Dedekind 0.0.0
A structuralist C++23 Module Library
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dedekind::algebra::IsRig Concept Referenceexport
module dedekind.algebra

Concept definition

template<typename X, typename Add std::plus<typename X::Domain>, typename Mult std::multiplies<typename X::Domain>>
concept dedekind::algebra::IsRig = dedekind::category::IsRig<typename X::Domain, Add, Mult> &&
IsAdditiveMonoid<X, Add> && IsMultiplicativeMonoid<X, Mult>
dedekind::algebra::IsAdditiveMonoid
Proposition: a set object X whose carrier is a monoid under +.
Definition monoid.cppm:63
dedekind::algebra::IsMultiplicativeMonoid
Proposition: a set object X whose carrier is a monoid under *.
Definition monoid.cppm:76
dedekind::algebra::IsRig
Definition ring.cppm:117
dedekind::category::IsRig
A Semiring without Negatives (Addition is a Monoid).
Definition total.cppm:751

Detailed Description

: The "Natural" Harmony (No negatives).

As with IsSemiring, the algebra-layer rig is a bona-fide algebraic set: the axiomatic category::IsRig proof conjoined with the additive- and multiplicative-monoid rungs (each of which pins the IsAlgebra closure tier).