The Perfect Species (Rig ∩ Rng). More...

Concept definition

template<typename T, typename Add, typename Mult>

concept dedekind::category::IsRing = IsRig<T, Add, Mult> && IsRng<T, Add, Mult>

dedekind::category::IsRig

A Semiring without Negatives (Addition is a Monoid).

Definition total.cppm:751

dedekind::category::IsRing

The Perfect Species (Rig ∩ Rng).

Definition total.cppm:791

dedekind::category::IsRng

A Ring without Identity (Multiplication is a Semigroup).

Definition total.cppm:770

Detailed Description

The Perfect Species (Rig ∩ Rng).

A Ring combines an Abelian Group for addition and a Monoid for multiplication, with mutual distributivity. unsigned int with (+, *) forms a Ring (arithmetic in Z/2ⁿZ). Signed int does not satisfy this partition's totality requirements due to undefined overflow.