base-4.11.1.0: Basic libraries

Data.Ratio

Description

Standard functions on rational numbers

Synopsis

# Documentation

data Ratio a Source #

Rational numbers, with numerator and denominator of some Integral type.

Instances
 Integral a => Enum (Ratio a) # Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodssucc :: Ratio a -> Ratio a Source #pred :: Ratio a -> 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) # Instance detailsDefined in GHC.Real Methods(==) :: Ratio a -> Ratio a -> Bool Source #(/=) :: Ratio a -> Ratio a -> Bool Source # Integral a => Fractional (Ratio a) # Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods(/) :: Ratio a -> Ratio a -> Ratio a Source #recip :: Ratio a -> Ratio a Source # (Data a, Integral a) => Data (Ratio a) # Since: base-4.0.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (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 #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) # Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods(+) :: Ratio a -> Ratio a -> Ratio a Source #(-) :: Ratio a -> Ratio a -> Ratio a Source #(*) :: Ratio a -> Ratio a -> Ratio a Source #negate :: Ratio a -> Ratio a Source #abs :: Ratio a -> Ratio a Source #signum :: Ratio a -> Ratio a Source # Integral a => Ord (Ratio a) # Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodscompare :: Ratio a -> Ratio a -> Ordering Source #(<) :: Ratio a -> Ratio a -> Bool Source #(<=) :: Ratio a -> Ratio a -> Bool Source #(>) :: Ratio a -> Ratio a -> Bool Source #(>=) :: Ratio a -> Ratio a -> Bool Source #max :: Ratio a -> Ratio a -> Ratio a Source #min :: Ratio a -> Ratio a -> Ratio a Source # (Integral a, Read a) => Read (Ratio a) # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Integral a => Real (Ratio a) # Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Integral a => RealFrac (Ratio a) # Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsproperFraction :: Integral b => Ratio a -> (b, Ratio a) Source #truncate :: Integral b => Ratio a -> b Source #round :: Integral b => Ratio a -> b Source #ceiling :: Integral b => Ratio a -> b Source #floor :: Integral b => Ratio a -> b Source # Show a => Show (Ratio a) # Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsshowsPrec :: Int -> Ratio a -> ShowS Source #show :: Ratio a -> String Source #showList :: [Ratio a] -> ShowS Source # (Storable a, Integral a) => Storable (Ratio a) # Since: base-4.8.0.0 Instance detailsDefined in Foreign.Storable MethodssizeOf :: 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 #peek :: Ptr (Ratio a) -> IO (Ratio a) Source #poke :: Ptr (Ratio a) -> Ratio a -> IO () Source #

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

(%) :: Integral a => a -> a -> Ratio a infixl 7 Source #

Forms the ratio of two integral numbers.

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

• abs (numerator y) <= abs (numerator y'), and
• denominator y <= denominator y'.

Any real interval contains a unique simplest rational; in particular, note that 0/1 is the simplest rational of all.