algebra-4.2: Constructive abstract algebra

Numeric.Algebra.Division

# Documentation

class Unital r => Division r where Source

Minimal complete definition

Nothing

Methods

recip :: r -> r Source

(/) :: r -> r -> r infixl 7 Source

(\\) :: r -> r -> r infixl 7 Source

(^) :: Integral n => r -> n -> r infixr 8 Source

Instances

 Division () (Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Complex r) (TriviallyInvolutive r, Ring r, Division r) => Division (Quaternion r) (Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Dual r) (Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Hyper' r) (Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Dual' r) (TriviallyInvolutive r, Ring r, Division r) => Division (Quaternion' r) Group r => Division (Exp r) Division r => Division (Opposite r) (Rng r, Division r) => Division (RngRing r) Euclidean d => Division (Fraction d) (Unital r, DivisionAlgebra r a) => Division (a -> r) (Division a, Division b) => Division (a, b) (Division a, Division b, Division c) => Division (a, b, c) (Division a, Division b, Division c, Division d) => Division (a, b, c, d) (Division a, Division b, Division c, Division d, Division e) => Division (a, b, c, d, e)

class UnitalAlgebra r a => DivisionAlgebra r a where Source

Methods

recipriocal :: (a -> r) -> a -> r Source