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.
Note that Ratio
's instances inherit the deficiencies from the type
parameter's. For example, Ratio Natural
's Num
instance has similar
problems to Natural
's.
Instances
Integral a => Enum (Ratio a) Source # | Since: base-2.0.1 |
Defined in GHC.Real succ :: Ratio a -> Ratio a Source # pred :: Ratio a -> Ratio a Source # toEnum :: Int -> Ratio a Source # fromEnum :: Ratio a -> Int Source # enumFrom :: Ratio a -> [Ratio a] Source # enumFromThen :: Ratio a -> Ratio a -> [Ratio a] Source # enumFromTo :: Ratio a -> Ratio a -> [Ratio a] Source # enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] Source # | |
Eq a => Eq (Ratio a) Source # | Since: base-2.1 |
Integral a => Fractional (Ratio a) Source # | Since: base-2.0.1 |
(Data a, Integral a) => Data (Ratio a) Source # | Since: base-4.0.0.0 |
Defined in Data.Data gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ratio a -> c (Ratio a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ratio a) Source # toConstr :: Ratio a -> Constr Source # dataTypeOf :: Ratio a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ratio a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ratio a)) Source # gmapT :: (forall b. Data b => b -> b) -> Ratio a -> Ratio a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Ratio a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ratio a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) Source # | |
Integral a => Num (Ratio a) Source # | Since: base-2.0.1 |
Defined in GHC.Real | |
Integral a => Ord (Ratio a) Source # | Since: base-2.0.1 |
(Integral a, Read a) => Read (Ratio a) Source # | Since: base-2.1 |
Integral a => Real (Ratio a) Source # | Since: base-2.0.1 |
Integral a => RealFrac (Ratio a) Source # | Since: base-2.0.1 |
Show a => Show (Ratio a) Source # | Since: base-2.0.1 |
(Storable a, Integral a) => Storable (Ratio a) Source # | Since: base-4.8.0.0 |
Defined in Foreign.Storable sizeOf :: Ratio a -> Int Source # alignment :: Ratio a -> Int Source # peekElemOff :: Ptr (Ratio a) -> Int -> IO (Ratio a) Source # pokeElemOff :: Ptr (Ratio a) -> Int -> Ratio a -> IO () Source # peekByteOff :: Ptr b -> Int -> IO (Ratio a) Source # pokeByteOff :: Ptr b -> Int -> Ratio a -> IO () Source # |
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.