Safe Haskell	None
Language	Haskell2010

Algebra.Instances

Contents

Orphan instances

Description

This Library provides some *dangerous* instances for Doubles and Complex.

Orphan instances

Ring Double Source #
Instance details Methods fromInteger :: Integer -> Double
Rig Double Source #
Instance details Methods fromNatural :: Natural -> Double #
DecidableZero Double Source #
Instance details Methods isZero :: Double -> Bool #
Unital Double Source #
Instance details Methods one :: Double # pow :: Double -> Natural -> Double # productWith :: Foldable f => (a -> Double) -> f a -> Double #
Division Double Source #
Instance details Methods recip :: Double -> Double # (/) :: Double -> Double -> Double # (\\) :: Double -> Double -> Double # (^) :: Integral n => Double -> n -> Double
Commutative Double Source #
Instance details
Semiring Double Source #
Instance details
Multiplicative Double Source #
Instance details Methods (*) :: Double -> Double -> Double # pow1p :: Double -> Natural -> Double # productWith1 :: Foldable1 f => (a -> Double) -> f a -> Double #
Monoidal Double Source #
Instance details Methods zero :: Double # sinnum :: Natural -> Double -> Double # sumWith :: Foldable f => (a -> Double) -> f a -> Double #
Group Double Source #
Instance details Methods (-) :: Double -> Double -> Double # negate :: Double -> Double # subtract :: Double -> Double -> Double # times :: Integral n => n -> Double -> Double #
Additive Double Source #
Instance details Methods (+) :: Double -> Double -> Double # sinnum1p :: Natural -> Double -> Double # sumWith1 :: Foldable1 f => (a -> Double) -> f a -> Double #
Abelian Double Source #
Instance details
RightModule Integer Double Source #
Instance details Methods (*.) :: Double -> Integer -> Double #
RightModule Natural Double Source #
Instance details Methods (*.) :: Double -> Natural -> Double #
LeftModule Integer Double Source #
Instance details Methods (.*) :: Integer -> Double -> Double #
LeftModule Natural Double Source #
Instance details Methods (.*) :: Natural -> Double -> Double #
Integral r => RightModule Integer (Ratio r) Source #
Instance details Methods (*.) :: Ratio r -> Integer -> Ratio r #
Integral r => RightModule Natural (Ratio r) Source #
Instance details Methods (*.) :: Ratio r -> Natural -> Ratio r #
RightModule a r => RightModule a (Complex r) Source #
Instance details Methods (*.) :: Complex r -> a -> Complex r #
Integral r => LeftModule Integer (Ratio r) Source #
Instance details Methods (.*) :: Integer -> Ratio r -> Ratio r #
Integral r => LeftModule Natural (Ratio r) Source #
Instance details Methods (.*) :: Natural -> Ratio r -> Ratio r #
LeftModule a r => LeftModule a (Complex r) Source #
Instance details Methods (.*) :: a -> Complex r -> Complex r #
Integral r => Ring (Ratio r) Source #
Instance details Methods fromInteger :: Integer -> Ratio r
Ring r => Ring (Complex r) Source #
Instance details Methods fromInteger :: Integer -> Complex r
Integral r => Rig (Ratio r) Source #
Instance details Methods fromNatural :: Natural -> Ratio r #
(Group r, Rig r) => Rig (Complex r) Source #
Instance details Methods fromNatural :: Natural -> Complex r #
Integral r => DecidableZero (Ratio r) Source #
Instance details Methods isZero :: Ratio r -> Bool #
DecidableZero r => DecidableZero (Complex r) Source #	These Instances are not algebraically right, but for the sake of convenience.
Instance details Methods isZero :: Complex r -> Bool #
Integral r => DecidableUnits (Ratio r) Source #
Instance details Methods recipUnit :: Ratio r -> Maybe (Ratio r) # isUnit :: Ratio r -> Bool # (^?) :: Integral n => Ratio r -> n -> Maybe (Ratio r) #
Integral r => Unital (Ratio r) Source #
Instance details Methods one :: Ratio r # pow :: Ratio r -> Natural -> Ratio r # productWith :: Foldable f => (a -> Ratio r) -> f a -> Ratio r #
