CECCO::Embedding< SUBFIELD, SUPERFIELD > Class Template Reference

Functor representing the field embedding φ: SUBFIELD → SUPERFIELD, with reverse lookup. More...

#include <fields.hpp>

Public Member Functions
	Embedding ()
	Constructs the embedding (cached on first instantiation per template arguments).
constexpr SUPERFIELD	operator() (const SUBFIELD &sub) const
	Apply φ: SUBFIELD → SUPERFIELD.
constexpr SUBFIELD	extract (const SUPERFIELD &super) const
	Reverse φ: find the unique s ∈ SUBFIELD with φ(s) == super.

Detailed Description

template<FiniteFieldType SUBFIELD, FiniteFieldType SUPERFIELD>
requires SubfieldOf<SUPERFIELD, SUBFIELD>
class CECCO::Embedding< SUBFIELD, SUPERFIELD >

Functor representing the field embedding φ: SUBFIELD → SUPERFIELD, with reverse lookup.

Template Parameters

SUBFIELD	Subfield (finite-field type)
SUPERFIELD	Superfield (finite-field type, must satisfy SubfieldOf<SUPERFIELD, SUBFIELD>)

The embedding is determined by mapping a generator: with factor = (|SUPERFIELD| − 1) / (|SUBFIELD| − 1), it sends g_sub^k ↦ g_super^{k · factor}. Identities φ(0) = 0, φ(1) = 1 are fixed. The full table is computed once per template instantiation and cached.

Forward map (operator()) is an O(1) array lookup; extract reverses it via linear search through the cached map. When SUPERFIELD is an CECCO::Iso, extract walks the MAIN representation first, then each of OTHERS, until it finds one that contains SUBFIELD.

Warning

Mathematical containment is necessary but not sufficient — SUBFIELD must appear in the construction tower of SUPERFIELD (or in one of an Iso's components). Use an Iso to merge towers when needed.

Usage_Example

using F2  = Fp<2>;
using F4  = Ext<F2, {1, 1, 1}>;
using F16 = Ext<F4, {2, 1, 1}>;
 
Embedding<F4, F16> phi;
F4 a(2);
F16 b = phi(a);             // upcast — always succeeds
F4  c = phi.extract(b);     // throws std::invalid_argument if b ∉ φ(F4)

Definition at line 1301 of file fields.hpp.

Constructor & Destructor Documentation

Embedding()

template<FiniteFieldType SUBFIELD, FiniteFieldType SUPERFIELD>

CECCO::Embedding< SUBFIELD, SUPERFIELD >::Embedding

(

)

Constructs the embedding (cached on first instantiation per template arguments).

Definition at line 1337 of file fields.hpp.

Member Function Documentation

extract()

template<FiniteFieldType SUBFIELD, FiniteFieldType SUPERFIELD>

SUBFIELD CECCO::Embedding< SUBFIELD, SUPERFIELD >::extract ( const SUPERFIELD & super ) const

constexpr

Reverse φ: find the unique s ∈ SUBFIELD with φ(s) == super.

Exceptions

std::invalid_argument

if super is not in the image of φ

O(|SUBFIELD|) for regular fields; for Iso superfields, O(k · |SUBFIELD|) where k is the number of inspected components.

Definition at line 1346 of file fields.hpp.

operator()()

template<FiniteFieldType SUBFIELD, FiniteFieldType SUPERFIELD>

SUPERFIELD CECCO::Embedding< SUBFIELD, SUPERFIELD >::operator() ( const SUBFIELD & sub ) const

inlineconstexpr

Apply φ: SUBFIELD → SUPERFIELD.

Definition at line 1307 of file fields.hpp.

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The documentation for this class was generated from the following file:

• fields.hpp