Algebra.Classes

Documentation

type Natural = Integer

timesDefault :: (Additive a1, Additive a2, Integral a1) => a1 -> a2 -> a2

class Additive a where

Additive monoid

Minimal complete definition

(+), zero

Methods

(+) :: a -> a -> a infixl 6

zero :: a

times :: Natural -> a -> a

Instances

Additive CInt

Defined in Algebra.Classes

Methods

(+) :: CInt -> CInt -> CInt

zero :: CInt

times :: Natural -> CInt -> CInt

Additive Int16

Defined in Algebra.Classes

Methods

(+) :: Int16 -> Int16 -> Int16

zero :: Int16

times :: Natural -> Int16 -> Int16

Additive Int32

Defined in Algebra.Classes

Methods

(+) :: Int32 -> Int32 -> Int32

zero :: Int32

times :: Natural -> Int32 -> Int32

Additive Int8

Defined in Algebra.Classes

Methods

(+) :: Int8 -> Int8 -> Int8

zero :: Int8

times :: Natural -> Int8 -> Int8

Additive Word16

Defined in Algebra.Classes

Methods

(+) :: Word16 -> Word16 -> Word16

zero :: Word16

times :: Natural -> Word16 -> Word16

Additive Word32

Defined in Algebra.Classes

Methods

(+) :: Word32 -> Word32 -> Word32

zero :: Word32

times :: Natural -> Word32 -> Word32

Additive Word8

Defined in Algebra.Classes

Methods

(+) :: Word8 -> Word8 -> Word8

zero :: Word8

times :: Natural -> Word8 -> Word8

Additive Integer

Defined in Algebra.Classes

Methods

(+) :: Integer -> Integer -> Integer

zero :: Integer

times :: Natural -> Integer -> Integer

Additive Bool

Defined in Algebra.Classes

Methods

(+) :: Bool -> Bool -> Bool

zero :: Bool

times :: Natural -> Bool -> Bool

Additive Double

Defined in Algebra.Classes

Methods

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

zero :: Double

times :: Natural -> Double -> Double

Additive Float

Defined in Algebra.Classes

Methods

(+) :: Float -> Float -> Float

zero :: Float

times :: Natural -> Float -> Float

Additive Int

Defined in Algebra.Classes

Methods

(+) :: Int -> Int -> Int

zero :: Int

times :: Natural -> Int -> Int

Additive a => Additive (Complex a)

Defined in Algebra.Classes

Methods

(+) :: Complex a -> Complex a -> Complex a

zero :: Complex a

times :: Natural -> Complex a -> Complex a

Integral a => Additive (Ratio a)

Defined in Algebra.Classes

Methods

(+) :: Ratio a -> Ratio a -> Ratio a

zero :: Ratio a

times :: Natural -> Ratio a -> Ratio a

Multiplicative a => Additive (Log a)

Defined in Algebra.Morphism.Exponential

Methods

(+) :: Log a -> Log a -> Log a

zero :: Log a

times :: Natural -> Log a -> Log a

EuclideanDomain a => Additive (Ratio a)

Since: 2.0.1

Defined in Algebra.Morphism.Ratio

Methods

(+) :: Ratio a -> Ratio a -> Ratio a

zero :: Ratio a

times :: Natural -> Ratio a -> Ratio a

(Ord k, AbelianAdditive v) => Additive (Map k v)

Defined in Algebra.Classes

Methods

(+) :: Map k v -> Map k v -> Map k v

zero :: Map k v

times :: Natural -> Map k v -> Map k v

(Applicative f, Additive a) => Additive (App f a)

Defined in Algebra.Classes

Methods

(+) :: App f a -> App f a -> App f a

zero :: App f a

times :: Natural -> App f a -> App f a

(Ord x, AbelianAdditive c, DecidableZero c) => Additive (Affine x c)

Defined in Algebra.Morphism.Affine

Methods

(+) :: Affine x c -> Affine x c -> Affine x c

zero :: Affine x c

times :: Natural -> Affine x c -> Affine x c

(AbelianAdditive c, DecidableZero c, Ord e) => Additive (LinComb e c)

Defined in Algebra.Morphism.LinComb

Methods

(+) :: LinComb e c -> LinComb e c -> LinComb e c

zero :: LinComb e c

times :: Natural -> LinComb e c -> LinComb e c

Additive a => Additive (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

(+) :: Pointwise x a -> Pointwise x a -> Pointwise x a

zero :: Pointwise x a

times :: Natural -> Pointwise x a -> Pointwise x a

Additive v => Additive (k -> v)

Defined in Algebra.Classes

Methods

(+) :: (k -> v) -> (k -> v) -> k -> v

zero :: k -> v

times :: Natural -> (k -> v) -> k -> v

Additive s => Additive (M s a b)

Defined in Algebra.Category.BlockMatrix

Methods

(+) :: M s a b -> M s a b -> M s a b

zero :: M s a b

times :: Natural -> M s a b -> M s a b

Additive s => Additive (Rel s a b)

Defined in Algebra.Category.Relation

Methods

(+) :: Rel s a b -> Rel s a b -> Rel s a b

zero :: Rel s a b

times :: Natural -> Rel s a b -> Rel s a b

(Applicative f, Additive a) => Additive (Euclid f a)

Defined in Algebra.Linear

Methods

(+) :: Euclid f a -> Euclid f a -> Euclid f a

zero :: Euclid f a

times :: Natural -> Euclid f a -> Euclid f a

Additive (f b a) => Additive (Op f a b)

Defined in Algebra.Category.Op

Methods

(+) :: Op f a b -> Op f a b -> Op f a b

zero :: Op f a b

times :: Natural -> Op f a b -> Op f a b

(Applicative f, Applicative g, Additive a) => Additive (Mat a f g)

Defined in Algebra.Linear

Methods

(+) :: Mat a f g -> Mat a f g -> Mat a f g

zero :: Mat a f g

times :: Natural -> Mat a f g -> Mat a f g

class Show a => TestEqual a where

Methods

(=.=) :: a -> a -> Property infix 0

Instances

TestEqual Double

Defined in Algebra.Classes

Methods

(=.=) :: Double -> Double -> Property

TestEqual Int

Defined in Algebra.Classes

Methods

(=.=) :: Int -> Int -> Property

(Ord x, Show x, Arbitrary x, TestEqual a, Additive a) => TestEqual (Map x a)

