Numeric.Additive.Group

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

Methods

(-) :: Int -> Int -> Int

negate :: Int -> Int

subtract :: Int -> Int -> Int

times :: Integral n => n -> Int -> Int

Group Int8

Methods

(-) :: Int8 -> Int8 -> Int8

negate :: Int8 -> Int8

subtract :: Int8 -> Int8 -> Int8

times :: Integral n => n -> Int8 -> Int8

Group Int16

Methods

(-) :: Int16 -> Int16 -> Int16

negate :: Int16 -> Int16

subtract :: Int16 -> Int16 -> Int16

times :: Integral n => n -> Int16 -> Int16

Group Int32

Methods

(-) :: Int32 -> Int32 -> Int32

negate :: Int32 -> Int32

subtract :: Int32 -> Int32 -> Int32

times :: Integral n => n -> Int32 -> Int32

Group Int64

Methods

(-) :: Int64 -> Int64 -> Int64

negate :: Int64 -> Int64

subtract :: Int64 -> Int64 -> Int64

times :: Integral n => n -> Int64 -> Int64

Group Integer

Methods

(-) :: Integer -> Integer -> Integer

negate :: Integer -> Integer

subtract :: Integer -> Integer -> Integer

times :: Integral n => n -> Integer -> Integer

Group Word

Methods

(-) :: Word -> Word -> Word

negate :: Word -> Word

subtract :: Word -> Word -> Word

times :: Integral n => n -> Word -> Word

Group Word8

Methods

(-) :: Word8 -> Word8 -> Word8

negate :: Word8 -> Word8

subtract :: Word8 -> Word8 -> Word8

times :: Integral n => n -> Word8 -> Word8

Group Word16

Methods

(-) :: Word16 -> Word16 -> Word16

negate :: Word16 -> Word16

subtract :: Word16 -> Word16 -> Word16

times :: Integral n => n -> Word16 -> Word16

Group Word32

Methods

(-) :: Word32 -> Word32 -> Word32

negate :: Word32 -> Word32

subtract :: Word32 -> Word32 -> Word32

times :: Integral n => n -> Word32 -> Word32

Group Word64

Methods

(-) :: Word64 -> Word64 -> Word64

negate :: Word64 -> Word64

subtract :: Word64 -> Word64 -> Word64

times :: Integral n => n -> Word64 -> Word64

Group ()

Methods

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

negate :: () -> ()

subtract :: () -> () -> ()

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

Group Euclidean

Methods

(-) :: Euclidean -> Euclidean -> Euclidean

negate :: Euclidean -> Euclidean

subtract :: Euclidean -> Euclidean -> Euclidean

times :: Integral n => n -> Euclidean -> Euclidean

GCDDomain d => Group (Fraction d)

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 (Complex r)

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

Group r => Group (Dual r)

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 (Hyper' r)

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 (Quaternion r)

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 (Dual' r)

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 (Hyper r)

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 (Quaternion' r)

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 (Trig r)

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

Division r => Group (Log r)

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 (End r)

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

Group r => Group (Opposite r)

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

(Abelian r, Group r) => Group (RngRing r)

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 (ZeroRng r)

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

Group r => Group (e -> r)

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)

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)

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)

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)

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)

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)

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)