base-4.6.0.1: Basic libraries

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Data.Ratio

Description

Standard functions on rational numbers

Synopsis

# Documentation

data Ratio a Source

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 a) => Show (Ratio a)

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.