Numeric.Ring.Endomorphism

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