Defined in Algebra.Classes

Methods

(=.=) :: Map x a -> Map x a -> Property

(Show s, Additive s, TestEqual s) => TestEqual (M s a b)

Defined in Algebra.Category.BlockMatrix

Methods

(=.=) :: M s a b -> M s a b -> Property

TestEqual (f b a) => TestEqual (Op f a b)

Defined in Algebra.Category.Op

Methods

(=.=) :: Op f a b -> Op f a b -> Property

(TestEqual s, Arbitrary s, Arbitrary1 a, Arbitrary1 b, Show (a (b s)), VectorR b, VectorR a) => TestEqual (Mat s a b)

Defined in Algebra.Linear

Methods

(=.=) :: Mat s a b -> Mat s a b -> Property

law_refl :: TestEqual a => a -> Property

laws_testEqual :: forall a. Arbitrary a => TestEqual a => Property

nameLaw :: Testable prop => String -> prop -> Property

law_assoc :: forall a. TestEqual a => String -> (a -> a -> a) -> a -> a -> a -> Property

law_left_id :: forall a. TestEqual a => String -> (a -> a -> a) -> a -> a -> Property

law_right_id :: forall a. TestEqual a => String -> (a -> a -> a) -> a -> a -> Property

laws_monoid :: forall a. (Arbitrary a, TestEqual a) => String -> (a -> a -> a) -> a -> Property

law_commutative :: TestEqual a => String -> (a -> a -> a) -> a -> a -> Property

laws_comm_monoid :: forall a. (Arbitrary a, TestEqual a) => String -> (a -> a -> a) -> a -> Property

law_times :: (TestEqual a, Additive a) => Positive Integer -> a -> Property

laws_additive :: forall a. Arbitrary a => (Additive a, TestEqual a) => Property

law_exp_pos :: (TestEqual a, Multiplicative a) => a -> Property

laws_multiplicative :: forall a. Arbitrary a => (Multiplicative a, TestEqual a) => Property

law_fromInteger :: forall a. (TestEqual a, Ring a) => Integer -> Property

laws_ring :: forall a. Arbitrary a => (Ring a, TestEqual a) => Property

sum :: (Foldable t, Additive a) => t a -> a

class Additive r => DecidableZero r where

Methods

isZero :: r -> Bool

Instances

DecidableZero CInt

Defined in Algebra.Classes

Methods

isZero :: CInt -> Bool

DecidableZero Word16

Defined in Algebra.Classes

Methods

isZero :: Word16 -> Bool

DecidableZero Word32

Defined in Algebra.Classes

Methods

isZero :: Word32 -> Bool

DecidableZero Word8

Defined in Algebra.Classes

Methods

isZero :: Word8 -> Bool

DecidableZero Integer

Defined in Algebra.Classes

Methods

isZero :: Integer -> Bool

DecidableZero Double

Defined in Algebra.Classes

Methods

isZero :: Double -> Bool

DecidableZero Float

Defined in Algebra.Classes

Methods

isZero :: Float -> Bool

DecidableZero Int

Defined in Algebra.Classes

Methods

isZero :: Int -> Bool

DecidableZero x => DecidableZero (Complex x)

Defined in Algebra.Classes

Methods

isZero :: Complex x -> Bool

(Integral x, DecidableZero x) => DecidableZero (Ratio x)

Defined in Algebra.Classes

Methods

isZero :: Ratio x -> Bool

(Ord k, DecidableZero v, AbelianAdditive v) => DecidableZero (Map k v)

Defined in Algebra.Classes

Methods

isZero :: Map k v -> Bool

(AbelianAdditive c, Eq c, DecidableZero c, Ord e) => DecidableZero (LinComb e c)

Defined in Algebra.Morphism.LinComb

Methods

isZero :: LinComb e c -> Bool

law_decidable_zero :: forall a. (DecidableZero a, TestEqual a) => Property

class Additive a => AbelianAdditive a

Instances

AbelianAdditive CInt

Defined in Algebra.Classes

AbelianAdditive Int16

Defined in Algebra.Classes

AbelianAdditive Int32

Defined in Algebra.Classes

AbelianAdditive Int8

Defined in Algebra.Classes

AbelianAdditive Word16

Defined in Algebra.Classes

AbelianAdditive Word32

Defined in Algebra.Classes

AbelianAdditive Word8

Defined in Algebra.Classes

AbelianAdditive Integer

Defined in Algebra.Classes

AbelianAdditive Bool

Defined in Algebra.Classes

AbelianAdditive Double

Defined in Algebra.Classes

AbelianAdditive Float

Defined in Algebra.Classes

AbelianAdditive Int

Defined in Algebra.Classes

AbelianAdditive a => AbelianAdditive (Complex a)

Defined in Algebra.Classes

Integral a => AbelianAdditive (Ratio a)

Defined in Algebra.Classes

EuclideanDomain a => AbelianAdditive (Ratio a)

Defined in Algebra.Morphism.Ratio

(Ord k, AbelianAdditive v) => AbelianAdditive (Map k v)

Defined in Algebra.Classes

(Applicative f, AbelianAdditive a) => AbelianAdditive (App f a)

Defined in Algebra.Classes

(Ord x, AbelianAdditive c, DecidableZero c) => AbelianAdditive (Affine x c)

Defined in Algebra.Morphism.Affine

(AbelianAdditive c, DecidableZero c, Ord x) => AbelianAdditive (LinComb x c)

Defined in Algebra.Morphism.LinComb

Additive a => AbelianAdditive (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

AbelianAdditive v => AbelianAdditive (k -> v)

Defined in Algebra.Classes

(Applicative f, Applicative g, AbelianAdditive a) => AbelianAdditive (Mat a f g)

