Safe Haskell	Safe
Language	Haskell98

Numeric.Additive.Group

Contents

Additive Groups

Synopsis

class (LeftModule Integer r, RightModule Integer r, Monoidal r) => Group r where

Additive Groups

class (LeftModule Integer r, RightModule Integer r, Monoidal r) => Group r where #

Methods

(-) :: r -> r -> r infixl 6 #

negate :: r -> r #

subtract :: r -> r -> r #

times :: Integral n => n -> r -> r infixl 7 #

Instances

Group Int #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int -> Int -> Int # negate :: Int -> Int # subtract :: Int -> Int -> Int # times :: Integral n => n -> Int -> Int #
Group Int8 #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int8 -> Int8 -> Int8 # negate :: Int8 -> Int8 # subtract :: Int8 -> Int8 -> Int8 # times :: Integral n => n -> Int8 -> Int8 #
Group Int16 #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int16 -> Int16 -> Int16 # negate :: Int16 -> Int16 # subtract :: Int16 -> Int16 -> Int16 # times :: Integral n => n -> Int16 -> Int16 #
Group Int32 #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int32 -> Int32 -> Int32 # negate :: Int32 -> Int32 # subtract :: Int32 -> Int32 -> Int32 # times :: Integral n => n -> Int32 -> Int32 #
Group Int64 #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int64 -> Int64 -> Int64 # negate :: Int64 -> Int64 # subtract :: Int64 -> Int64 -> Int64 # times :: Integral n => n -> Int64 -> Int64 #
Group Integer #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # subtract :: Integer -> Integer -> Integer # times :: Integral n => n -> Integer -> Integer #
Group Word #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word -> Word -> Word # negate :: Word -> Word # subtract :: Word -> Word -> Word # times :: Integral n => n -> Word -> Word #
Group Word8 #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word8 -> Word8 -> Word8 # negate :: Word8 -> Word8 # subtract :: Word8 -> Word8 -> Word8 # times :: Integral n => n -> Word8 -> Word8 #
Group Word16 #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word16 -> Word16 -> Word16 # negate :: Word16 -> Word16 # subtract :: Word16 -> Word16 -> Word16 # times :: Integral n => n -> Word16 -> Word16 #
Group Word32 #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word32 -> Word32 -> Word32 # negate :: Word32 -> Word32 # subtract :: Word32 -> Word32 -> Word32 # times :: Integral n => n -> Word32 -> Word32 #
Group Word64 #
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word64 -> Word64 -> Word64 # negate :: Word64 -> Word64 # subtract :: Word64 -> Word64 -> Word64 # times :: Integral n => n -> Word64 -> Word64 #
Group () #
Instance details Defined in Numeric.Additive.Group Methods (-) :: () -> () -> () # negate :: () -> () # subtract :: () -> () -> () # times :: Integral n => n -> () -> () #
Group Euclidean #
Instance details Defined in Numeric.Coalgebra.Geometric Methods (-) :: Euclidean -> Euclidean -> Euclidean # negate :: Euclidean -> Euclidean # subtract :: Euclidean -> Euclidean -> Euclidean # times :: Integral n => n -> Euclidean -> Euclidean #
Group r => Group (ZeroRng r) #
Instance details Defined in Numeric.Rng.Zero Methods (-) :: ZeroRng r -> ZeroRng r -> ZeroRng r # negate :: ZeroRng r -> ZeroRng r # subtract :: ZeroRng r -> ZeroRng r -> ZeroRng r # times :: Integral n => n -> ZeroRng r -> ZeroRng r #
(Abelian r, Group r) => Group (RngRing r) #
Instance details Defined in Numeric.Ring.Rng Methods (-) :: RngRing r -> RngRing r -> RngRing r # negate :: RngRing r -> RngRing r # subtract :: RngRing r -> RngRing r -> RngRing r # times :: Integral n => n -> RngRing r -> RngRing r #
Group r => Group (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite Methods (-) :: Opposite r -> Opposite r -> Opposite r # negate :: Opposite r -> Opposite r # subtract :: Opposite r -> Opposite r -> Opposite r # times :: Integral n => n -> Opposite r -> Opposite r #
Group r => Group (End r) #
Instance details Defined in Numeric.Ring.Endomorphism Methods (-) :: End r -> End r -> End r # negate :: End r -> End r # subtract :: End r -> End r -> End r # times :: Integral n => n -> End r -> End r #
Division r => Group (Log r) #
Instance details Defined in Numeric.Log Methods (-) :: Log r -> Log r -> Log r # negate :: Log r -> Log r # subtract :: Log r -> Log r -> Log r # times :: Integral n => n -> Log r -> Log r #
Group r => Group (Trig r) #
