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Ratio
Synopsis
data Integral a => 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 Integral a => Ratio a Source
Rational numbers, with numerator and denominator of some Integral type.
show/hide Instances
type Rational = Ratio IntegerSource
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 aSource
Forms the ratio of two integral numbers.
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

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

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