| Portability | portable |
|---|---|
| Stability | stable |
| Maintainer | libraries@haskell.org |
| Safe Haskell | Safe |
Data.Ratio
Description
Standard functions on rational numbers
Documentation
data Ratio a
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) |
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
-
, andabs(numeratory) <=abs(numeratory') -
.denominatory <=denominatory'
Any real interval contains a unique simplest rational;
in particular, note that 0/1 is the simplest rational of all.