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 |
Standard functions on rational numbers
Documentation
Rational numbers, with numerator and denominator of some Integral
type.
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 # | |
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 :: (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.