algebra-4.1: Constructive abstract algebra

Safe HaskellSafe-Inferred

Numeric.Algebra.Unital

Contents

Synopsis

Unital Multiplication (Multiplicative monoid)

class Multiplicative r => Unital r whereSource

Methods

one :: rSource

pow :: Whole n => r -> n -> rSource

productWith :: Foldable f => (a -> r) -> f a -> rSource

product :: (Foldable f, Unital r) => f r -> rSource

Unital Associative Algebra

class Algebra r a => UnitalAlgebra r a whereSource

An associative unital algebra over a semiring, built using a free module

Methods

unit :: r -> a -> rSource

Unital Coassociative Coalgebra

Bialgebra

class (UnitalAlgebra r a, CounitalCoalgebra r a) => Bialgebra r a Source

A bialgebra is both a unital algebra and counital coalgebra where the mult and unit are compatible in some sense with the comult and counit. That is to say that mult and unit are a coalgebra homomorphisms or (equivalently) that comult and counit are an algebra homomorphisms.

Instances