# coya: Coya monoids

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**Warnings:**

- 'ghc-options: -O2' is rarely needed. Check that it is giving a real benefit and not just imposing longer compile times on your users.

Take some log semiring R. Then, for any two x,y :: R, the following holds:

x ^ log y == y ^ log x == e ^ (log x * log y)

A Coya monoid is some commutative monoid (R, #), where x # y = x ^ log y. The following laws hold:

e # x = x (Left Identity)

x # e = x (Right Identity)

(x # y) # z == x # (y # z) (Associativity)

x # y == y # x (Commutativity)

If the R is a poset where all elements in R are greater than one, then R also forms a group:

x # (e ^ (1 / log (x))) == x

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## Properties

Versions | 0.1, 0.1, 0.1.0.1 |
---|---|

Change log | CHANGELOG.md |

Dependencies | base (>=4.10.1 && <4.13), groups (>=0.4), primitive (>=0.6.4), refined (>=0.3), semirings (>=0.3) [details] |

License | BSD-3-Clause |

Copyright | 2019 chessai |

Author | chessai |

Maintainer | chessai1996@gmail.com |

Category | Data, Math |

Home page | https://github.com/chessai/coya |

Bug tracker | https://github.com/chessai/coya/issues |

Source repo | head: git clone https://github.com/chessai/coya.git |

Uploaded | by chessai at 2019-04-11T18:05:18Z |

## Modules

[Index]

## Downloads

- coya-0.1.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)

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