# Data.Ratio

#### Description

Standard functions on rational numbers

data Ratio a Source

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

#### Instances

Integral a => Enum (Ratio a)

Since: 2.0.1

#### Methods

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)

#### Methods

(==) :: Ratio a -> Ratio a -> Bool Source

(/=) :: Ratio a -> Ratio a -> Bool Source

Integral a => Fractional (Ratio a)

Since: 2.0.1

#### Methods

(/) :: Ratio a -> Ratio a -> Ratio a Source

recip :: Ratio a -> Ratio a Source

(Data a, Integral a) => Data (Ratio a)

Since: 4.0.0.0

#### Methods

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

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: 2.0.1

#### 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: 2.0.1

#### Methods

compare :: 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

Since: 2.1

#### Methods

Integral a => Real (Ratio a)

Since: 2.0.1

#### Methods

Integral a => RealFrac (Ratio a)

Since: 2.0.1

#### Methods

properFraction :: 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: 2.0.1

#### Methods

showsPrec :: Int -> Ratio a -> ShowS Source

show :: Ratio a -> String Source

showList :: [Ratio a] -> ShowS Source

(Storable a, Integral a) => Storable (Ratio a)

Since: 4.8.0.0

#### Methods

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

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.

© The University of Glasgow and others