base-4.3.1.0: Basic libraries

Portability | portable
Stability | stable
Maintainer | libraries@haskell.org

Data.Ratio

Description

Standard functions on rational numbers

Synopsis

- data Integral a => Ratio a
- type Rational = Ratio Integer
- (%) :: Integral a => a -> a -> Ratio a
- numerator :: Integral a => Ratio a -> a
- denominator :: Integral a => Ratio a -> a
- approxRational :: RealFrac a => a -> a -> Rational

# Documentation

data Integral a => Ratio a

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

Instances

Typeable1 Ratio |
Integral a => Enum (Ratio a) |
Integral 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.