Safe Haskell	Safe
Language	Haskell98

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 #