Portability  portable 

Stability  stable 
Maintainer  libraries@haskell.org 
Safe Haskell  Safe 
Standard functions on rational numbers
Documentation
Rational numbers, with numerator and denominator of some Integral
type.
Typeable1 Ratio  
Integral a => Enum (Ratio a)  
Eq a => Eq (Ratio a)  
(Num (Ratio a), Integral a) => Fractional (Ratio a)  
(Typeable (Ratio a), Data a, Integral a) => Data (Ratio a)  
Integral a => Num (Ratio a)  
(Eq (Ratio a), Integral a) => Ord (Ratio a)  
(Integral a, Read a) => Read (Ratio a)  
(Num (Ratio a), Ord (Ratio a), Integral a) => Real (Ratio a)  
(Real (Ratio a), Fractional (Ratio a), Integral a) => RealFrac (Ratio a)  
(Integral a, Show a) => Show (Ratio a) 
numerator :: Integral a => Ratio a > aSource
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 > aSource
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 > RationalSource
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

, andabs
(numerator
y) <=abs
(numerator
y') 
.denominator
y <=denominator
y'
Any real interval contains a unique simplest rational;
in particular, note that 0/1
is the simplest rational of all.