Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
Documentation
Rational numbers, with numerator and denominator of some Integral
type.
Instances
NFData1 Ratio | Available on Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Integral a => Enum (Ratio a) | Since: base-2.0.1 |
Eq a => Eq (Ratio a) | |
Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
(Data a, Integral a) => Data (Ratio a) | 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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ratio a) # toConstr :: Ratio a -> Constr # dataTypeOf :: Ratio a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ratio a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ratio a)) # gmapT :: (forall b. Data b => b -> b) -> Ratio a -> Ratio a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r # gmapQ :: (forall d. Data d => d -> u) -> Ratio a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ratio a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) # | |
Integral a => Num (Ratio a) | Since: base-2.0.1 |
Integral a => Ord (Ratio a) | Since: base-2.0.1 |
(Integral a, Read a) => Read (Ratio a) | Since: base-2.1 |
Integral a => Real (Ratio a) | Since: base-2.0.1 |
Defined in GHC.Real toRational :: Ratio a -> Rational # | |
Integral a => RealFrac (Ratio a) | Since: base-2.0.1 |
Show a => Show (Ratio a) | Since: base-2.0.1 |
Integral a => Lift (Ratio a) | |
Hashable a => Hashable (Ratio a) | |
Defined in Data.Hashable.Class | |
(ToJSON a, Integral a) => ToJSON (Ratio a) | |
Defined in Data.Aeson.Types.ToJSON | |
(FromJSON a, Integral a) => FromJSON (Ratio a) | |
(Storable a, Integral a) => Storable (Ratio a) | Since: base-4.8.0.0 |
NFData a => NFData (Ratio a) | |
Defined in Control.DeepSeq | |
(Serialise a, Integral a) => Serialise (Ratio a) | Since: serialise-0.2.0.0 |
(Eq a) :=> (Eq (Ratio a)) | |
(Integral a) :=> (RealFrac (Ratio a)) | |
(Integral a) :=> (Real (Ratio a)) | |
(Integral a) :=> (Ord (Ratio a)) | |
(Integral a) :=> (Num (Ratio a)) | |
(Integral a) :=> (Fractional (Ratio a)) | |
Defined in Data.Constraint | |
(Integral a) :=> (Enum (Ratio a)) | |
(Integral a, Show a) :=> (Show (Ratio a)) | |
(Integral a, Read a) :=> (Read (Ratio a)) | |
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 #
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
(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.