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, y = x ^ log y. The following laws hold:

e # x = x (Left Identity)

x # e = x (Right Identity)

(x z == x z) (Associativity)

x 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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Versions0.1, 0.1
Dependenciesbase (>=4.10.1 && <4.13), groups (>=0.4), primitive (>=0.6.4), refined (>=0.3), semirings (>=0.3) [details]
Copyright2019 chessai
CategoryData, Math
Home page
Bug tracker
Source repositoryhead: git clone
UploadedThu Apr 11 18:05:18 UTC 2019 by chessai




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