Defined in Algebra.Linear

laws_abelian_additive :: forall a. (Arbitrary a, AbelianAdditive a, TestEqual a) => Property

multDefault :: Group a => Natural -> a -> a

class Additive a => Group a where

Minimal complete definition

(negate | (-) | subtract)

Methods

(-) :: a -> a -> a infixl 6

subtract :: a -> a -> a

negate :: a -> a

mult :: Integer -> a -> a

Instances

Group CInt

Defined in Algebra.Classes

Methods

(-) :: CInt -> CInt -> CInt

subtract :: CInt -> CInt -> CInt

negate :: CInt -> CInt

mult :: Integer -> CInt -> CInt

Group Int16

Defined in Algebra.Classes

Methods

(-) :: Int16 -> Int16 -> Int16

subtract :: Int16 -> Int16 -> Int16

negate :: Int16 -> Int16

mult :: Integer -> Int16 -> Int16

Group Int32

Defined in Algebra.Classes

Methods

(-) :: Int32 -> Int32 -> Int32

subtract :: Int32 -> Int32 -> Int32

negate :: Int32 -> Int32

mult :: Integer -> Int32 -> Int32

Group Int8

Defined in Algebra.Classes

Methods

(-) :: Int8 -> Int8 -> Int8

subtract :: Int8 -> Int8 -> Int8

negate :: Int8 -> Int8

mult :: Integer -> Int8 -> Int8

Group Word16

Defined in Algebra.Classes

Methods

(-) :: Word16 -> Word16 -> Word16

subtract :: Word16 -> Word16 -> Word16

negate :: Word16 -> Word16

mult :: Integer -> Word16 -> Word16

Group Word32

Defined in Algebra.Classes

Methods

(-) :: Word32 -> Word32 -> Word32

subtract :: Word32 -> Word32 -> Word32

negate :: Word32 -> Word32

mult :: Integer -> Word32 -> Word32

Group Word8

Defined in Algebra.Classes

Methods

(-) :: Word8 -> Word8 -> Word8

subtract :: Word8 -> Word8 -> Word8

negate :: Word8 -> Word8

mult :: Integer -> Word8 -> Word8

Group Integer

Defined in Algebra.Classes

Methods

(-) :: Integer -> Integer -> Integer

subtract :: Integer -> Integer -> Integer

negate :: Integer -> Integer

mult :: Integer -> Integer -> Integer

Group Double

Defined in Algebra.Classes

Methods

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

subtract :: Double -> Double -> Double

negate :: Double -> Double

mult :: Integer -> Double -> Double

Group Float

Defined in Algebra.Classes

Methods

(-) :: Float -> Float -> Float

subtract :: Float -> Float -> Float

negate :: Float -> Float

mult :: Integer -> Float -> Float

Group Int

Defined in Algebra.Classes

Methods

(-) :: Int -> Int -> Int

subtract :: Int -> Int -> Int

negate :: Int -> Int

mult :: Integer -> Int -> Int

Group a => Group (Complex a)

Defined in Algebra.Classes

Methods

(-) :: Complex a -> Complex a -> Complex a

subtract :: Complex a -> Complex a -> Complex a

negate :: Complex a -> Complex a

mult :: Integer -> Complex a -> Complex a

Integral a => Group (Ratio a)

Defined in Algebra.Classes

Methods

(-) :: Ratio a -> Ratio a -> Ratio a

subtract :: Ratio a -> Ratio a -> Ratio a

negate :: Ratio a -> Ratio a

mult :: Integer -> Ratio a -> Ratio a

Division a => Group (Log a)

Defined in Algebra.Morphism.Exponential

Methods

(-) :: Log a -> Log a -> Log a

subtract :: Log a -> Log a -> Log a

negate :: Log a -> Log a

mult :: Integer -> Log a -> Log a

EuclideanDomain a => Group (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

(-) :: Ratio a -> Ratio a -> Ratio a

subtract :: Ratio a -> Ratio a -> Ratio a

negate :: Ratio a -> Ratio a

mult :: Integer -> Ratio a -> Ratio a

(Ord k, Group v, AbelianAdditive v) => Group (Map k v)

Defined in Algebra.Classes

Methods

(-) :: Map k v -> Map k v -> Map k v

subtract :: Map k v -> Map k v -> Map k v

negate :: Map k v -> Map k v

mult :: Integer -> Map k v -> Map k v

(Applicative f, Group a) => Group (App f a)

Defined in Algebra.Classes

Methods

(-) :: App f a -> App f a -> App f a

subtract :: App f a -> App f a -> App f a

negate :: App f a -> App f a

mult :: Integer -> App f a -> App f a

(Ord x, AbelianAdditive c, Group c, DecidableZero c) => Group (Affine x c)

Defined in Algebra.Morphism.Affine

Methods

(-) :: Affine x c -> Affine x c -> Affine x c

subtract :: Affine x c -> Affine x c -> Affine x c

negate :: Affine x c -> Affine x c

mult :: Integer -> Affine x c -> Affine x c

(AbelianAdditive c, Group c, DecidableZero c, Ord e) => Group (LinComb e c)

Defined in Algebra.Morphism.LinComb

Methods

(-) :: LinComb e c -> LinComb e c -> LinComb e c

subtract :: LinComb e c -> LinComb e c -> LinComb e c

negate :: LinComb e c -> LinComb e c

mult :: Integer -> LinComb e c -> LinComb e c

Group a => Group (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

(-) :: Pointwise x a -> Pointwise x a -> Pointwise x a

subtract :: Pointwise x a -> Pointwise x a -> Pointwise x a

negate :: Pointwise x a -> Pointwise x a

mult :: Integer -> Pointwise x a -> Pointwise x a

Group v => Group (k -> v)

Defined in Algebra.Classes

Methods

(-) :: (k -> v) -> (k -> v) -> k -> v

subtract :: (k -> v) -> (k -> v) -> k -> v

negate :: (k -> v) -> k -> v

mult :: Integer -> (k -> v) -> k -> v

Group s => Group (M s a b)

Defined in Algebra.Category.BlockMatrix

Methods

(-) :: M s a b -> M s a b -> M s a b

subtract :: M s a b -> M s a b -> M s a b

negate :: M s a b -> M s a b

mult :: Integer -> M s a b -> M s a b

(Applicative f, Group a) => Group (Euclid f a)

