Safe Haskell	Safe-Inferred
Language	Haskell98

Numeric.Field.Fraction

Synopsis

data Fraction d
numerator :: Fraction t -> t
denominator :: Fraction t -> t
type Ratio = Fraction
(%) :: GCDDomain d => d -> d -> Fraction d

Documentation

data Fraction d Source #

Fraction field k(D) of GCDDomain domain D.

Instances

Instances details

GCDDomain d => LeftModule Integer (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods (.*) :: Integer -> Fraction d -> Fraction d Source #
GCDDomain d => LeftModule Natural (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods (.*) :: Natural -> Fraction d -> Fraction d Source #
GCDDomain d => RightModule Integer (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods (*.) :: Fraction d -> Integer -> Fraction d Source #
GCDDomain d => RightModule Natural (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods (*.) :: Fraction d -> Natural -> Fraction d Source #
GCDDomain d => Abelian (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction
GCDDomain d => Additive (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods (+) :: Fraction d -> Fraction d -> Fraction d Source # sinnum1p :: Natural -> Fraction d -> Fraction d Source # sumWith1 :: Foldable1 f => (a -> Fraction d) -> f a -> Fraction d Source #
GCDDomain d => Group (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods (-) :: Fraction d -> Fraction d -> Fraction d Source # negate :: Fraction d -> Fraction d Source # subtract :: Fraction d -> Fraction d -> Fraction d Source # times :: Integral n => n -> Fraction d -> Fraction d Source #
GCDDomain d => Monoidal (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods zero :: Fraction d Source # sinnum :: Natural -> Fraction d -> Fraction d Source # sumWith :: Foldable f => (a -> Fraction d) -> f a -> Fraction d Source #
GCDDomain d => Multiplicative (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods (*) :: Fraction d -> Fraction d -> Fraction d Source # pow1p :: Fraction d -> Natural -> Fraction d Source # productWith1 :: Foldable1 f => (a -> Fraction d) -> f a -> Fraction d Source #
GCDDomain d => Semiring (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction
GCDDomain d => Commutative (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction
GCDDomain d => Division (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods recip :: Fraction d -> Fraction d Source # (/) :: Fraction d -> Fraction d -> Fraction d Source # (\\) :: Fraction d -> Fraction d -> Fraction d Source # (^) :: Integral n => Fraction d -> n -> Fraction d Source #
GCDDomain d => Unital (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods one :: Fraction d Source # pow :: Fraction d -> Natural -> Fraction d Source # productWith :: Foldable f => (a -> Fraction d) -> f a -> Fraction d Source #
GCDDomain d => UnitNormalForm (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods splitUnit :: Fraction d -> (Fraction d, Fraction d) Source #
GCDDomain d => DecidableAssociates (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods isAssociate :: Fraction d -> Fraction d -> Bool Source #
GCDDomain d => DecidableUnits (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods recipUnit :: Fraction d -> Maybe (Fraction d) Source # isUnit :: Fraction d -> Bool Source # (^?) :: Integral n => Fraction d -> n -> Maybe (Fraction d) Source #
GCDDomain d => DecidableZero (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods isZero :: Fraction d -> Bool Source #
GCDDomain d => Euclidean (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods degree :: Fraction d -> Maybe Natural Source # divide :: Fraction d -> Fraction d -> (Fraction d, Fraction d) Source # quot :: Fraction d -> Fraction d -> Fraction d Source # rem :: Fraction d -> Fraction d -> Fraction d Source #
GCDDomain d => GCDDomain (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods gcd :: Fraction d -> Fraction d -> Fraction d Source # reduceFraction :: Fraction d -> Fraction d -> (Fraction d, Fraction d) Source # lcm :: Fraction d -> Fraction d -> Fraction d Source #
GCDDomain d => IntegralDomain (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods divides :: Fraction d -> Fraction d -> Bool Source # maybeQuot :: Fraction d -> Fraction d -> Maybe (Fraction d) Source #
GCDDomain d => PID (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods egcd :: Fraction d -> Fraction d -> (Fraction d, Fraction d, Fraction d) Source #
GCDDomain d => UFD (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction
(Characteristic d, GCDDomain d) => Characteristic (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods char :: proxy (Fraction d) -> Natural Source #
GCDDomain d => Rig (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods fromNatural :: Natural -> Fraction d Source #
GCDDomain d => Ring (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods fromInteger :: Integer -> Fraction d Source #
GCDDomain d => ZeroProductSemiring (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction
(Eq d, Show d, Unital d) => Show (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods showsPrec :: Int -> Fraction d -> ShowS # show :: Fraction d -> String # showList :: [Fraction d] -> ShowS #
(Eq d, GCDDomain d) => Eq (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods (==) :: Fraction d -> Fraction d -> Bool # (/=) :: Fraction d -> Fraction d -> Bool #
(Ord d, GCDDomain d) => Ord (Fraction d) Source #
Instance details Defined in Numeric.Field.Fraction Methods compare :: Fraction d -> Fraction d -> Ordering # (<) :: Fraction d -> Fraction d -> Bool # (<=) :: Fraction d -> Fraction d -> Bool # (>) :: Fraction d -> Fraction d -> Bool # (>=) :: Fraction d -> Fraction d -> Bool # max :: Fraction d -> Fraction d -> Fraction d # min :: Fraction d -> Fraction d -> Fraction d #

numerator :: Fraction t -> t Source #

denominator :: Fraction t -> t Source #

type Ratio = Fraction Source #

Convenient synonym for Fraction.

(%) :: GCDDomain d => d -> d -> Fraction d infixl 7 Source #