Copyright	(c) The University of Glasgow 2001
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Stability	stable
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.Ratio

Description

Standard functions on rational numbers

Synopsis

Documentation

data Ratio aSource

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)
Typeable (* -> *) Ratio

type Rational = Ratio Integer Source

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 -> Rational Source

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.