A Monoid with two-sided Inverses (The Perfect Symmetry). More...

Concept definition

template<typename T, typename Op>

concept dedekind::category::IsGroup = IsMonoid<T, Op> && IsLoop<T, Op>

dedekind::category::IsGroup

A Monoid with two-sided Inverses (The Perfect Symmetry).

Definition total.cppm:624

dedekind::category::IsLoop

A UnitalMagma with Inverses (-x).

Definition total.cppm:556

dedekind::category::IsMonoid

A Semigroup with a two-sided Identity element.

Definition total.cppm:584

Detailed Description

A Monoid with two-sided Inverses (The Perfect Symmetry).

Every element a has a unique inverse a⁻¹ such that a ⊕ a⁻¹ = e. unsigned int with addition is a Group (modular inverse exists for every element in Z/2ⁿZ). Signed int with addition is not, as overflow is undefined behaviour.