(Group r, Monoidal r, Unital r) => Unital (Complex r) Source #
Instance details Methods one :: Complex r # pow :: Complex r -> Natural -> Complex r # productWith :: Foldable f => (a -> Complex r) -> f a -> Complex r #
Integral r => Division (Ratio r) Source #
Instance details Methods recip :: Ratio r -> Ratio r # (/) :: Ratio r -> Ratio r -> Ratio r # (\\) :: Ratio r -> Ratio r -> Ratio r # (^) :: Integral n => Ratio r -> n -> Ratio r
Integral r => Commutative (Ratio r) Source #
Instance details
(Group r, Commutative r) => Commutative (Complex r) Source #
Instance details
Integral r => Semiring (Ratio r) Source #
Instance details
(Group r, Semiring r) => Semiring (Complex r) Source #
Instance details
Integral r => Multiplicative (Ratio r) Source #
Instance details Methods (*) :: Ratio r -> Ratio r -> Ratio r # pow1p :: Ratio r -> Natural -> Ratio r # productWith1 :: Foldable1 f => (a -> Ratio r) -> f a -> Ratio r #
(Group r, Multiplicative r) => Multiplicative (Complex r) Source #
Instance details Methods (*) :: Complex r -> Complex r -> Complex r # pow1p :: Complex r -> Natural -> Complex r # productWith1 :: Foldable1 f => (a -> Complex r) -> f a -> Complex r #
Integral r => Monoidal (Ratio r) Source #
Instance details Methods zero :: Ratio r # sinnum :: Natural -> Ratio r -> Ratio r # sumWith :: Foldable f => (a -> Ratio r) -> f a -> Ratio r #
Monoidal r => Monoidal (Complex r) Source #
Instance details Methods zero :: Complex r # sinnum :: Natural -> Complex r -> Complex r # sumWith :: Foldable f => (a -> Complex r) -> f a -> Complex r #
Integral r => Group (Ratio r) Source #
Instance details Methods (-) :: Ratio r -> Ratio r -> Ratio r # negate :: Ratio r -> Ratio r # subtract :: Ratio r -> Ratio r -> Ratio r # times :: Integral n => n -> Ratio r -> Ratio r #
Group r => Group (Complex r) Source #
Instance details Methods (-) :: Complex r -> Complex r -> Complex r # negate :: Complex r -> Complex r # subtract :: Complex r -> Complex r -> Complex r # times :: Integral n => n -> Complex r -> Complex r #
Integral r => Additive (Ratio r) Source #
Instance details Methods (+) :: Ratio r -> Ratio r -> Ratio r # sinnum1p :: Natural -> Ratio r -> Ratio r # sumWith1 :: Foldable1 f => (a -> Ratio r) -> f a -> Ratio r #
Additive r => Additive (Vector r) Source #
Instance details Methods (+) :: Vector r -> Vector r -> Vector r # sinnum1p :: Natural -> Vector r -> Vector r # sumWith1 :: Foldable1 f => (a -> Vector r) -> f a -> Vector r #
Additive r => Additive (Complex r) Source #
Instance details Methods (+) :: Complex r -> Complex r -> Complex r # sinnum1p :: Natural -> Complex r -> Complex r # sumWith1 :: Foldable1 f => (a -> Complex r) -> f a -> Complex r #
Integral r => Abelian (Ratio r) Source #
Instance details
Abelian r => Abelian (Complex r) Source #
Instance details
NFData a => NFData (Fraction a) Source #
Instance details Methods rnf :: Fraction a -> () #
Random (Fraction Integer) Source #
Instance details Methods randomR :: RandomGen g => (Fraction Integer, Fraction Integer) -> g -> (Fraction Integer, g) random :: RandomGen g => g -> (Fraction Integer, g) randomRs :: RandomGen g => (Fraction Integer, Fraction Integer) -> g -> [Fraction Integer] randoms :: RandomGen g => g -> [Fraction Integer]
Convertible (Fraction Integer) Double Source #
Instance details Methods safeConvert :: Fraction Integer -> ConvertResult Double
(Semiring r, Integral r) => RightModule (Scalar r) (Ratio r) Source #
Instance details Methods (*.) :: Ratio r -> Scalar r -> Ratio r #
(Semiring r, Integral r) => LeftModule (Scalar r) (Ratio r) Source #
Instance details Methods (.*) :: Scalar r -> Ratio r -> Ratio r #
Convertible (Fraction Integer) (Complex Double) Source #
Instance details Methods safeConvert :: Fraction Integer -> ConvertResult (Complex Double)