linear-1.20.8: Linear Algebra

Linear.Algebra

Description

Synopsis

# 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 () # Instance detailsDefined in Linear.Algebra Methodsmult :: (() -> () -> r) -> () -> r #unital :: r -> () -> r # Num r => Algebra r Void # Instance detailsDefined in Linear.Algebra Methodsmult :: (Void -> Void -> r) -> Void -> r #unital :: r -> Void -> r # (Num r, TrivialConjugate r) => Algebra r (E Quaternion) # Instance detailsDefined in Linear.Algebra Methodsmult :: (E Quaternion -> E Quaternion -> r) -> E Quaternion -> r #unital :: r -> E Quaternion -> r # Num r => Algebra r (E Complex) # Instance detailsDefined in Linear.Algebra Methodsmult :: (E Complex -> E Complex -> r) -> E Complex -> r #unital :: r -> E Complex -> r # Num r => Algebra r (E V1) # Instance detailsDefined in Linear.Algebra Methodsmult :: (E V1 -> E V1 -> r) -> E V1 -> r #unital :: r -> E V1 -> r # Num r => Algebra r (E V0) # Instance detailsDefined in Linear.Algebra Methodsmult :: (E V0 -> E V0 -> r) -> E V0 -> r #unital :: r -> E V0 -> r # (Algebra r a, Algebra r b) => Algebra r (a, b) # Instance detailsDefined in Linear.Algebra Methodsmult :: ((a, b) -> (a, b) -> r) -> (a, b) -> r #unital :: r -> (a, b) -> r #

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 () # Instance detailsDefined in Linear.Algebra Methodscomult :: (() -> r) -> () -> () -> r #counital :: (() -> r) -> r # Num r => Coalgebra r Void # Instance detailsDefined in Linear.Algebra Methodscomult :: (Void -> r) -> Void -> Void -> r #counital :: (Void -> r) -> r # (Num r, TrivialConjugate r) => Coalgebra r (E Quaternion) # Instance detailsDefined in Linear.Algebra Methodscomult :: (E Quaternion -> r) -> E Quaternion -> E Quaternion -> r #counital :: (E Quaternion -> r) -> r # Num r => Coalgebra r (E Complex) # Instance detailsDefined in Linear.Algebra Methodscomult :: (E Complex -> r) -> E Complex -> E Complex -> r #counital :: (E Complex -> r) -> r # Num r => Coalgebra r (E V4) # Instance detailsDefined in Linear.Algebra Methodscomult :: (E V4 -> r) -> E V4 -> E V4 -> r #counital :: (E V4 -> r) -> r # Num r => Coalgebra r (E V3) # Instance detailsDefined in Linear.Algebra Methodscomult :: (E V3 -> r) -> E V3 -> E V3 -> r #counital :: (E V3 -> r) -> r # Num r => Coalgebra r (E V2) # Instance detailsDefined in Linear.Algebra Methodscomult :: (E V2 -> r) -> E V2 -> E V2 -> r #counital :: (E V2 -> r) -> r # Num r => Coalgebra r (E V1) # Instance detailsDefined in Linear.Algebra Methodscomult :: (E V1 -> r) -> E V1 -> E V1 -> r #counital :: (E V1 -> r) -> r # Num r => Coalgebra r (E V0) # Instance detailsDefined in Linear.Algebra Methodscomult :: (E V0 -> r) -> E V0 -> E V0 -> r #counital :: (E V0 -> r) -> r # (Coalgebra r m, Coalgebra r n) => Coalgebra r (m, n) # Instance detailsDefined in Linear.Algebra Methodscomult :: ((m, n) -> r) -> (m, n) -> (m, n) -> r #counital :: ((m, n) -> r) -> r #

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 #