Instance details Defined in Numeric.Coalgebra.Trigonometric Methods (-) :: Trig r -> Trig r -> Trig r # negate :: Trig r -> Trig r # subtract :: Trig r -> Trig r -> Trig r # times :: Integral n => n -> Trig r -> Trig r #
Group r => Group (Quaternion' r) #
Instance details Defined in Numeric.Coalgebra.Quaternion Methods (-) :: Quaternion' r -> Quaternion' r -> Quaternion' r # negate :: Quaternion' r -> Quaternion' r # subtract :: Quaternion' r -> Quaternion' r -> Quaternion' r # times :: Integral n => n -> Quaternion' r -> Quaternion' r #
Group r => Group (Hyper r) #
Instance details Defined in Numeric.Coalgebra.Hyperbolic Methods (-) :: Hyper r -> Hyper r -> Hyper r # negate :: Hyper r -> Hyper r # subtract :: Hyper r -> Hyper r -> Hyper r # times :: Integral n => n -> Hyper r -> Hyper r #
Group r => Group (Dual' r) #
Instance details Defined in Numeric.Coalgebra.Dual Methods (-) :: Dual' r -> Dual' r -> Dual' r # negate :: Dual' r -> Dual' r # subtract :: Dual' r -> Dual' r -> Dual' r # times :: Integral n => n -> Dual' r -> Dual' r #
Group r => Group (Quaternion r) #
Instance details Defined in Numeric.Algebra.Quaternion Methods (-) :: Quaternion r -> Quaternion r -> Quaternion r # negate :: Quaternion r -> Quaternion r # subtract :: Quaternion r -> Quaternion r -> Quaternion r # times :: Integral n => n -> Quaternion r -> Quaternion r #
Group r => Group (Hyper' r) #
Instance details Defined in Numeric.Algebra.Hyperbolic Methods (-) :: Hyper' r -> Hyper' r -> Hyper' r # negate :: Hyper' r -> Hyper' r # subtract :: Hyper' r -> Hyper' r -> Hyper' r # times :: Integral n => n -> Hyper' r -> Hyper' r #
Group r => Group (Dual r) #
Instance details Defined in Numeric.Algebra.Dual Methods (-) :: Dual r -> Dual r -> Dual r # negate :: Dual r -> Dual r # subtract :: Dual r -> Dual r -> Dual r # times :: Integral n => n -> Dual r -> Dual r #
Group r => Group (Complex r) #
Instance details Defined in Numeric.Algebra.Complex Methods (-) :: Complex r -> Complex r -> Complex r # negate :: Complex r -> Complex r # subtract :: Complex r -> Complex r -> Complex r # times :: Integral n => n -> Complex r -> Complex r #
GCDDomain d => Group (Fraction d) #
Instance details Defined in Numeric.Field.Fraction Methods (-) :: Fraction d -> Fraction d -> Fraction d # negate :: Fraction d -> Fraction d # subtract :: Fraction d -> Fraction d -> Fraction d # times :: Integral n => n -> Fraction d -> Fraction d #
Group r => Group (e -> r) #
Instance details Defined in Numeric.Additive.Group Methods (-) :: (e -> r) -> (e -> r) -> e -> r # negate :: (e -> r) -> e -> r # subtract :: (e -> r) -> (e -> r) -> e -> r # times :: Integral n => n -> (e -> r) -> e -> r #
(Group a, Group b) => Group (a, b) #
Instance details Defined in Numeric.Additive.Group Methods (-) :: (a, b) -> (a, b) -> (a, b) # negate :: (a, b) -> (a, b) # subtract :: (a, b) -> (a, b) -> (a, b) # times :: Integral n => n -> (a, b) -> (a, b) #
Group s => Group (Covector s a) #
Instance details Defined in Numeric.Covector Methods (-) :: Covector s a -> Covector s a -> Covector s a # negate :: Covector s a -> Covector s a # subtract :: Covector s a -> Covector s a -> Covector s a # times :: Integral n => n -> Covector s a -> Covector s a #
(Group a, Group b, Group c) => Group (a, b, c) #
Instance details Defined in Numeric.Additive.Group Methods (-) :: (a, b, c) -> (a, b, c) -> (a, b, c) # negate :: (a, b, c) -> (a, b, c) # subtract :: (a, b, c) -> (a, b, c) -> (a, b, c) # times :: Integral n => n -> (a, b, c) -> (a, b, c) #
Group s => Group (Map s b a) #
Instance details Defined in Numeric.Map Methods (-) :: Map s b a -> Map s b a -> Map s b a # negate :: Map s b a -> Map s b a # subtract :: Map s b a -> Map s b a -> Map s b a # times :: Integral n => n -> Map s b a -> Map s b a #
(Group a, Group b, Group c, Group d) => Group (a, b, c, d) #
Instance details Defined in Numeric.Additive.Group Methods (-) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # negate :: (a, b, c, d) -> (a, b, c, d) # subtract :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # times :: Integral n => n -> (a, b, c, d) -> (a, b, c, d) #
(Group a, Group b, Group c, Group d, Group e) => Group (a, b, c, d, e) #
Instance details Defined in Numeric.Additive.Group Methods (-) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # negate :: (a, b, c, d, e) -> (a, b, c, d, e) # subtract :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # times :: Integral n => n -> (a, b, c, d, e) -> (a, b, c, d, e) #