Safe Haskell	Safe
Language	Haskell98

Numeric.Field.Fraction

Synopsis

Documentation

data Fraction d #

Fraction field k(D) of GCDDomain domain D.

Instances

GCDDomain d => RightModule Integer (Fraction d) #
Methods (*.) :: Fraction d -> Integer -> Fraction d #
GCDDomain d => RightModule Natural (Fraction d) #
Methods (*.) :: Fraction d -> Natural -> Fraction d #
GCDDomain d => LeftModule Integer (Fraction d) #
Methods (.*) :: Integer -> Fraction d -> Fraction d #
GCDDomain d => LeftModule Natural (Fraction d) #
Methods (.*) :: Natural -> Fraction d -> Fraction d #
(Eq d, GCDDomain d) => Eq (Fraction d) #
Methods (==) :: Fraction d -> Fraction d -> Bool # (/=) :: Fraction d -> Fraction d -> Bool #
(Ord d, GCDDomain d) => Ord (Fraction d) #
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 #
(Eq d, Show d, Unital d) => Show (Fraction d) #
Methods showsPrec :: Int -> Fraction d -> ShowS # show :: Fraction d -> String # showList :: [Fraction d] -> ShowS #
GCDDomain d => Abelian (Fraction d) #

GCDDomain d => Additive (Fraction d) #
Methods (+) :: Fraction d -> Fraction d -> Fraction d # sinnum1p :: Natural -> Fraction d -> Fraction d # sumWith1 :: Foldable1 f => (a -> Fraction d) -> f a -> Fraction d #
GCDDomain d => Monoidal (Fraction d) #
Methods zero :: Fraction d # sinnum :: Natural -> Fraction d -> Fraction d # sumWith :: Foldable f => (a -> Fraction d) -> f a -> Fraction d #
GCDDomain d => Semiring (Fraction d) #

GCDDomain d => Multiplicative (Fraction d) #
Methods (*) :: Fraction d -> Fraction d -> Fraction d # pow1p :: Fraction d -> Natural -> Fraction d # productWith1 :: Foldable1 f => (a -> Fraction d) -> f a -> Fraction d #
GCDDomain d => Group (Fraction d) #
Methods (-) :: Fraction d -> Fraction d -> Fraction d # negate :: Fraction d -> Fraction d # subtract :: Fraction d -> Fraction d -> Fraction d # times :: Integral n => n -> Fraction d -> Fraction d #
GCDDomain d => Unital (Fraction d) #
Methods one :: Fraction d # pow :: Fraction d -> Natural -> Fraction d # productWith :: Foldable f => (a -> Fraction d) -> f a -> Fraction d #
GCDDomain d => Division (Fraction d) #
Methods recip :: Fraction d -> Fraction d # (/) :: Fraction d -> Fraction d -> Fraction d # (\\) :: Fraction d -> Fraction d -> Fraction d # (^) :: Integral n => Fraction d -> n -> Fraction d #
GCDDomain d => Commutative (Fraction d) #

GCDDomain d => DecidableAssociates (Fraction d) #
Methods isAssociate :: Fraction d -> Fraction d -> Bool #
GCDDomain d => DecidableUnits (Fraction d) #
Methods recipUnit :: Fraction d -> Maybe (Fraction d) # isUnit :: Fraction d -> Bool # (^?) :: Integral n => Fraction d -> n -> Maybe (Fraction d) #
GCDDomain d => DecidableZero (Fraction d) #
Methods isZero :: Fraction d -> Bool #
GCDDomain d => Rig (Fraction d) #
Methods fromNatural :: Natural -> Fraction d #
(Characteristic d, GCDDomain d) => Characteristic (Fraction d) #
Methods char :: proxy (Fraction d) -> Natural #
GCDDomain d => Ring (Fraction d) #
Methods fromInteger :: Integer -> Fraction d #
GCDDomain d => ZeroProductSemiring (Fraction d) #

GCDDomain d => UnitNormalForm (Fraction d) #
Methods splitUnit :: Fraction d -> (Fraction d, Fraction d) #
GCDDomain d => Euclidean (Fraction d) #
Methods degree :: Fraction d -> Maybe Natural # divide :: Fraction d -> Fraction d -> (Fraction d, Fraction d) # quot :: Fraction d -> Fraction d -> Fraction d # rem :: Fraction d -> Fraction d -> Fraction d #
GCDDomain d => PID (Fraction d) #
Methods egcd :: Fraction d -> Fraction d -> (Fraction d, Fraction d, Fraction d) #
GCDDomain d => UFD (Fraction d) #

GCDDomain d => GCDDomain (Fraction d) #
Methods gcd :: Fraction d -> Fraction d -> Fraction d # reduceFraction :: Fraction d -> Fraction d -> (Fraction d, Fraction d) # lcm :: Fraction d -> Fraction d -> Fraction d #
GCDDomain d => IntegralDomain (Fraction d) #
Methods divides :: Fraction d -> Fraction d -> Bool # maybeQuot :: Fraction d -> Fraction d -> Maybe (Fraction d) #

numerator :: Fraction t -> t #

denominator :: Fraction t -> t #

type Ratio = Fraction #

Convenient synonym for Fraction.

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