A commutative monoid M on which the semiring S acts linearly. More...

Concept definition

template<typename M, typename S, typename AddM std::plus<M>, typename AddS std::plus<S>, typename MultS std::multiplies<S>, typename Act std::multiplies<>>
concept dedekind::category::IsSemimodule = 
    IsCommutativeMonoid<M, AddM> && IsSemiring<S, AddS, MultS> &&
    IsLeftAction<S, M, Act> && is_linear_action_v<M, S, AddM, AddS, MultS, Act>

Detailed Description

A commutative monoid M on which the semiring S acts linearly.

Template Parameters

M	The module carrier.
S	The scalar carrier.
AddM	Additive law on M.
AddS	Additive law on S.
MultS	Multiplicative law on S.
Act	The action S x M -> M.

The laws are the trait is_linear_action_v; dedekind.algebra builds its modules and vector spaces on this shape.