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

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

Stability | provisional |

Portability | portable |

Safe Haskell | None |

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 () Source # | |

Num r => Algebra r Void 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 Complex) Source # | |

Num r => Algebra r (E V1) Source # | |

Num r => Algebra r (E V0) 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 () Source # | |

Num r => Coalgebra r Void 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 Complex) Source # | |

Num r => Coalgebra r (E V4) Source # | |

Num r => Coalgebra r (E V3) Source # | |

Num r => Coalgebra r (E V2) Source # | |

Num r => Coalgebra r (E V1) Source # | |

Num r => Coalgebra r (E V0) Source # | |

(Coalgebra r m, Coalgebra r n) => Coalgebra r (m, n) Source # | |

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