CECCO::SubfieldOf Concept Reference

SUBFIELD ⊆ SUPERFIELD as constructed in this library (Iso paths included). More...

#include <field_concepts_traits.hpp>

Concept definition

template<typename SUPERFIELD, typename SUBFIELD>
concept SubfieldOf = details::is_subfield_of_v<SUPERFIELD, SUBFIELD>

Detailed Description

SUBFIELD ⊆ SUPERFIELD as constructed in this library (Iso paths included).

Template Parameters

SUPERFIELD	Larger field
SUBFIELD	Candidate smaller field

Walks the construction tower of SUPERFIELD; for Iso operands, every representation is inspected, so a subfield reachable through any of MAIN / OTHERS counts. Reflexive: SubfieldOf<F, F> is always true.

Warning

This is the construction tower, not the mathematical tower. A field that exists mathematically between SUBFIELD and SUPERFIELD but was never constructed (or never bridged by an Iso) is invisible. Construct an Iso over equivalent representations to merge towers.

Usage_Examples

using F2     = Fp<2>;
using F4_a   = Ext<F2, {1, 1, 1}>;
using F4_b   = Ext<F2, {1, 0, 1}>;
using F4_Iso = Iso<F4_a, F4_b>;
using F16    = Ext<F4_Iso, {2, 1, 1}>;
 
static_assert(SubfieldOf<F16, F4_Iso>);  // direct construction
static_assert(SubfieldOf<F16, F4_a>);    // via Iso: F4_a in F4_Iso ⊆ F16
static_assert(SubfieldOf<F16, F2>);      // recursive descent

Definition at line 402 of file field_concepts_traits.hpp.