix(&self) -> &Matrix<R>

Matrix A in the convention v -> A sigma^r(v).

pub fn frobenius_exponent(&self) -> u64

Unreduced nonnegative Frobenius exponent r.

pub fn source_dimension(&self) -> usize

Dimension of the source free module.

pub fn target_dimension(&self) -> usize

Dimension of the target free module.

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

Recheck the matrix context and dimensions defining this map.

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

where Matrix<R>: Serialize,

Serialize the complete context, matrix, and Frobenius exponent.

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

where for<'de> Matrix<R>: Deserialize<'de>,

Deserialize and revalidate a semilinear map and its exact context.

impl<R: CoefficientFrobeniusContext> FrobeniusSemilinearMap<R>

pub fn apply(&self, vector: &Vector<R>) -> Result<Vector<R>, SemilinearMapError>

Apply v -> A sigma^r(v) after checking context and dimension.

pub fn apply_block( &self, block: &Matrix<R>, ) -> Result<Matrix<R>, SemilinearMapError>

Apply the semilinear map independently to every column of a dense block.

pub fn compose(&self, inner: &Self) -> Result<Self, SemilinearMapError>

Compose self after inner.

If self(v) = A sigma^r(v) and inner(v) = B sigma^s(v), the result is A sigma^r(B) sigma^(r+s)(v).

impl FrobeniusSemilinearMap<QadicRing>

pub fn restrict_scalars(&self) -> Result<Matrix<PadicRing>, SemilinearMapError>

Restrict this semilinear map to an ordinary Z_p-linear matrix.

Module coordinates are flattened in module-major order, with each q-adic coordinate expanded in ascending power-basis order.

impl FrobeniusSemilinearMap<QadicField>

pub fn restrict_scalars(&self) -> Result<Matrix<PadicField>, SemilinearMapError>

Restrict this semilinear map to an ordinary Q_p-linear matrix.

Module coordinates are flattened in module-major order, with each q-adic coordinate expanded in ascending power-basis order.

Trait Implementations

impl<R: Clone + CoefficientFrobeniusContext> Clone for FrobeniusSemilinearMap<R>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<R: CoefficientFrobeniusContext> Debug for FrobeniusSemilinearMap<R>

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

Formats the value using the given formatter.

impl<R: CoefficientFrobeniusContext> Display for FrobeniusSemilinearMap<R>

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

Formats the value using the given formatter.

impl<R: PartialEq + CoefficientFrobeniusContext> PartialEq for FrobeniusSemilinearMap<R>

fn eq(&self, other: &FrobeniusSemilinearMap<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: CoefficientFrobeniusContext> SemanticType for FrobeniusSemilinearMap<R>

const TYPE_ID: &'static str = "noether/linalg/FrobeniusSemilinearMap@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: Eq + CoefficientFrobeniusContext> Eq for FrobeniusSemilinearMap<R>

impl<R: CoefficientFrobeniusContext> StructuralPartialEq for FrobeniusSemilinearMap<R>