coya: Coya monoids
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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| Versions [RSS] | 0.1, 0.1.0.1 |
|---|---|
| Change log | CHANGELOG.md |
| Dependencies | base (>=4.10.1 && <5), groups (>=0.4), primitive (>=0.6.4), refined (>=0.3), semirings (>=0.3) [details] |
| Tested with | ghc ==8.2.2, ghc ==8.4.4, ghc ==8.6.3 |
| 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 2020-07-09T05:00:08Z |
| Distributions | NixOS:0.1.0.1 |
| Downloads | 752 total (6 in the last 30 days) |
| Rating | (no votes yet) [estimated by Bayesian average] |
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| Status | Docs available [build log] Last success reported on 2020-07-09 [all 1 reports] |
