License | BSD-style (see the file LICENSE) |
---|---|

Maintainer | Edward Kmett <ekmett@gmail.com> |

Stability | provisional |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell98 |

## 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 #

An associative unital algebra over a ring

## Instances

Num r => Algebra r () # | |

Defined in Linear.Algebra | |

Num r => Algebra r Void # | |

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

Defined in Linear.Algebra mult :: (E Quaternion -> E Quaternion -> r) -> E Quaternion -> r # unital :: r -> E Quaternion -> r # | |

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) # | |

Defined in Linear.Algebra |

class Num r => Coalgebra r m where #

A coassociative counital coalgebra over a ring

## Instances

Num r => Coalgebra r () # | |

Defined in Linear.Algebra | |

Num r => Coalgebra r Void # | |

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

Defined in Linear.Algebra comult :: (E Quaternion -> r) -> E Quaternion -> E Quaternion -> r # counital :: (E Quaternion -> r) -> r # | |

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) # | |

Defined in Linear.Algebra |

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 #