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

, 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.