Defined in Algebra.Linear

Methods

(-) :: Euclid f a -> Euclid f a -> Euclid f a

subtract :: Euclid f a -> Euclid f a -> Euclid f a

negate :: Euclid f a -> Euclid f a

mult :: Integer -> Euclid f a -> Euclid f a

Group (f b a) => Group (Op f a b)

Defined in Algebra.Category.Op

Methods

(-) :: Op f a b -> Op f a b -> Op f a b

subtract :: Op f a b -> Op f a b -> Op f a b

negate :: Op f a b -> Op f a b

mult :: Integer -> Op f a b -> Op f a b

(Applicative f, Applicative g, Group a) => Group (Mat a f g)

Defined in Algebra.Linear

Methods

(-) :: Mat a f g -> Mat a f g -> Mat a f g

subtract :: Mat a f g -> Mat a f g -> Mat a f g

negate :: Mat a f g -> Mat a f g

mult :: Integer -> Mat a f g -> Mat a f g

law_negate_minus :: (TestEqual a, Group a) => a -> a -> Property

law_mult :: (TestEqual a, Group a) => Integer -> a -> Property

laws_group :: forall a. Arbitrary a => (Group a, TestEqual a) => Property

laws_abelian_group :: forall a. Arbitrary a => (Group a, TestEqual a) => Property

(*<) :: (Functor f, Multiplicative a) => a -> f a -> f a infixr 7

Functorial scaling. Compared to (*^) this operator disambiguates the scalar type, by using the functor structure and using the multiplicative instance for scalars.

class Scalable s a where

Any instance must preserve the following invariants: 1. if Multiplicative a and Scalable a a, then (*) = (*^) for a. 2. Scalable must define a partial order relation, in particular, instances of the form (Scalable s a) => Scalable s (T ... a ...) are acceptable, and should be declared overlappable.

Methods

(*^) :: s -> a -> a infixr 7

Instances

Scalable CInt CInt

Defined in Algebra.Classes

Methods

(*^) :: CInt -> CInt -> CInt

Scalable Int16 Int16

Defined in Algebra.Classes

Methods

(*^) :: Int16 -> Int16 -> Int16

Scalable Int32 Int32

Defined in Algebra.Classes

Methods

(*^) :: Int32 -> Int32 -> Int32

Scalable Int8 Int8

Defined in Algebra.Classes

Methods

(*^) :: Int8 -> Int8 -> Int8

Scalable Rational Double

Defined in Algebra.Classes

Methods

(*^) :: Rational -> Double -> Double

Scalable Word16 Word16

Defined in Algebra.Classes

Methods

(*^) :: Word16 -> Word16 -> Word16

Scalable Word32 Word32

Defined in Algebra.Classes

Methods

(*^) :: Word32 -> Word32 -> Word32

Scalable Word8 Word8

Defined in Algebra.Classes

Methods

(*^) :: Word8 -> Word8 -> Word8

Scalable Integer Integer

Defined in Algebra.Classes

Methods

(*^) :: Integer -> Integer -> Integer

Scalable Double Double

Defined in Algebra.Classes

Methods

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

Scalable Float Float

Defined in Algebra.Classes

Methods

(*^) :: Float -> Float -> Float

Scalable Int Int

Defined in Algebra.Classes

Methods

(*^) :: Int -> Int -> Int

Multiplicative a => Scalable Integer (Log a)

Defined in Algebra.Morphism.Exponential

Methods

(*^) :: Integer -> Log a -> Log a

Scalable s a => Scalable s (Complex a)

Defined in Algebra.Classes

Methods

(*^) :: s -> Complex a -> Complex a

Multiplicative c => Scalable c (Affine x c)

Defined in Algebra.Morphism.Affine

Methods

(*^) :: c -> Affine x c -> Affine x c

Scalable s a => Scalable s (Map k a)

Defined in Algebra.Classes

Methods

(*^) :: s -> Map k a -> Map k a

Scalable s a => Scalable s (LinComb k a)

Defined in Algebra.Morphism.LinComb

Methods

(*^) :: s -> LinComb k a -> LinComb k a

Scalable s a => Scalable s (k -> a)

Defined in Algebra.Classes

Methods

(*^) :: s -> (k -> a) -> k -> a

Ring s => Scalable s (M s a b)

Defined in Algebra.Category.BlockMatrix

Methods

(*^) :: s -> M s a b -> M s a b

(Functor f, Scalable s a) => Scalable s (Euclid f a)

Defined in Algebra.Linear

Methods

(*^) :: s -> Euclid f a -> Euclid f a

(Functor f, Functor g, Scalable s a) => Scalable s (Mat a f g)

Defined in Algebra.Linear

Methods

(*^) :: s -> Mat a f g -> Mat a f g

Ring a => Scalable (Complex a) (Complex a)

Defined in Algebra.Classes

Methods

(*^) :: Complex a -> Complex a -> Complex a

Integral a => Scalable (Ratio a) (Ratio a)

Defined in Algebra.Classes

Methods

(*^) :: Ratio a -> Ratio a -> Ratio a

EuclideanDomain a => Scalable (Ratio a) (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

(*^) :: Ratio a -> Ratio a -> Ratio a

(Applicative f, Scalable s a) => Scalable (App f s) (App f a)

Defined in Algebra.Classes

Methods

(*^) :: App f s -> App f a -> App f a

Multiplicative a => Scalable (Pointwise x a) (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

(*^) :: Pointwise x a -> Pointwise x a -> Pointwise x a

class Scalable' a where

"Most natural" scaling. Also disambiguates the scalar type, but using a fundep.

