dedekind::algebra::IsEuclidean Concept Reference

A Commutative Ring endowed with a division algorithm. More...

Concept definition

template<typename T, typename Add std::plus<T>, typename Mult std::multiplies<T>, typename Div std::divides<T>, typename Rem std::modulus<T>>
concept dedekind::algebra::IsEuclidean =  dedekind::category::IsCommutativeRing<T, Add, Mult> &&
                      IsDividableChain<T> && requires(T a, T b) {
                        { a / b } -> std::same_as<T>;
                        { a % b } -> std::same_as<T>;
                        { Div{}(a, b) } -> std::same_as<T>;
                        { Rem{}(a, b) } -> std::same_as<T>;
                      }

Detailed Description

A Commutative Ring endowed with a division algorithm.

Template Parameters

T	The carrier type.
Add	Additive operation witness (defaults to std::plus<T>).
Mult	Multiplicative operation witness (defaults to std::multiplies<T>).
Div	Division operation witness (defaults to std::divides<T>).
Rem	Remainder operation witness (defaults to std::modulus<T>).