NumHask.Algebra.Basis

Element-by-element operations

Documentation

class Additive a => AdditiveBasis m a where

element by element addition

(a .+. b) .+. c == a .+. (b .+. c)
zero .+. a = a
a .+. zero = a
a .+. b == b .+. a

Minimal complete definition

(.+.)

Methods

(.+.) :: m a -> m a -> m a infixl 7

class AdditiveGroup a => AdditiveGroupBasis m a where

element by element subtraction

a .-. a = singleton zero

Minimal complete definition

(.-.)

Methods

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

class Multiplicative a => MultiplicativeBasis m a where

element by element multiplication

(a .*. b) .*. c == a .*. (b .*. c)
singleton one .*. a = a
a .*. singelton one = a
a .*. b == b .*. a

Minimal complete definition

(.*.)

Methods

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

class MultiplicativeGroup a => MultiplicativeGroupBasis m a where

element by element division

a ./. a == singleton one

Minimal complete definition

(./.)

Methods

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