Copyright	(c) Henning Thielemann 2011-2012 (c) Dylan Thurston 2006
Maintainer	numericprelude@henning-thielemann.de
Stability	provisional
Portability	portable (?)
Safe Haskell	None
Language	Haskell98

Number.Ratio

Description

Ratios of mathematical objects.

Synopsis

data T a = (:%) {
- numerator :: !a
- denominator :: !a
}
(%) :: C a => a -> a -> T a
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)
showsPrecAuto :: (Eq a, C a, Show a) => Int -> T a -> String -> String
toRational98 :: Integral a => T a -> Ratio a

Documentation

data T a Source #

Constructors

(:%)
Fields numerator :: !a denominator :: !a

Instances

C a => C Integer (T a) Source #
Instance details Defined in Algebra.Module Methods (*>) :: Integer -> T a -> T a Source #
Eq a => Eq (T a) Source #
Instance details Defined in Number.Ratio Methods (==) :: T a -> T a -> Bool # (/=) :: T a -> T a -> Bool #
Integral a => Fractional (T a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Number.Ratio Methods arbitrary :: Gen (T a) # shrink :: T a -> [T a] #
(Storable a, C a) => Storable (T a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Number.Ratio Methods compare :: T a -> T a -> Ordering Source #
C a => C (T a) Source #
Instance details Defined in Number.Ratio Methods zero :: T a Source # (+) :: T a -> T a -> T a Source # (-) :: T a -> T a -> T a Source # negate :: T a -> T a Source #
(C a, C a) => C (T a) Source #
Instance details Defined in Number.Ratio Methods isZero :: T a -> Bool Source #
C a => C (T a) Source #
Instance details Defined in Number.Ratio Methods (*) :: T a -> T a -> T a Source # one :: T a Source # fromInteger :: Integer -> T a Source # (^) :: T a -> Integer -> T a Source #
(C a, C a) => C (T a) Source #
Instance details Defined in Number.Ratio Methods abs :: T a -> T a Source # signum :: T a -> T a Source #
C a => C (T a) Source #
Instance details Defined in Algebra.Field Methods (/) :: T a -> T a -> T a Source # recip :: T a -> T a Source # fromRational' :: Rational -> T a Source # (^-) :: T a -> Integer -> T a Source #
(C a, C a) => C (T a) Source #
Instance details Defined in Algebra.ToInteger Methods toRational :: T a -> Rational Source #
(C a, C a) => C (T a) Source #
Instance details Defined in Algebra.RealRing Methods splitFraction :: C b => T a -> (b, T a) Source # fraction :: T a -> T a Source # ceiling :: C b => T a -> b Source # floor :: C b => T a -> b Source # truncate :: C b => T a -> b Source # round :: C b => T a -> b Source #
(C a, C a) => C (T a) Source #
Instance details Defined in Algebra.RealField
(Ord a, C a) => C (T a) Source #
Instance details Defined in Algebra.Lattice Methods up :: T a -> T a -> T a Source # dn :: T a -> T a -> T a Source #
C a => C (T a) (T a) Source #
Instance details Defined in Algebra.Module Methods (*>) :: T a -> T a -> T a Source #
C a => C (T a) (T a) Source #
Instance details Defined in Algebra.VectorSpace
C a => C (T a) (T a) Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: T a -> [T a] Source # flatten :: T a -> [T a] Source # dimension :: T a -> T a -> Int Source #
(C a, C a) => C (T a) (T a) Source #
Instance details Defined in Algebra.NormedSpace.Sum Methods norm :: T a -> T a Source #
(C a, C a, C a) => C (T a) (T a) Source #
Instance details Defined in Algebra.NormedSpace.Maximum Methods norm :: T a -> T a Source #
(C a, C a) => Sqr (T a) (T a) Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: T a -> T a Source #

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

type Rational = T Integer Source #

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

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

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

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

similar to splitFraction

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

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

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

Necessary when mixing NumericPrelude.Numeric Rationals with Prelude98 Rationals