Safe Haskell	Safe
Language	Haskell98

Numeric.Ring.Endomorphism

Synopsis

Documentation

newtype End a #

The endomorphism ring of an abelian group or the endomorphism semiring of an abelian monoid

http://en.wikipedia.org/wiki/Endomorphism_ring

Constructors

End
Fields appEnd :: a -> a

Instances

RightModule r m => RightModule r (End m) #
Methods (*.) :: End m -> r -> End m #
LeftModule r m => LeftModule r (End m) #
Methods (.*) :: r -> End m -> End m #
Semigroup (End r) #
Methods (<>) :: End r -> End r -> End r # sconcat :: NonEmpty (End r) -> End r # stimes :: Integral b => b -> End r -> End r #
Monoid (End r) #
Methods mempty :: End r # mappend :: End r -> End r -> End r # mconcat :: [End r] -> End r #
Abelian r => Abelian (End r) #

Additive r => Additive (End r) #
Methods (+) :: End r -> End r -> End r # sinnum1p :: Natural -> End r -> End r # sumWith1 :: Foldable1 f => (a -> End r) -> f a -> End r #
Monoidal r => Monoidal (End r) #
Methods zero :: End r # sinnum :: Natural -> End r -> End r # sumWith :: Foldable f => (a -> End r) -> f a -> End r #
(Abelian r, Monoidal r) => Semiring (End r) #

Multiplicative (End r) #
Methods (*) :: End r -> End r -> End r # pow1p :: End r -> Natural -> End r # productWith1 :: Foldable1 f => (a -> End r) -> f a -> End r #
Group r => Group (End r) #
Methods (-) :: End r -> End r -> End r # negate :: End r -> End r # subtract :: End r -> End r -> End r # times :: Integral n => n -> End r -> End r #
Unital (End r) #
Methods one :: End r # pow :: End r -> Natural -> End r # productWith :: Foldable f => (a -> End r) -> f a -> End r #
(Abelian r, Commutative r) => Commutative (End r) #

(Abelian r, Monoidal r) => Rig (End r) #
Methods fromNatural :: Natural -> End r #
(Abelian r, Group r) => Ring (End r) #
Methods fromInteger :: Integer -> End r #
(Monoidal m, Abelian m) => RightModule (End m) (End m) #
Methods (*.) :: End m -> End m -> End m #
(Monoidal m, Abelian m) => LeftModule (End m) (End m) #
Methods (.*) :: End m -> End m -> End m #

toEnd :: Multiplicative r => r -> End r #

fromEnd :: Unital r => End r -> r #

frobenius :: Characteristic r => End r #