Data.Ratio

Standard functions on rational numbers

Documentation

data Ratio a

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

Instances

Typeable1 Ratio

Integral a => Enum (Ratio a)

Eq a => Eq (Ratio a)

Integral a => Fractional (Ratio a)

(Data a, Integral a) => Data (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 (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

• abs (numerator y) <= abs (numerator y'), and
• denominator y <= denominator y'.

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