Data.Ratio

Copyright (c) The University of Glasgow 2001
License BSD-style (see the file libraries/base/LICENSE)
Maintainer [email protected]
Stability stable
Portability portable
Safe Haskell Safe
Language Haskell2010

Description

Standard functions on rational numbers

data Ratio a Source

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

Instances

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)
(Storable a, Integral a) => Storable (Ratio a)

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 a infixl 7 Source

Forms the ratio of two integral numbers.

numerator :: Integral a => Ratio a -> a Source

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 Source

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

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

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/7.10.3/docs/html/libraries/base-4.8.2.0/Data-Ratio.html