Associated Types

type Scalar a

Methods

(!*^) :: Scalar a -> a -> a

type SemiModule s a = (AbelianAdditive a, SemiRing s, Scalable s a)

A prefix variant of (*^), useful when using type applications. scale :: forall s a. Scalable s a => s -> a -> a scale = (*^)

type Module s a = (SemiModule s a, Group s, Group a)

law_module_zero :: forall s a. (Module s a, TestEqual a) => s -> Property

law_module_one :: forall s a. (Module s a, TestEqual a) => a -> Property

law_module_sum :: forall s a. (Module s a, TestEqual a) => s -> a -> a -> Property

law_module_sum_left :: forall s a. (Module s a, TestEqual a) => s -> s -> a -> Property

law_module_mul :: forall s a. (Module s a, TestEqual a) => s -> s -> a -> Property

laws_module :: forall s a. Arbitrary a => (Module s a, TestEqual a, Arbitrary s, Show s) => Property

class Multiplicative a where

Multiplicative monoid

Minimal complete definition

(*), one

Methods

(*) :: a -> a -> a infixl 7

one :: a

(^+) :: a -> Natural -> a infixr 8

Instances

Multiplicative Property

Defined in Algebra.Classes

Methods

(*) :: Property -> Property -> Property

one :: Property

(^+) :: Property -> Natural -> Property

Multiplicative CInt

Defined in Algebra.Classes

Methods

(*) :: CInt -> CInt -> CInt

one :: CInt

(^+) :: CInt -> Natural -> CInt

Multiplicative Int16

Defined in Algebra.Classes

Methods

(*) :: Int16 -> Int16 -> Int16

one :: Int16

(^+) :: Int16 -> Natural -> Int16

Multiplicative Int32

Defined in Algebra.Classes

Methods

(*) :: Int32 -> Int32 -> Int32

one :: Int32

(^+) :: Int32 -> Natural -> Int32

Multiplicative Int8

Defined in Algebra.Classes

Methods

(*) :: Int8 -> Int8 -> Int8

one :: Int8

(^+) :: Int8 -> Natural -> Int8

Multiplicative Word16

Defined in Algebra.Classes

Methods

(*) :: Word16 -> Word16 -> Word16

one :: Word16

(^+) :: Word16 -> Natural -> Word16

Multiplicative Word32

Defined in Algebra.Classes

Methods

(*) :: Word32 -> Word32 -> Word32

one :: Word32

(^+) :: Word32 -> Natural -> Word32

Multiplicative Word8

Defined in Algebra.Classes

Methods

(*) :: Word8 -> Word8 -> Word8

one :: Word8

(^+) :: Word8 -> Natural -> Word8

Multiplicative Integer

Defined in Algebra.Classes

Methods

(*) :: Integer -> Integer -> Integer

one :: Integer

(^+) :: Integer -> Natural -> Integer

Multiplicative Bool

Defined in Algebra.Classes

Methods

(*) :: Bool -> Bool -> Bool

one :: Bool

(^+) :: Bool -> Natural -> Bool

Multiplicative Double

Defined in Algebra.Classes

Methods

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

one :: Double

(^+) :: Double -> Natural -> Double

Multiplicative Float

Defined in Algebra.Classes

Methods

(*) :: Float -> Float -> Float

one :: Float

(^+) :: Float -> Natural -> Float

Multiplicative Int

Defined in Algebra.Classes

Methods

(*) :: Int -> Int -> Int

one :: Int

(^+) :: Int -> Natural -> Int

Ring a => Multiplicative (Complex a)

Defined in Algebra.Classes

Methods

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

one :: Complex a

(^+) :: Complex a -> Natural -> Complex a

Integral a => Multiplicative (Ratio a)

Defined in Algebra.Classes

Methods

(*) :: Ratio a -> Ratio a -> Ratio a

one :: Ratio a

(^+) :: Ratio a -> Natural -> Ratio a

Additive a => Multiplicative (Exp a)

Defined in Algebra.Morphism.Exponential

Methods

(*) :: Exp a -> Exp a -> Exp a

one :: Exp a

(^+) :: Exp a -> Natural -> Exp a

EuclideanDomain a => Multiplicative (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

(*) :: Ratio a -> Ratio a -> Ratio a

one :: Ratio a

(^+) :: Ratio a -> Natural -> Ratio a

(Category cat, Obj cat a) => Multiplicative (Endo cat a)

Defined in Algebra.Category.Endo

Methods

(*) :: Endo cat a -> Endo cat a -> Endo cat a

one :: Endo cat a

(^+) :: Endo cat a -> Natural -> Endo cat a

(Applicative f, Multiplicative a) => Multiplicative (App f a)

Defined in Algebra.Classes

Methods

(*) :: App f a -> App f a -> App f a

one :: App f a

(^+) :: App f a -> Natural -> App f a

Multiplicative a => Multiplicative (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

(*) :: Pointwise x a -> Pointwise x a -> Pointwise x a

one :: Pointwise x a

(^+) :: Pointwise x a -> Natural -> Pointwise x a

positiveExponentDefault :: Multiplicative a => a -> Natural -> a

product :: (Multiplicative a, Foldable f) => f a -> a

type SemiRing a = (Multiplicative a, AbelianAdditive a)

type PreRing a = (SemiRing a, Group a)

fromIntegerDefault :: PreRing a => Integer -> a

class (Module a a, PreRing a) => Ring a where

Minimal complete definition

Nothing

Methods

fromInteger :: Integer -> a

Instances

Ring CInt

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> CInt

Ring Int16

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Int16

Ring Int32

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Int32

Ring Int8

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Int8

Ring Word16

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Word16

Ring Word32

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Word32

Ring Word8

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Word8

Ring Integer

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Integer

Ring Double

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Double

Ring Float

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Float

Ring Int

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Int

Ring a => Ring (Complex a)

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Complex a

Integral a => Ring (Ratio a)

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> Ratio a

EuclideanDomain a => Ring (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

fromInteger :: Integer -> Ratio a

(Applicative f, Ring a) => Ring (App f a)

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> App f a

Ring a => Ring (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

fromInteger :: Integer -> Pointwise x a

class Multiplicative a => Division a where

Minimal complete definition

(recip | (/))

Methods

recip :: a -> a

(/) :: a -> a -> a infixl 7

(^) :: a -> Integer -> a infixr 8

Instances

Division Double

Defined in Algebra.Classes

Methods

recip :: Double -> Double

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

(^) :: Double -> Integer -> Double

Division Float

Defined in Algebra.Classes

Methods

recip :: Float -> Float

(/) :: Float -> Float -> Float

(^) :: Float -> Integer -> Float

Field a => Division (Complex a)

