Linear.Algebra

Documentation

class Num r => Algebra r m where

An associative unital algebra over a ring

Methods

mult :: (m -> m -> r) -> m -> r

unital :: r -> m -> r

Instances

Num r => Algebra r ()

Num r => Algebra r Void

(Num r, TrivialConjugate r) => Algebra r (E Quaternion)

Num r => Algebra r (E Complex)

Num r => Algebra r (E V1)

Num r => Algebra r (E V0)

(Algebra r a, Algebra r b) => Algebra r (a, b)

class Num r => Coalgebra r m where

A coassociative counital coalgebra over a ring

Methods

comult :: (m -> r) -> m -> m -> r

counital :: (m -> r) -> r

Instances

Num r => Coalgebra r ()

Num r => Coalgebra r Void

(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion)

Num r => Coalgebra r (E Complex)

Num r => Coalgebra r (E V4)

Num r => Coalgebra r (E V3)

Num r => Coalgebra r (E V2)

Num r => Coalgebra r (E V1)

Num r => Coalgebra r (E V0)

(Coalgebra r m, Coalgebra r n) => Coalgebra r (m, n)

multRep :: (Representable f, Algebra r (Rep f)) => f (f r) -> f r

unitalRep :: (Representable f, Algebra r (Rep f)) => r -> f r

comultRep :: (Representable f, Coalgebra r (Rep f)) => f r -> f (f r)

counitalRep :: (Representable f, Coalgebra r (Rep f)) => f r -> r