Number.Ratio

Ratios of mathematical objects.

Documentation

data T a

Constructors

(:%)

Fields

• numerator :: !a
• denominator :: !a

Instances

C a => C Integer (T a)

Defined in Algebra.Module

Methods

(*>) :: Integer -> T a -> T a

Eq a => Eq (T a)

Defined in Number.Ratio

Methods

(==) :: T a -> T a -> Bool

(/=) :: T a -> T a -> Bool

Integral a => Fractional (T a)

Defined in Number.Ratio

Methods

(/) :: T a -> T a -> T a

recip :: T a -> T a

fromRational :: Rational -> T a

Integral a => Num (T a)

Defined in Number.Ratio

Methods

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

(*) :: T a -> T a -> T a

negate :: T a -> T a

abs :: T a -> T a

signum :: T a -> T a

fromInteger :: Integer -> T a

(Ord a, C a) => Ord (T a)

Defined in Number.Ratio

Methods

compare :: T a -> T a -> Ordering

(<) :: T a -> T a -> Bool

(<=) :: T a -> T a -> Bool

(>) :: T a -> T a -> Bool

(>=) :: T a -> T a -> Bool

max :: T a -> T a -> T a

min :: T a -> T a -> T a

(Read a, C a) => Read (T a)

Defined in Number.Ratio

Methods

readsPrec :: Int -> ReadS (T a)

readList :: ReadS [T a]

readPrec :: ReadPrec (T a)

readListPrec :: ReadPrec [T a]

(Show a, C a) => Show (T a)

Defined in Number.Ratio

Methods

showsPrec :: Int -> T a -> ShowS

show :: T a -> String

showList :: [T a] -> ShowS

(Arbitrary a, C a, C a) => Arbitrary (T a)

Defined in Number.Ratio

Methods

arbitrary :: Gen (T a)

shrink :: T a -> [T a]

(Storable a, C a) => Storable (T a)

Defined in Number.Ratio

Methods

sizeOf :: T a -> Int

alignment :: T a -> Int

peekElemOff :: Ptr (T a) -> Int -> IO (T a)

pokeElemOff :: Ptr (T a) -> Int -> T a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (T a)

pokeByteOff :: Ptr b -> Int -> T a -> IO ()

peek :: Ptr (T a) -> IO (T a)

poke :: Ptr (T a) -> T a -> IO ()

(Random a, C a, C a) => Random (T a)

Defined in Number.Ratio

Methods

randomR :: RandomGen g => (T a, T a) -> g -> (T a, g)

random :: RandomGen g => g -> (T a, g)

randomRs :: RandomGen g => (T a, T a) -> g -> [T a]

randoms :: RandomGen g => g -> [T a]

(Ord a, C a) => C (T a)

Defined in Number.Ratio

Methods

compare :: T a -> T a -> Ordering

C a => C (T a)

Defined in Number.Ratio

Methods

zero :: T a

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

negate :: T a -> T a

(C a, C a) => C (T a)

Defined in Number.Ratio

Methods

isZero :: T a -> Bool

C a => C (T a)

Defined in Number.Ratio

Methods

(*) :: T a -> T a -> T a

one :: T a

fromInteger :: Integer -> T a

(^) :: T a -> Integer -> T a

(C a, C a) => C (T a)

Defined in Number.Ratio

Methods

abs :: T a -> T a

signum :: T a -> T a

C a => C (T a)

Defined in Algebra.Field

Methods

(/) :: T a -> T a -> T a

recip :: T a -> T a

fromRational' :: Rational -> T a

(^-) :: T a -> Integer -> T a

(C a, C a) => C (T a)

Defined in Algebra.ToInteger

Methods

toRational :: T a -> Rational

(C a, C a) => C (T a)

Defined in Algebra.RealRing

Methods

splitFraction :: C b => T a -> (b, T a)

fraction :: T a -> T a

ceiling :: C b => T a -> b

floor :: C b => T a -> b

truncate :: C b => T a -> b

round :: C b => T a -> b

(C a, C a) => C (T a)

Defined in Algebra.RealField

(Ord a, C a) => C (T a)

Defined in Algebra.Lattice

Methods

up :: T a -> T a -> T a

dn :: T a -> T a -> T a

C a => C (T a) (T a)

Defined in Algebra.Module

Methods

(*>) :: T a -> T a -> T a

C a => C (T a) (T a)

Defined in Algebra.VectorSpace

C a => C (T a) (T a)

Defined in Algebra.ModuleBasis

Methods

basis :: T a -> [T a]

flatten :: T a -> [T a]

dimension :: T a -> T a -> Int

(C a, C a) => C (T a) (T a)

Defined in Algebra.NormedSpace.Sum

Methods

norm :: T a -> T a

(C a, C a, C a) => C (T a) (T a)

Defined in Algebra.NormedSpace.Maximum

Methods

norm :: T a -> T a

(C a, C a) => Sqr (T a) (T a)

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: T a -> T a

(%) :: C a => a -> a -> T a infixl 7

type Rational = T Integer

fromValue :: C a => a -> T a

recip :: (C a, C a) => T a -> T a

scale :: C a => a -> T a -> T a

split :: C a => T a -> (a, T a)

similar to splitFraction

showsPrecAuto :: (Eq a, C a, Show a) => Int -> T a -> String -> String

This is an alternative show method that is more user-friendly but also potentially more ambigious.

toRational98 :: Integral a => T a -> Ratio a

Necessary when mixing NumericPrelude.Numeric Rationals with Prelude98 Rationals