Haskell Hierarchical Libraries (base package)ContentsIndex
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
(Integral a, NFData a) => NFData (Ratio a)
(Data a, Integral a) => Data (Ratio a)
Typeable1 Ratio
(Integral a, Read a) => Read (Ratio a)
Integral a => Ord (Ratio a)
Integral a => Num (Ratio a)
Integral a => Fractional (Ratio a)
Integral a => Real (Ratio a)
Integral a => RealFrac (Ratio a)
Integral a => Show (Ratio a)
Integral a => Enum (Ratio a)
(Integral a, Eq a) => Eq (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.

Produced by Haddock version 0.6