[−][src]Trait mathru::algebra::abstr::Quasigroup

pub trait Quasigroup<O: Operator>: Magma<O> + Identity<O> + PartialEq { }

A quasigroup is a magma which has the divisibility property (or Latin square property). Divisibility is a weak form of right and left invertibility.

$\forall a, b \in \mathbb{Q}, \exists! r, l \in \mathbb{Q}$ such that $l ∘ a = b$ and $a ∘ r = b$

The solutions for $r$ and $l$ are:

$r = a \ b$ and $l = b / a$

where $\$ is the left and $/$ is th right division.

Implementations on Foreign Types

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