Algebra.Instances

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

Orphan instances

Commutative Double

Ring Double

Methods

fromInteger :: Integer -> Double

Rig Double

Methods

fromNatural :: Natural -> Double

DecidableZero Double

Methods

isZero :: Double -> Bool

Division Double

Methods

recip :: Double -> Double

(/) :: Double -> Double -> Double

(\\) :: Double -> Double -> Double

(^) :: Integral n => Double -> n -> Double

Unital Double

Methods

one :: Double

pow :: Double -> Natural -> Double

productWith :: Foldable f => (a -> Double) -> f a -> Double

Group Double

Methods

(-) :: Double -> Double -> Double

negate :: Double -> Double

subtract :: Double -> Double -> Double

times :: Integral n => n -> Double -> Double

Multiplicative Double

Methods

(*) :: Double -> Double -> Double

pow1p :: Double -> Natural -> Double

productWith1 :: Foldable1 f => (a -> Double) -> f a -> Double

Semiring Double

Monoidal Double

Methods

zero :: Double

sinnum :: Natural -> Double -> Double

sumWith :: Foldable f => (a -> Double) -> f a -> Double

Additive Double

Methods

(+) :: Double -> Double -> Double

sinnum1p :: Natural -> Double -> Double

sumWith1 :: Foldable1 f => (a -> Double) -> f a -> Double

Abelian Double

LeftModule Integer Double

Methods

(.*) :: Integer -> Double -> Double

LeftModule Natural Double

Methods

(.*) :: Natural -> Double -> Double

RightModule Integer Double

Methods

(*.) :: Double -> Integer -> Double

RightModule Natural Double

Methods

(*.) :: Double -> Natural -> Double

Integral r => LeftModule Integer (Ratio r)

Methods

(.*) :: Integer -> Ratio r -> Ratio r

LeftModule a r => LeftModule a (Complex r)

Methods

(.*) :: a -> Complex r -> Complex r

Integral r => LeftModule Natural (Ratio r)

Methods

(.*) :: Natural -> Ratio r -> Ratio r

Integral r => RightModule Integer (Ratio r)

Methods

(*.) :: Ratio r -> Integer -> Ratio r

RightModule a r => RightModule a (Complex r)

Methods

(*.) :: Complex r -> a -> Complex r

Integral r => RightModule Natural (Ratio r)

Methods

(*.) :: Ratio r -> Natural -> Ratio r

Random (Fraction Integer)

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]

randomRIO :: (Fraction Integer, Fraction Integer) -> IO (Fraction Integer)

randomIO :: IO (Fraction Integer)

Integral r => Commutative (Ratio r)

(Group r, Commutative r) => Commutative (Complex r)

Integral r => Ring (Ratio r)

Methods

fromInteger :: Integer -> Ratio r

Ring r => Ring (Complex r)

Methods

fromInteger :: Integer -> Complex r

Integral r => Rig (Ratio r)

Methods

fromNatural :: Natural -> Ratio r

(Group r, Rig r) => Rig (Complex r)

Methods

fromNatural :: Natural -> Complex r

Integral r => DecidableZero (Ratio r)

Methods

isZero :: Ratio r -> Bool

DecidableZero r => DecidableZero (Complex r)

These Instances are not algebraically right, but for the sake of convenience.

Methods

isZero :: Complex r -> Bool

Integral r => DecidableUnits (Ratio r)

Methods

recipUnit :: Ratio r -> Maybe (Ratio r)

isUnit :: Ratio r -> Bool

(^?) :: Integral n => Ratio r -> n -> Maybe (Ratio r)

Integral r => Division (Ratio r)

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 => Unital (Ratio r)

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)

Methods

one :: Complex r

pow :: Complex r -> Natural -> Complex r

productWith :: Foldable f => (a -> Complex r) -> f a -> Complex r

Integral r => Group (Ratio r)

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)

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 => Multiplicative (Ratio r)

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)

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 => Semiring (Ratio r)

(Group r, Semiring r) => Semiring (Complex r)

Integral r => Monoidal (Ratio r)

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)

Methods

zero :: Complex r

sinnum :: Natural -> Complex r -> Complex r

sumWith :: Foldable f => (a -> Complex r) -> f a -> Complex r

Integral r => Additive (Ratio r)

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)

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)

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)

Abelian r => Abelian (Complex r)

Hashable a => Hashable (Vector a)

Methods

hashWithSalt :: Int -> Vector a -> Int

hash :: Vector a -> Int

NFData a => NFData (Fraction a)

Methods

rnf :: Fraction a -> ()

Convertible (Fraction Integer) Double

Methods

safeConvert :: Fraction Integer -> ConvertResult Double

(Semiring r, Integral r) => LeftModule (Scalar r) (Ratio r)

Methods

(.*) :: Scalar r -> Ratio r -> Ratio r

(Semiring r, Integral r) => RightModule (Scalar r) (Ratio r)

Methods

(*.) :: Ratio r -> Scalar r -> Ratio r

Convertible (Fraction Integer) (Complex Double)

Methods

safeConvert :: Fraction Integer -> ConvertResult (Complex Double)