Numeric.Ring.Rng

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

(Semiring Integer, Additive (RngRing r), Abelian r, Group r) => RightModule Integer (RngRing r)

(Semiring Natural, Additive (RngRing r), Abelian r, Monoidal r) => RightModule Natural (RngRing r)

(Semiring Integer, Additive (RngRing r), Abelian r, Group r) => LeftModule Integer (RngRing r)

(Semiring Natural, Additive (RngRing r), Abelian r, Monoidal r) => LeftModule Natural (RngRing r)

Read r => Read (RngRing r)

Show r => Show (RngRing r)

(Additive (RngRing r), Abelian r) => Abelian (RngRing r)

Abelian r => Additive (RngRing r)

(LeftModule Natural (RngRing r), RightModule Natural (RngRing r), Abelian r, Monoidal r) => Monoidal (RngRing r)

(Additive (RngRing r), Abelian (RngRing r), Multiplicative (RngRing r), Rng r) => Semiring (RngRing r)

Rng r => Multiplicative (RngRing r)

(LeftModule Integer (RngRing r), RightModule Integer (RngRing r), Monoidal (RngRing r), Abelian r, Group r) => Group (RngRing r)

(Multiplicative (RngRing r), Rng r) => Unital (RngRing r)

(Unital (RngRing r), Rng r, Division r) => Division (RngRing r)

(Semiring (RngRing r), Unital (RngRing r), Monoidal (RngRing r), Rng r) => Rig (RngRing r)

(Rig (RngRing r), Rng (RngRing r), Rng r) => Ring (RngRing r)

(Multiplicative (RngRing r), Commutative r, Rng r) => Commutative (RngRing r)

(Semiring (RngRing s), Additive (RngRing s), Rng s) => RightModule (RngRing s) (RngRing s)

(Semiring (RngRing s), Additive (RngRing s), Rng s) => LeftModule (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.