coya: Coya monoids

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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 0.1, 0.1,
Change log
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
Category Data, Math
Home page
Bug tracker
Source repo head: git clone
Uploaded by chessai at 2019-04-11T18:05:18Z




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