coya

Coya monoids

Latest on Hackage:

0.1.0.1

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BSD-3-Clause licensed by chessai

Maintained by [email protected]

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