NumHask.Algebra.Abstract.Multiplicative

Multiplicative

Documentation

class Multiplicative a where

For practical reasons, Multiplicative has no super classes. Using Associative and Unital from this library, or using Semigroup and Monoid from base tends to complexify the interface once you start having to disinguish between (say) monoidal addition and monoidal multiplication.

one * a == a
a * one == a
(a * b) * c == a * (b * c)
a * b == b * a

By convention, (*) is regarded as commutative, but this is not universal, and the introduction of another symbol which means non-commutative multiplication seems a bit dogmatic.

Methods

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

one :: a

Instances

Multiplicative Bool

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Bool

Multiplicative Double

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Double

Multiplicative Float

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Float

Multiplicative Int

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Int

Multiplicative Int8

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Int8

Multiplicative Int16

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Int16

Multiplicative Int32

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Int32

Multiplicative Int64

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

(*) :: Int64 -> Int64 -> Int64

one :: Int64

Multiplicative Integer

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Integer

Multiplicative Natural

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

(*) :: Natural -> Natural -> Natural

one :: Natural

Multiplicative Word

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

(*) :: Word -> Word -> Word

one :: Word

Multiplicative Word8

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Word8

Multiplicative Word16

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Word16

Multiplicative Word32

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: Word32

Multiplicative Word64

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

(*) :: Word64 -> Word64 -> Word64

one :: Word64

(Subtractive a, Multiplicative a) => Multiplicative (Complex a)

Defined in NumHask.Data.Complex

Methods

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

one :: Complex a

GCDConstraints a => Multiplicative (Ratio a)

Defined in NumHask.Data.Rational

Methods

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

one :: Ratio a

Multiplicative a => Multiplicative (Pair a)

Defined in NumHask.Data.Pair

Methods

(*) :: Pair a -> Pair a -> Pair a

one :: Pair a

(LowerBoundedField a, Eq a) => Multiplicative (LogField a)

Defined in NumHask.Data.LogField

Methods

(*) :: LogField a -> LogField a -> LogField a

one :: LogField a

Multiplicative a => Multiplicative (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

(*) :: Wrapped a -> Wrapped a -> Wrapped a

one :: Wrapped a

Multiplicative a => Multiplicative (Positive a)

Defined in NumHask.Data.Positive

Methods

(*) :: Positive a -> Positive a -> Positive a

one :: Positive a

Multiplicative b => Multiplicative (a -> b)

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

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

one :: a -> b

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

Compute the product of a Foldable.

class Multiplicative a => Divisive a where

a / a = one
recip a = one / a
recip a * a = one
a * recip a = one

Minimal complete definition

recip

Methods

recip :: a -> a

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

Instances

Divisive Double

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

recip :: Double -> Double

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

Divisive Float

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

recip :: Float -> Float

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

(Subtractive a, Divisive a) => Divisive (Complex a)

Defined in NumHask.Data.Complex

Methods

recip :: Complex a -> Complex a

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

GCDConstraints a => Divisive (Ratio a)

Defined in NumHask.Data.Rational

Methods

recip :: Ratio a -> Ratio a

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

Divisive a => Divisive (Pair a)

Defined in NumHask.Data.Pair

Methods

recip :: Pair a -> Pair a

(/) :: Pair a -> Pair a -> Pair a

(LowerBoundedField a, Eq a) => Divisive (LogField a)

Defined in NumHask.Data.LogField

Methods

recip :: LogField a -> LogField a

(/) :: LogField a -> LogField a -> LogField a

Divisive a => Divisive (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

recip :: Wrapped a -> Wrapped a

(/) :: Wrapped a -> Wrapped a -> Wrapped a

Divisive a => Divisive (Positive a)

Defined in NumHask.Data.Positive

Methods

recip :: Positive a -> Positive a

(/) :: Positive a -> Positive a -> Positive a

Divisive b => Divisive (a -> b)

Defined in NumHask.Algebra.Abstract.Multiplicative

Methods

recip :: (a -> b) -> a -> b

(/) :: (a -> b) -> (a -> b) -> a -> b