Data.Ring.Semi.Tropical

monoids-0.1.36: Monoids, specialized containers and a general map/reduce framework

Data.Ring.Semi.Tropical

Contents

Tropical Semirings

Synopsis

module Data.Monoid.Reducer

module Data.Ring

infinity :: Tropical a

newtype Tropical a = Tropical {

getTropical :: Maybe a

}

Documentation

module Data.Monoid.Reducer

module Data.Ring

Tropical Semirings

infinity :: Tropical a

newtype Tropical a

The SemiRing (min,+) over a extended with infinity. When a has a Num instance with an addition that respects order, then this is transformed into a tropical semiring. It is assumed that 0 is the least element of a.

http://hal.archives-ouvertes.fr/docs/00/11/37/79/PDF/Tropical.pdf

Constructors

Tropical

getTropical :: Maybe a

show/hide

Instances

Functor Tropical

Pointed Tropical

Ord a => Reducer a (Tropical a)

(Ord a, Num a) => Bimodule Natural (Tropical a)

(Ord a, Num a) => RightModule Natural (Tropical a)

(Ord a, Num a) => LeftModule Natural (Tropical a)

(Ord a, Num a) => Module Natural (Tropical a)

Eq a => Eq (Tropical a)

Ord a => Ord (Tropical a)

Read a => Read (Tropical a)

Show a => Show (Tropical a)

Arbitrary a => Arbitrary (Tropical a)

CoArbitrary a => CoArbitrary (Tropical a)

Ord a => Monoid (Tropical a)

Num a => Multiplicative (Tropical a)

(Ord a, Num a) => SemiRing (Tropical a)

(Ord a, Num a) => RightSemiNearRing (Tropical a)

(Ord a, Num a) => LeftSemiNearRing (Tropical a)

(Ord a, Num a) => Ringoid (Tropical a)

Ord a => Reducer (Maybe a) (Tropical a)

Ord a => Reducer (MinPriority a) (Tropical a)

(Ord a, Num a) => Bimodule (Tropical a) (Tropical a)

(Ord a, Num a) => RightModule (Tropical a) (Tropical a)

(Ord a, Num a) => LeftModule (Tropical a) (Tropical a)

(Ord a, Num a) => Module (Tropical a) (Tropical a)

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