algebra-4.3: Constructive abstract algebra

Numeric.Algebra.Division

# Documentation

class Unital r => Division r where Source #

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 () Source # Methodsrecip :: () -> () Source #(/) :: () -> () -> () Source #(\\) :: () -> () -> () Source #(^) :: Integral n => () -> n -> () Source # GCDDomain d => Division (Fraction d) Source # Methodsrecip :: Fraction d -> Fraction d Source #(/) :: Fraction d -> Fraction d -> Fraction d Source #(\\) :: Fraction d -> Fraction d -> Fraction d Source #(^) :: Integral n => Fraction d -> n -> Fraction d Source # Source # Methodsrecip :: Complex r -> Complex r Source #(/) :: Complex r -> Complex r -> Complex r Source #(\\) :: Complex r -> Complex r -> Complex r Source #(^) :: Integral n => Complex r -> n -> Complex r Source # Source # Methodsrecip :: Dual r -> Dual r Source #(/) :: Dual r -> Dual r -> Dual r Source #(\\) :: Dual r -> Dual r -> Dual r Source #(^) :: Integral n => Dual r -> n -> Dual r Source # Source # Methodsrecip :: Hyper' r -> Hyper' r Source #(/) :: Hyper' r -> Hyper' r -> Hyper' r Source #(\\) :: Hyper' r -> Hyper' r -> Hyper' r Source #(^) :: Integral n => Hyper' r -> n -> Hyper' r Source # (TriviallyInvolutive r, Ring r, Division r) => Division (Quaternion r) Source # Methods(/) :: Quaternion r -> Quaternion r -> Quaternion r Source #(\\) :: Quaternion r -> Quaternion r -> Quaternion r Source #(^) :: Integral n => Quaternion r -> n -> Quaternion r Source # Source # Methodsrecip :: Dual' r -> Dual' r Source #(/) :: Dual' r -> Dual' r -> Dual' r Source #(\\) :: Dual' r -> Dual' r -> Dual' r Source #(^) :: Integral n => Dual' r -> n -> Dual' r Source # (TriviallyInvolutive r, Ring r, Division r) => Division (Quaternion' r) Source # Methods(/) :: Quaternion' r -> Quaternion' r -> Quaternion' r Source #(\\) :: Quaternion' r -> Quaternion' r -> Quaternion' r Source #(^) :: Integral n => Quaternion' r -> n -> Quaternion' r Source # Group r => Division (Exp r) Source # Methodsrecip :: Exp r -> Exp r Source #(/) :: Exp r -> Exp r -> Exp r Source #(\\) :: Exp r -> Exp r -> Exp r Source #(^) :: Integral n => Exp r -> n -> Exp r Source # Division r => Division (Opposite r) Source # Methodsrecip :: Opposite r -> Opposite r Source #(/) :: Opposite r -> Opposite r -> Opposite r Source #(\\) :: Opposite r -> Opposite r -> Opposite r Source #(^) :: Integral n => Opposite r -> n -> Opposite r Source # (Rng r, Division r) => Division (RngRing r) Source # Methodsrecip :: RngRing r -> RngRing r Source #(/) :: RngRing r -> RngRing r -> RngRing r Source #(\\) :: RngRing r -> RngRing r -> RngRing r Source #(^) :: Integral n => RngRing r -> n -> RngRing r Source # (Unital r, DivisionAlgebra r a) => Division (a -> r) Source # Methodsrecip :: (a -> r) -> a -> r Source #(/) :: (a -> r) -> (a -> r) -> a -> r Source #(\\) :: (a -> r) -> (a -> r) -> a -> r Source #(^) :: Integral n => (a -> r) -> n -> a -> r Source # (Division a, Division b) => Division (a, b) Source # Methodsrecip :: (a, b) -> (a, b) Source #(/) :: (a, b) -> (a, b) -> (a, b) Source #(\\) :: (a, b) -> (a, b) -> (a, b) Source #(^) :: Integral n => (a, b) -> n -> (a, b) Source # (Division a, Division b, Division c) => Division (a, b, c) Source # Methodsrecip :: (a, b, c) -> (a, b, c) Source #(/) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #(\\) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #(^) :: Integral n => (a, b, c) -> n -> (a, b, c) Source # (Division a, Division b, Division c, Division d) => Division (a, b, c, d) Source # Methodsrecip :: (a, b, c, d) -> (a, b, c, d) Source #(/) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #(\\) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #(^) :: Integral n => (a, b, c, d) -> n -> (a, b, c, d) Source # (Division a, Division b, Division c, Division d, Division e) => Division (a, b, c, d, e) Source # Methodsrecip :: (a, b, c, d, e) -> (a, b, c, d, e) Source #(/) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #(\\) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #(^) :: Integral n => (a, b, c, d, e) -> n -> (a, b, c, d, e) Source #

class UnitalAlgebra r a => DivisionAlgebra r a where Source #

Minimal complete definition

recipriocal

Methods

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