Portability  portable 

Stability  stable 
Maintainer  libraries@haskell.org 
Safe Haskell  SafeInfered 
Standard functions on rational numbers.
This version uses the same type as Data.Ratio, but with components
generalized from Integral
to EuclideanDomain
. However using the
same type means we have the old, more constrained, instances of Ord
,
Show
and Read
.
 data Ratio a
 type Rational = Ratio Integer
 (%) :: EuclideanDomain a => a > a > Ratio a
 numerator :: EuclideanDomain a => Ratio a > a
 denominator :: EuclideanDomain a => Ratio a > a
 approxRational :: RealFrac a => a > a > Rational
Documentation
data Ratio a
Rational numbers, with numerator and denominator of some Integral
type.
Integral a => Enum (Ratio a)  
Eq a => Eq (Ratio a)  
Integral a => Fractional (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 a) => Show (Ratio a)  
EuclideanDomain a => Field (Ratio a)  
EuclideanDomain a => Ring (Ratio a)  
EuclideanDomain a => AbelianGroup (Ratio a)  
(Integral a, Integral a) => RealFrac (Ratio a)  
(Integral a, Integral a) => Fractional (Ratio a)  
(Integral a, Integral a) => Real (Ratio a)  
(Integral a, Integral a) => Num (Ratio a) 
(%) :: EuclideanDomain a => a > a > Ratio aSource
Forms the ratio of two values in a Euclidean domain (e.g. Integer
).
numerator :: EuclideanDomain 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 :: EuclideanDomain 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.