base-4.6.0.0: Basic libraries

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) (Num (Ratio a), Integral a) => Fractional (Ratio a) (Typeable (Ratio a), Data a, Integral a) => Data (Ratio a) Integral a => Num (Ratio a) (Eq (Ratio a), Integral a) => Ord (Ratio a) (Integral a, Read a) => Read (Ratio a) (Num (Ratio a), Ord (Ratio a), Integral a) => Real (Ratio a) (Real (Ratio a), Fractional (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

• `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.