Safe Haskell	Safe
Language	Haskell98

Numeric.Ring.Rng

Synopsis

data RngRing r = RngRing !Integer r
rngRingHom :: r -> RngRing r
liftRngHom :: Ring s => (r -> s) -> RngRing r -> s

Documentation

data RngRing r #

The free Ring given a Rng obtained by adjoining Z, such that

RngRing r = n*1 + r

This ring is commonly denoted r^.

Constructors

RngRing !Integer r

Instances

(Abelian r, Group r) => RightModule Integer (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods (*.) :: RngRing r -> Integer -> RngRing r #
(Abelian r, Monoidal r) => RightModule Natural (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods (*.) :: RngRing r -> Natural -> RngRing r #
(Abelian r, Group r) => LeftModule Integer (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods (.*) :: Integer -> RngRing r -> RngRing r #
(Abelian r, Monoidal r) => LeftModule Natural (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods (.*) :: Natural -> RngRing r -> RngRing r #
Read r => Read (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods readsPrec :: Int -> ReadS (RngRing r) # readList :: ReadS [RngRing r] # readPrec :: ReadPrec (RngRing r) # readListPrec :: ReadPrec [RngRing r] #
Show r => Show (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods showsPrec :: Int -> RngRing r -> ShowS # show :: RngRing r -> String # showList :: [RngRing r] -> ShowS #
Abelian r => Abelian (RngRing r) #
Instance details Defined in Numeric.Ring.Rng
Abelian r => Additive (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods (+) :: RngRing r -> RngRing r -> RngRing r # sinnum1p :: Natural -> RngRing r -> RngRing r # sumWith1 :: Foldable1 f => (a -> RngRing r) -> f a -> RngRing r #
(Abelian r, Monoidal r) => Monoidal (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods zero :: RngRing r # sinnum :: Natural -> RngRing r -> RngRing r # sumWith :: Foldable f => (a -> RngRing r) -> f a -> RngRing r #
Rng r => Semiring (RngRing r) #
Instance details Defined in Numeric.Ring.Rng
Rng r => Multiplicative (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods (*) :: RngRing r -> RngRing r -> RngRing r # pow1p :: RngRing r -> Natural -> RngRing r # productWith1 :: Foldable1 f => (a -> RngRing r) -> f a -> RngRing r #
(Abelian r, Group r) => Group (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods (-) :: RngRing r -> RngRing r -> RngRing r # negate :: RngRing r -> RngRing r # subtract :: RngRing r -> RngRing r -> RngRing r # times :: Integral n => n -> RngRing r -> RngRing r #
Rng r => Unital (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods one :: RngRing r # pow :: RngRing r -> Natural -> RngRing r # productWith :: Foldable f => (a -> RngRing r) -> f a -> RngRing r #
(Rng r, Division r) => Division (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods recip :: RngRing r -> RngRing r # (/) :: RngRing r -> RngRing r -> RngRing r # (\\) :: RngRing r -> RngRing r -> RngRing r # (^) :: Integral n => RngRing r -> n -> RngRing r #
(Commutative r, Rng r) => Commutative (RngRing r) #
Instance details Defined in Numeric.Ring.Rng
Rng r => Rig (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods fromNatural :: Natural -> RngRing r #
Rng r => Ring (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods fromInteger :: Integer -> RngRing r #
Rng s => RightModule (RngRing s) (RngRing s) #
Instance details Defined in Numeric.Ring.Rng Methods (*.) :: RngRing s -> RngRing s -> RngRing s #
Rng s => LeftModule (RngRing s) (RngRing s) #
Instance details Defined in Numeric.Ring.Rng Methods (.*) :: RngRing s -> RngRing s -> RngRing s #

rngRingHom :: r -> RngRing r #

The rng homomorphism from r to RngRing r

liftRngHom :: Ring s => (r -> s) -> RngRing r -> s #

given a rng homomorphism from a rng r into a ring s, liftRngHom yields a ring homomorphism from the ring `r^` into s.