numhask-0.2.2.0: numeric classes

Safe HaskellNone
LanguageHaskell2010

NumHask.Algebra.Basis

Description

Element-by-element operations

Synopsis

Documentation

class Additive a => AdditiveBasis m a where Source #

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 Source #

class AdditiveGroup a => AdditiveGroupBasis m a where Source #

element by element subtraction

a .-. a = singleton zero

Minimal complete definition

(.-.)

Methods

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

class Multiplicative a => MultiplicativeBasis m a where Source #

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 Source #

class MultiplicativeGroup a => MultiplicativeGroupBasis m a where Source #

element by element division

a ./. a == singleton one

Minimal complete definition

(./.)

Methods

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