Numeric.Algebra.Division

Documentation

class Unital r => Division r where

Methods

recip :: r -> r

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

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

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

Instances

Division ()

Methods

recip :: () -> ()

(/) :: () -> () -> ()

(\\) :: () -> () -> ()

(^) :: Integral n => () -> n -> ()

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

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

Division r => Division (Opposite r)

Methods

recip :: Opposite r -> Opposite r

(/) :: Opposite r -> Opposite r -> Opposite r

(\\) :: Opposite r -> Opposite r -> Opposite r

(^) :: Integral n => Opposite r -> n -> Opposite r

Group r => Division (Exp r)

Methods

recip :: Exp r -> Exp r

(/) :: Exp r -> Exp r -> Exp r

(\\) :: Exp r -> Exp r -> Exp r

(^) :: Integral n => Exp r -> n -> Exp r

(TriviallyInvolutive r, Ring r, Division r) => Division (Quaternion' r)

Methods

recip :: Quaternion' r -> Quaternion' r

(/) :: Quaternion' r -> Quaternion' r -> Quaternion' r

(\\) :: Quaternion' r -> Quaternion' r -> Quaternion' r

(^) :: Integral n => Quaternion' r -> n -> Quaternion' r

(Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Dual' r)

Methods

recip :: Dual' r -> Dual' r

(/) :: Dual' r -> Dual' r -> Dual' r

(\\) :: Dual' r -> Dual' r -> Dual' r

(^) :: Integral n => Dual' r -> n -> Dual' r

(TriviallyInvolutive r, Ring r, Division r) => Division (Quaternion r)

Methods

recip :: Quaternion r -> Quaternion r

(/) :: Quaternion r -> Quaternion r -> Quaternion r

(\\) :: Quaternion r -> Quaternion r -> Quaternion r

(^) :: Integral n => Quaternion r -> n -> Quaternion r

(Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Hyper' r)

Methods

recip :: Hyper' r -> Hyper' r

(/) :: Hyper' r -> Hyper' r -> Hyper' r

(\\) :: Hyper' r -> Hyper' r -> Hyper' r

(^) :: Integral n => Hyper' r -> n -> Hyper' r

(Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Dual r)

Methods

recip :: Dual r -> Dual r

(/) :: Dual r -> Dual r -> Dual r

(\\) :: Dual r -> Dual r -> Dual r

(^) :: Integral n => Dual r -> n -> Dual r

(Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Complex r)

Methods

recip :: Complex r -> Complex r

(/) :: Complex r -> Complex r -> Complex r

(\\) :: Complex r -> Complex r -> Complex r

(^) :: Integral n => Complex r -> n -> Complex r

GCDDomain d => Division (Fraction d)

Methods

recip :: Fraction d -> Fraction d

(/) :: Fraction d -> Fraction d -> Fraction d

(\\) :: Fraction d -> Fraction d -> Fraction d

(^) :: Integral n => Fraction d -> n -> Fraction d

(Unital r, DivisionAlgebra r a) => Division (a -> r)

Methods

recip :: (a -> r) -> a -> r

(/) :: (a -> r) -> (a -> r) -> a -> r

(\\) :: (a -> r) -> (a -> r) -> a -> r

(^) :: Integral n => (a -> r) -> n -> a -> r

(Division a, Division b) => Division (a, b)

Methods

recip :: (a, b) -> (a, b)

(/) :: (a, b) -> (a, b) -> (a, b)

(\\) :: (a, b) -> (a, b) -> (a, b)

(^) :: Integral n => (a, b) -> n -> (a, b)

(Division a, Division b, Division c) => Division (a, b, c)

Methods

recip :: (a, b, c) -> (a, b, c)

(/) :: (a, b, c) -> (a, b, c) -> (a, b, c)

(\\) :: (a, b, c) -> (a, b, c) -> (a, b, c)

(^) :: Integral n => (a, b, c) -> n -> (a, b, c)

(Division a, Division b, Division c, Division d) => Division (a, b, c, d)

Methods

recip :: (a, b, c, d) -> (a, b, c, d)

(/) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

(\\) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

(^) :: Integral n => (a, b, c, d) -> n -> (a, b, c, d)

(Division a, Division b, Division c, Division d, Division e) => Division (a, b, c, d, e)

Methods

recip :: (a, b, c, d, e) -> (a, b, c, d, e)

(/) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

(\\) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

(^) :: Integral n => (a, b, c, d, e) -> n -> (a, b, c, d, e)

class UnitalAlgebra r a => DivisionAlgebra r a where

Minimal complete definition

recipriocal

Methods

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