License | BSD-style (see the file LICENSE) |
---|---|
Maintainer | Edward Kmett <ekmett@gmail.com> |
Stability | provisional |
Portability | portable |
Safe Haskell | Safe-Inferred |
Language | Haskell2010 |
Synopsis
- class Num r => Algebra r m where
- class Num r => Coalgebra r m where
- 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
Documentation
class Num r => Algebra r m where Source #
An associative unital algebra over a ring
Instances
Num r => Algebra r Void Source # | |
Num r => Algebra r () Source # | |
Num r => Algebra r (E Complex) Source # | |
(Num r, TrivialConjugate r) => Algebra r (E Quaternion) Source # | |
Defined in Linear.Algebra mult :: (E Quaternion -> E Quaternion -> r) -> E Quaternion -> r Source # unital :: r -> E Quaternion -> r Source # | |
Num r => Algebra r (E V0) Source # | |
Num r => Algebra r (E V1) Source # | |
(Algebra r a, Algebra r b) => Algebra r (a, b) Source # | |
class Num r => Coalgebra r m where Source #
A coassociative counital coalgebra over a ring
Instances
Num r => Coalgebra r Void Source # | |
Num r => Coalgebra r () Source # | |
Num r => Coalgebra r (E Complex) Source # | |
(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion) Source # | |
Defined in Linear.Algebra comult :: (E Quaternion -> r) -> E Quaternion -> E Quaternion -> r Source # counital :: (E Quaternion -> r) -> r Source # | |
Num r => Coalgebra r (E V0) Source # | |
Num r => Coalgebra r (E V1) Source # | |
Num r => Coalgebra r (E V2) Source # | |
Num r => Coalgebra r (E V3) Source # | |
Num r => Coalgebra r (E V4) Source # | |
(Coalgebra r m, Coalgebra r n) => Coalgebra r (m, n) Source # | |
counitalRep :: (Representable f, Coalgebra r (Rep f)) => f r -> r Source #