Defined in Algebra.Classes

Methods

recip :: Complex a -> Complex a

(/) :: Complex a -> Complex a -> Complex a

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

Integral a => Division (Ratio a)

Defined in Algebra.Classes

Methods

recip :: Ratio a -> Ratio a

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

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

Group a => Division (Exp a)

Defined in Algebra.Morphism.Exponential

Methods

recip :: Exp a -> Exp a

(/) :: Exp a -> Exp a -> Exp a

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

EuclideanDomain a => Division (Ratio a)

Since: 2.0.1

Defined in Algebra.Morphism.Ratio

Methods

recip :: Ratio a -> Ratio a

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

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

(Dagger cat, Obj cat a) => Division (Endo cat a)

Defined in Algebra.Category.Endo

Methods

recip :: Endo cat a -> Endo cat a

(/) :: Endo cat a -> Endo cat a -> Endo cat a

(^) :: Endo cat a -> Integer -> Endo cat a

(Applicative f, Division s) => Division (App f s)

Defined in Algebra.Classes

Methods

recip :: App f s -> App f s

(/) :: App f s -> App f s -> App f s

(^) :: App f s -> Integer -> App f s

Division a => Division (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

recip :: Pointwise x a -> Pointwise x a

(/) :: Pointwise x a -> Pointwise x a -> Pointwise x a

(^) :: Pointwise x a -> Integer -> Pointwise x a

class (Ring a, Division a) => Field a where

Minimal complete definition

Nothing

Methods

fromRational :: Rational -> a

Instances

Field Double

Defined in Algebra.Classes

Methods

fromRational :: Rational -> Double

Field Float

Defined in Algebra.Classes

Methods

fromRational :: Rational -> Float

Field a => Field (Complex a)

Defined in Algebra.Classes

Methods

fromRational :: Rational -> Complex a

Integral a => Field (Ratio a)

Defined in Algebra.Classes

Methods

fromRational :: Rational -> Ratio a

EuclideanDomain a => Field (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

fromRational :: Rational -> Ratio a

(Applicative f, Field s) => Field (App f s)

Defined in Algebra.Classes

Methods

fromRational :: Rational -> App f s

Field a => Field (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

fromRational :: Rational -> Pointwise x a

class (Ring a, DecidableZero a) => EuclideanDomain a where

Minimal complete definition

(stdUnit | normalize), (quotRem | quot, rem)

Methods

stdAssociate :: a -> a

stdUnit :: a -> a

normalize :: a -> (a, a)

quot :: a -> a -> a infixl 7

rem :: a -> a -> a infixl 7

quotRem :: a -> a -> (a, a)

Instances

EuclideanDomain CInt

Defined in Algebra.Classes

Methods

stdAssociate :: CInt -> CInt

stdUnit :: CInt -> CInt

normalize :: CInt -> (CInt, CInt)

quot :: CInt -> CInt -> CInt

rem :: CInt -> CInt -> CInt

quotRem :: CInt -> CInt -> (CInt, CInt)

EuclideanDomain Integer

Defined in Algebra.Classes

Methods

stdAssociate :: Integer -> Integer

stdUnit :: Integer -> Integer

normalize :: Integer -> (Integer, Integer)

quot :: Integer -> Integer -> Integer

rem :: Integer -> Integer -> Integer

quotRem :: Integer -> Integer -> (Integer, Integer)

EuclideanDomain Int

Defined in Algebra.Classes

Methods

stdAssociate :: Int -> Int

stdUnit :: Int -> Int

normalize :: Int -> (Int, Int)

quot :: Int -> Int -> Int

rem :: Int -> Int -> Int

quotRem :: Int -> Int -> (Int, Int)

gcd :: EuclideanDomain a => a -> a -> a

lcm :: EuclideanDomain a => a -> a -> a

lcm x y is the smallest positive integer that both x and y divide.

class (Ord a, Ring a, Enum a, EuclideanDomain a) => Integral a where

Minimal complete definition

toInteger

Methods

div :: a -> a -> a infixl 7

mod :: a -> a -> a infixl 7

divMod :: a -> a -> (a, a)

toInteger :: a -> Integer

Instances

Integral Integer

Defined in Algebra.Classes

Methods

div :: Integer -> Integer -> Integer

mod :: Integer -> Integer -> Integer

divMod :: Integer -> Integer -> (Integer, Integer)

toInteger :: Integer -> Integer

Integral Int

Defined in Algebra.Classes

Methods

div :: Int -> Int -> Int

mod :: Int -> Int -> Int

divMod :: Int -> Int -> (Int, Int)

toInteger :: Int -> Integer

ifThenElse :: Bool -> t -> t -> t

class Division a => Roots a where

Minimal complete definition

root | (^/)

Methods

sqrt :: a -> a

root :: Integer -> a -> a

(^/) :: a -> Rational -> a infixr 8

Instances

Roots Double

Defined in Algebra.Classes

Methods

sqrt :: Double -> Double

root :: Integer -> Double -> Double

(^/) :: Double -> Rational -> Double

Roots Float

Defined in Algebra.Classes

Methods

sqrt :: Float -> Float

root :: Integer -> Float -> Float

(^/) :: Float -> Rational -> Float

(RealFloat a, Ord a, Algebraic a) => Roots (Complex a)

Defined in Algebra.Classes

Methods

sqrt :: Complex a -> Complex a

root :: Integer -> Complex a -> Complex a

(^/) :: Complex a -> Rational -> Complex a

Field a => Roots (Exp a)

Defined in Algebra.Morphism.Exponential

Methods

sqrt :: Exp a -> Exp a

root :: Integer -> Exp a -> Exp a

(^/) :: Exp a -> Rational -> Exp a

(Applicative f, Roots s) => Roots (App f s)

Defined in Algebra.Classes

Methods

sqrt :: App f s -> App f s

root :: Integer -> App f s -> App f s

(^/) :: App f s -> Rational -> App f s

Roots a => Roots (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

sqrt :: Pointwise x a -> Pointwise x a

root :: Integer -> Pointwise x a -> Pointwise x a

(^/) :: Pointwise x a -> Rational -> Pointwise x a

type Algebraic a = (Roots a, Field a)

class Algebraic a => Transcendental a where

Class providing transcendental functions

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a

exp :: a -> a

log :: a -> a

(**) :: a -> a -> a infixr 8

logBase :: a -> a -> a

sin :: a -> a

cos :: a -> a

tan :: a -> a

asin :: a -> a

acos :: a -> a

atan :: a -> a

sinh :: a -> a

cosh :: a -> a

tanh :: a -> a

asinh :: a -> a

acosh :: a -> a

atanh :: a -> a

log1p :: a -> a

log1p x computes log (1 + x), but provides more precise results for small (absolute) values of x if possible.

