linear-1.16: Linear Algebra

Safe HaskellNone
LanguageHaskell98

Linear.Algebra

Synopsis

Documentation

class Num r => Algebra r m where Source

An associative unital algebra over a ring

Methods

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

unital :: r -> m -> r Source

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 Source

A coassociative counital coalgebra over a ring

Methods

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

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

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 Source

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

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

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