CECCO::Isomorphic Concept Reference

A and B are finite fields of the same size (and thus isomorphic). More...

#include <field_concepts_traits.hpp>

Concept definition

template<typename A, typename B>
concept Isomorphic = FiniteFieldType<A> && FiniteFieldType<B> && requires { requires A::get_size() == B::get_size(); }

Detailed Description

A and B are finite fields of the same size (and thus isomorphic).

Template Parameters

A	First field type
B	Second field type

Two finite fields of the same cardinality are isomorphic. The check is on size only — the explicit isomorphism (a concrete field homomorphism) is computed by CECCO::Isomorphism.

Usage_Examples

using F2   = Fp<2>;
using F4_a = Ext<F2, {1, 1, 1}>;     // 𝔽₄ via x² + x + 1
using F4_b = Ext<F2, {1, 0, 1}>;     // 𝔽₄ via x² + 1
using F8   = Ext<F2, {1, 1, 0, 1}>;
using F64_a = Ext<F8,   {7, 1, 1}>;
using F64_b = Ext<F4_a, {1, 2, 0, 1}>;
 
static_assert(Isomorphic<F64_a, F64_b>);  // same size, different constructions
static_assert(Isomorphic<F4_a, F4_b>);
static_assert(!Isomorphic<F4_a, F8>);     // 4 ≠ 8

Definition at line 263 of file field_concepts_traits.hpp.