Since: 4.9.0.0

expm1 :: a -> a

expm1 x computes exp x - 1, but provides more precise results for small (absolute) values of x if possible.

Since: 4.9.0.0

log1pexp :: a -> a

log1pexp x computes log (1 + exp x), but provides more precise results if possible.

Examples:

• if x is a large negative number, log (1 + exp x) will be imprecise for the reasons given in log1p.
• if exp x is close to -1, log (1 + exp x) will be imprecise for the reasons given in expm1.

Since: 4.9.0.0

log1mexp :: a -> a

log1mexp x computes log (1 - exp x), but provides more precise results if possible.

Examples:

• if x is a large negative number, log (1 - exp x) will be imprecise for the reasons given in log1p.
• if exp x is close to 1, log (1 - exp x) will be imprecise for the reasons given in expm1.

Since: 4.9.0.0

Instances

Transcendental Double

Defined in Algebra.Classes

Methods

pi :: Double

exp :: Double -> Double

log :: Double -> Double

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

logBase :: Double -> Double -> Double

sin :: Double -> Double

cos :: Double -> Double

tan :: Double -> Double

asin :: Double -> Double

acos :: Double -> Double

atan :: Double -> Double

sinh :: Double -> Double

cosh :: Double -> Double

tanh :: Double -> Double

asinh :: Double -> Double

acosh :: Double -> Double

atanh :: Double -> Double

log1p :: Double -> Double

expm1 :: Double -> Double

log1pexp :: Double -> Double

log1mexp :: Double -> Double

Transcendental Float

Defined in Algebra.Classes

Methods

pi :: Float

exp :: Float -> Float

log :: Float -> Float

(**) :: Float -> Float -> Float

logBase :: Float -> Float -> Float

sin :: Float -> Float

cos :: Float -> Float

tan :: Float -> Float

asin :: Float -> Float

acos :: Float -> Float

atan :: Float -> Float

sinh :: Float -> Float

cosh :: Float -> Float

tanh :: Float -> Float

asinh :: Float -> Float

acosh :: Float -> Float

atanh :: Float -> Float

log1p :: Float -> Float

expm1 :: Float -> Float

log1pexp :: Float -> Float

log1mexp :: Float -> Float

(RealFloat a, Transcendental a) => Transcendental (Complex a)

Defined in Algebra.Classes

Methods

pi :: Complex a

exp :: Complex a -> Complex a

log :: Complex a -> Complex a

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

logBase :: Complex a -> Complex a -> Complex a

sin :: Complex a -> Complex a

cos :: Complex a -> Complex a

tan :: Complex a -> Complex a

asin :: Complex a -> Complex a

acos :: Complex a -> Complex a

atan :: Complex a -> Complex a

sinh :: Complex a -> Complex a

cosh :: Complex a -> Complex a

tanh :: Complex a -> Complex a

asinh :: Complex a -> Complex a

acosh :: Complex a -> Complex a

atanh :: Complex a -> Complex a

log1p :: Complex a -> Complex a

expm1 :: Complex a -> Complex a

log1pexp :: Complex a -> Complex a

log1mexp :: Complex a -> Complex a

(Applicative f, Transcendental s) => Transcendental (App f s)

Defined in Algebra.Classes

Methods

pi :: App f s

exp :: App f s -> App f s

log :: App f s -> App f s

(**) :: App f s -> App f s -> App f s

logBase :: App f s -> App f s -> App f s

sin :: App f s -> App f s

cos :: App f s -> App f s

tan :: App f s -> App f s

asin :: App f s -> App f s

acos :: App f s -> App f s

atan :: App f s -> App f s

sinh :: App f s -> App f s

cosh :: App f s -> App f s

tanh :: App f s -> App f s

asinh :: App f s -> App f s

acosh :: App f s -> App f s

atanh :: App f s -> App f s

log1p :: App f s -> App f s

expm1 :: App f s -> App f s

log1pexp :: App f s -> App f s

log1mexp :: App f s -> App f s

Transcendental a => Transcendental (Pointwise x a)

Defined in Algebra.Morphism.Pointwise

Methods

pi :: Pointwise x a

exp :: Pointwise x a -> Pointwise x a

log :: Pointwise x a -> Pointwise x a

(**) :: Pointwise x a -> Pointwise x a -> Pointwise x a

logBase :: Pointwise x a -> Pointwise x a -> Pointwise x a

sin :: Pointwise x a -> Pointwise x a

cos :: Pointwise x a -> Pointwise x a

tan :: Pointwise x a -> Pointwise x a

asin :: Pointwise x a -> Pointwise x a

acos :: Pointwise x a -> Pointwise x a

atan :: Pointwise x a -> Pointwise x a

sinh :: Pointwise x a -> Pointwise x a

cosh :: Pointwise x a -> Pointwise x a

tanh :: Pointwise x a -> Pointwise x a

asinh :: Pointwise x a -> Pointwise x a

acosh :: Pointwise x a -> Pointwise x a

atanh :: Pointwise x a -> Pointwise x a

log1p :: Pointwise x a -> Pointwise x a

expm1 :: Pointwise x a -> Pointwise x a

log1pexp :: Pointwise x a -> Pointwise x a

log1mexp :: Pointwise x a -> Pointwise x a

(^?) :: Transcendental a => a -> a -> a infixr 8

class Algebraic a => AlgebraicallyClosed a where

Minimal complete definition

rootOfUnity

Methods

imaginaryUnit :: a

rootOfUnity :: Integer -> Integer -> a

rootOfUnity n give the nth roots of unity. The 2nd argument specifies which one is demanded

