Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Ratio

Synopsis

data Ratio a
type Rational = Ratio Integer
(%) :: Integral a => a -> a -> Ratio a
numerator :: Ratio a -> a
denominator :: Ratio a -> a
approxRational :: RealFrac a => a -> a -> Rational

Documentation

data Ratio a #

Rational numbers, with numerator and denominator of some Integral type.

Instances

Instances details

Integral a => Enum (Ratio a) #
Instance details Defined in NumHierarchy Methods succ :: Ratio a -> Ratio a # pred :: Ratio a -> Ratio a # toEnum :: Int -> Ratio a # fromEnum :: Ratio a -> Int # enumFrom :: Ratio a -> [Ratio a] # enumFromThen :: Ratio a -> Ratio a -> [Ratio a] # enumFromTo :: Ratio a -> Ratio a -> [Ratio a] # enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #
Integral a => Eq (Ratio a) #
Instance details Defined in NumHierarchy Methods (==) :: Ratio a -> Ratio a -> Bool # (/=) :: Ratio a -> Ratio a -> Bool #
Integral a => Ord (Ratio a) #
Instance details Defined in NumHierarchy Methods compare :: Ratio a -> Ratio a -> Ordering # (<) :: Ratio a -> Ratio a -> Bool # (<=) :: Ratio a -> Ratio a -> Bool # (>=) :: Ratio a -> Ratio a -> Bool # (>) :: Ratio a -> Ratio a -> Bool # max :: Ratio a -> Ratio a -> Ratio a # min :: Ratio a -> Ratio a -> Ratio a #
Integral a => Fractional (Ratio a) #
Instance details Defined in NumHierarchy Methods (/) :: Ratio a -> Ratio a -> Ratio a # recip :: Ratio a -> Ratio a # fromRational :: Rational -> Ratio a #
Integral a => Num (Ratio a) #
Instance details Defined in NumHierarchy Methods (+) :: Ratio a -> Ratio a -> Ratio a # (-) :: Ratio a -> Ratio a -> Ratio a # (*) :: Ratio a -> Ratio a -> Ratio a # negate :: Ratio a -> Ratio a # abs :: Ratio a -> Ratio a # signum :: Ratio a -> Ratio a # fromInteger :: Integer -> Ratio a #
Integral a => Real (Ratio a) #
Instance details Defined in NumHierarchy Methods toRational :: Ratio a -> Rational #
Integral a => RealFrac (Ratio a) #
Instance details Defined in NumHierarchy Methods properFraction :: Integral b => Ratio a -> (b, Ratio a) # truncate :: Integral b => Ratio a -> b # round :: Integral b => Ratio a -> b # ceiling :: Integral b => Ratio a -> b # floor :: Integral b => Ratio a -> b #
(Integral a, Read a) => Read (Ratio a) #
Instance details Defined in NumHierarchy Methods readsPrec :: Int -> ReadS (Ratio a) # readList :: ReadS [Ratio a] #
Integral a => Show (Ratio a) #
Instance details Defined in NumHierarchy Methods showsPrec :: Int -> Ratio a -> ShowS # show :: Ratio a -> String # showList :: [Ratio a] -> ShowS #

type Rational = Ratio Integer #

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

(%) :: Integral a => a -> a -> Ratio a infixl 7 #

Forms the ratio of two integral numbers.

numerator :: Ratio a -> a #

Extract the numerator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

denominator :: Ratio a -> a #

Extract the denominator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

approxRational :: RealFrac a => a -> a -> Rational #

approxRational, applied to two real fractional numbers x and epsilon, returns the simplest rational number within epsilon of x. A rational number y is said to be simpler than another y’ if

abs (numerator y) <= abs (numerator y’), and
denominator y <= denominator y’.

Any real interval contains a unique simplest rational; in particular, note that 0/1 is the simplest rational of all.