NumHask.Algebra.Multiplicative

Multiplicative classes

Documentation

class Multiplicative a where

or Multiplication

For practical reasons, we begin the class tree with Additive and Multiplicative. Starting with Associative and Unital, or using Semigroup and Monoid from base tends to confuse the interface once you start having to disinguish between (say) monoidal addition and monoidal multiplication.

\a -> one * a == a

\a -> a * one == a

\a b c -> (a * b) * c == a * (b * c)

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

>>> one * 2
2

>>> 2 * 3
6

Methods

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

one :: a

Instances

Multiplicative Int16

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Int16

Multiplicative Int32

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Int32

Multiplicative Int64

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Int64

Multiplicative Int8

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Int8

Multiplicative Word16

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Word16

Multiplicative Word32

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Word32

Multiplicative Word64

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Word64

Multiplicative Word8

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Word8

Multiplicative Integer

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Integer

Multiplicative Natural

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Natural

Multiplicative Bool

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Bool

Multiplicative Double

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Double

Multiplicative Float

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Float

Multiplicative Int

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Int

Multiplicative Word

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: Word

Multiplicative a => Multiplicative (EuclideanPair a)

Defined in NumHask.Algebra.Metric

Methods

(*) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a

one :: EuclideanPair a

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

Defined in NumHask.Data.Complex

Methods

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

one :: Complex a

(Ord a, EndoBased a, Integral a, Ring a) => Multiplicative (Ratio a)

Defined in NumHask.Data.Rational

Methods

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

one :: Ratio a

Multiplicative b => Multiplicative (a -> b)

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: a -> b

newtype Product a

A wrapper for an Multiplicative which distinguishes the multiplicative structure

Constructors

Product

Fields

• getProduct :: a

Instances

Multiplicative a => Monoid (Product a)

Defined in NumHask.Algebra.Multiplicative

Methods

mempty :: Product a

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

mconcat :: [Product a] -> Product a

Multiplicative a => Semigroup (Product a)

Defined in NumHask.Algebra.Multiplicative

Methods

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

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

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

Show a => Show (Product a)

Defined in NumHask.Algebra.Multiplicative

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Eq a => Eq (Product a)

Defined in NumHask.Algebra.Multiplicative

Methods

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

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

Ord a => Ord (Product a)

Defined in NumHask.Algebra.Multiplicative

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

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

Compute the product of a Foldable.

>>> product [1..5]
120

accproduct :: (Multiplicative a, Traversable f) => f a -> f a

Compute the accumulating product of a Traversable.

>>> accproduct [1..5]
[1,2,6,24,120]

class Multiplicative a => Divisive a where

or Division

Though unusual, the term Divisive usefully fits in with the grammer of other classes and avoids name clashes that occur with some popular libraries.

\(a :: Double) -> a / a ~= one || a == zero

\(a :: Double) -> recip a ~= one / a || a == zero

\(a :: Double) -> recip a * a ~= one || a == zero

\(a :: Double) -> a * recip a ~= one || a == zero

>>> recip 2.0
0.5

>>> 1 / 2
0.5

Minimal complete definition

(/) | recip

Methods

recip :: a -> a

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

Instances

Divisive Double

Defined in NumHask.Algebra.Multiplicative

Methods

recip :: Double -> Double

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

Divisive Float

Defined in NumHask.Algebra.Multiplicative

Methods

recip :: Float -> Float

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

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

Defined in NumHask.Algebra.Metric

Methods

recip :: EuclideanPair a -> EuclideanPair a

(/) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a

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

Defined in NumHask.Data.Complex

Methods

recip :: Complex a -> Complex a

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

(Ord a, EndoBased a, Integral a, Ring a) => Divisive (Ratio a)

Defined in NumHask.Data.Rational

Methods

recip :: Ratio a -> Ratio a

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

Divisive b => Divisive (a -> b)

Defined in NumHask.Algebra.Multiplicative

Methods

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

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