Instances

(RealFloat a, Transcendental a) => AlgebraicallyClosed (Complex a)

Defined in Algebra.Classes

Methods

imaginaryUnit :: Complex a

rootOfUnity :: Integer -> Integer -> Complex a

newtype Sum a

Constructors

Sum

Fields

• fromSum :: a

Instances

Additive a => Monoid (Sum a)

Defined in Algebra.Classes

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Additive a => Semigroup (Sum a)

Defined in Algebra.Classes

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

Generic (Sum a)

Defined in Algebra.Classes

Associated Types

type Rep (Sum a) :: Type -> Type

Methods

from :: Sum a -> Rep (Sum a) x

to :: Rep (Sum a) x -> Sum a

Show a => Show (Sum a)

Defined in Algebra.Classes

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Binary a => Binary (Sum a)

Defined in Algebra.Classes

Methods

put :: Sum a -> Put

get :: Get (Sum a)

putList :: [Sum a] -> Put

Eq a => Eq (Sum a)

Defined in Algebra.Classes

Methods

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

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

Ord a => Ord (Sum a)

Defined in Algebra.Classes

Methods

compare :: Sum a -> Sum a -> Ordering

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

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

(>) :: Sum a -> Sum a -> Bool

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

max :: Sum a -> Sum a -> Sum a

min :: Sum a -> Sum a -> Sum a

type Rep (Sum a)

Defined in Algebra.Classes

type Rep (Sum a) = D1 ('MetaData "Sum" "Algebra.Classes" "gasp-1.4.0.0-4Z31dYmTpJbCzuuYkBBWRm" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "fromSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Product a

Constructors

Product

Fields

• fromProduct :: a

Instances

Multiplicative a => Monoid (Product a)

Defined in Algebra.Classes

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Multiplicative a => Semigroup (Product a)

Defined in Algebra.Classes

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Generic (Product a)

Defined in Algebra.Classes

Associated Types

type Rep (Product a) :: Type -> Type

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

Show a => Show (Product a)

Defined in Algebra.Classes

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Eq a => Eq (Product a)

Defined in Algebra.Classes

Methods

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

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

Ord a => Ord (Product a)

Defined in Algebra.Classes

Methods

compare :: Product a -> Product a -> Ordering

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

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

(>) :: Product a -> Product a -> Bool

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

max :: Product a -> Product a -> Product a

min :: Product a -> Product a -> Product a

type Rep (Product a)

Defined in Algebra.Classes

type Rep (Product a) = D1 ('MetaData "Product" "Algebra.Classes" "gasp-1.4.0.0-4Z31dYmTpJbCzuuYkBBWRm" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "fromProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype App f x

Constructors

App (f x)

Instances

Applicative f => Applicative (App f)

Defined in Algebra.Classes

Methods

pure :: a -> App f a

(<*>) :: App f (a -> b) -> App f a -> App f b

liftA2 :: (a -> b -> c) -> App f a -> App f b -> App f c

(*>) :: App f a -> App f b -> App f b

(<*) :: App f a -> App f b -> App f a

Functor f => Functor (App f)

Defined in Algebra.Classes

Methods

fmap :: (a -> b) -> App f a -> App f b

(<$) :: a -> App f b -> App f a

(Applicative f, AbelianAdditive a) => AbelianAdditive (App f a)

Defined in Algebra.Classes

(Applicative f, Additive a) => Additive (App f a)

Defined in Algebra.Classes

Methods

(+) :: App f a -> App f a -> App f a

zero :: App f a

times :: Natural -> App f a -> App f a

(Applicative f, Division s) => Division (App f s)

Defined in Algebra.Classes

Methods

recip :: App f s -> App f s

(/) :: App f s -> App f s -> App f s

(^) :: App f s -> Integer -> App f s

(Applicative f, Field s) => Field (App f s)

Defined in Algebra.Classes

Methods

fromRational :: Rational -> App f s

(Applicative f, Group a) => Group (App f a)

Defined in Algebra.Classes

Methods

(-) :: App f a -> App f a -> App f a

subtract :: App f a -> App f a -> App f a

negate :: App f a -> App f a

mult :: Integer -> App f a -> App f a

(Applicative f, Multiplicative a) => Multiplicative (App f a)

Defined in Algebra.Classes

Methods

(*) :: App f a -> App f a -> App f a

one :: App f a

(^+) :: App f a -> Natural -> App f a

(Applicative f, Ring a) => Ring (App f a)

Defined in Algebra.Classes

Methods

fromInteger :: Integer -> App f a

(Applicative f, Roots s) => Roots (App f s)

Defined in Algebra.Classes

Methods

sqrt :: App f s -> App f s

root :: Integer -> App f s -> App f s

(^/) :: App f s -> Rational -> App f s

(Applicative f, Transcendental s) => Transcendental (App f s)

Defined in Algebra.Classes

Methods

pi :: App f s

exp :: App f s -> App f s

log :: App f s -> App f s

(**) :: App f s -> App f s -> App f s

logBase :: App f s -> App f s -> App f s

sin :: App f s -> App f s

cos :: App f s -> App f s

tan :: App f s -> App f s

asin :: App f s -> App f s

acos :: App f s -> App f s

atan :: App f s -> App f s

sinh :: App f s -> App f s

cosh :: App f s -> App f s

tanh :: App f s -> App f s

asinh :: App f s -> App f s

acosh :: App f s -> App f s

atanh :: App f s -> App f s

log1p :: App f s -> App f s

expm1 :: App f s -> App f s

log1pexp :: App f s -> App f s

log1mexp :: App f s -> App f s

(Applicative f, Scalable s a) => Scalable (App f s) (App f a)

Defined in Algebra.Classes

Methods

(*^) :: App f s -> App f a -> App f a