Data.Ratio
 Portability portable Stability stable Maintainer libraries@haskell.org
Description
Standard functions on rational numbers
Synopsis
 data Ratio a type Rational = Ratio Integer (%) :: Integral a => a -> a -> Ratio a numerator :: Integral a => Ratio a -> a denominator :: Integral a => Ratio a -> a approxRational :: RealFrac a => a -> a -> Rational
Documentation
data Ratio a
Rational numbers, with numerator and denominator of some Integral type.
Instances
 Typeable1 Ratio (Data a, Integral a) => Data (Ratio a) Integral a => Enum (Ratio a) (Integral a, Eq a) => Eq (Ratio a) Integral a => Fractional (Ratio a) (Integral a, NFData a) => NFData (Ratio a) Integral a => Num (Ratio a) Integral a => Ord (Ratio a) (Integral a, Read a) => Read (Ratio a) Integral a => Real (Ratio a) Integral a => RealFrac (Ratio a) Integral a => Show (Ratio a)
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
Forms the ratio of two integral numbers.
numerator :: Integral a => 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 :: Integral a => 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

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