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 |
Standard functions on rational numbers
Documentation
Rational numbers, with numerator and denominator of some Integral
type.
Integral a => Enum (Ratio a) # | Since: 2.0.1 |
Eq a => Eq (Ratio a) # | |
Integral a => Fractional (Ratio a) # | Since: 2.0.1 |
(Data a, Integral a) => Data (Ratio a) # | Since: 4.0.0.0 |
Integral a => Num (Ratio a) # | Since: 2.0.1 |
Integral a => Ord (Ratio a) # | Since: 2.0.1 |
(Integral a, Read a) => Read (Ratio a) # | Since: 2.1 |
Integral a => Real (Ratio a) # | Since: 2.0.1 |
Integral a => RealFrac (Ratio a) # | Since: 2.0.1 |
Show a => Show (Ratio a) # | Since: 2.0.1 |
(Storable a, Integral a) => Storable (Ratio a) # | Since: 4.8.0.0 |
numerator :: 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 :: 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
, andabs
(numerator
y) <=abs
(numerator
y')
.denominator
y <=denominator
y'
Any real interval contains a unique simplest rational;
in particular, note that 0/1
is the simplest rational of all.