algebra-4.1: Constructive abstract algebra

Numeric.Field.Fraction

Synopsis

# Documentation

data Fraction d Source

Fraction field `k(D)` of `Euclidean` domain `D`.

Instances

 Euclidean d => RightModule Integer (Fraction d) Euclidean d => RightModule Natural (Fraction d) Euclidean d => LeftModule Integer (Fraction d) Euclidean d => LeftModule Natural (Fraction d) (Eq d, Multiplicative d) => Eq (Fraction d) (Ord d, Multiplicative d) => Ord (Fraction d) (Eq d, Show d, Unital d) => Show (Fraction d) Euclidean d => Abelian (Fraction d) Euclidean d => Additive (Fraction d) Euclidean d => Monoidal (Fraction d) Euclidean d => Semiring (Fraction d) Euclidean d => Multiplicative (Fraction d) Euclidean d => Group (Fraction d) Euclidean d => Unital (Fraction d) Euclidean d => Division (Fraction d) Euclidean d => DecidableUnits (Fraction d) Euclidean d => DecidableZero (Fraction d) Euclidean d => Rig (Fraction d) (Characteristic d, Euclidean d) => Characteristic (Fraction d) Euclidean d => Ring (Fraction d) Euclidean d => IntegralSemiring (Fraction d) (Commutative d, Euclidean d) => Commutative (Fraction d)

type Ratio = FractionSource

Convenient synonym for `Fraction`.

(%) :: Euclidean d => d -> d -> Fraction dSource

lcm :: Euclidean r => r -> r -> rSource